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1
Persson, Jens. "Selected Topics in Homogenization." Doctoral thesis, Mittuniversitetet, Institutionen för teknik och hållbar utveckling, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-16230.
Full textAbstract:
The main focus of the present thesis is on the homogenization of some selected elliptic and parabolic problems. More precisely, we homogenize: non-periodic linear elliptic problems in two dimensions exhibiting a homothetic scaling property; two types of evolution-multiscale linear parabolic problems, one having two spatial and two temporal microscopic scales where the latter ones are given in terms of a two-parameter family, and one having two spatial and three temporal microscopic scales that are fixed power functions; and, finally, evolution-multiscale monotone parabolic problems with one spatial and an arbitrary number of temporal microscopic scales that are not restricted to be given in terms of power functions. In order to achieve homogenization results for these problems we study and enrich the theory of two-scale convergence and its kins. In particular the concept of very weak two-scale convergence and generalizations is developed, and we study an application of this convergence mode where it is employed to detect scales of heterogeneity.Huvudsakligt fokus i avhandlingen ligger på homogeniseringen av vissa elliptiska och paraboliska problem. Mer precist så homogeniserar vi: ickeperiodiska linjära elliptiska problem i två dimensioner med homotetisk skalning; två typer av evolutionsmultiskaliga linjära paraboliska problem, en med två mikroskopiska skalor i både rum och tid där de senare ges i form av en tvåparameterfamilj, och en med två mikroskopiska skalor i rum och tre i tid som ges i form av fixa potensfunktioner; samt, slutligen, evolutionsmultiskaliga monotona paraboliska problem med en mikroskopisk skala i rum och ett godtyckligt antal i tid som inte är begränsade till att vara givna i form av potensfunktioner. För att kunna uppnå homogeniseringsresultat för dessa problem så studerar och utvecklar vi teorin för tvåskalekonvergens och besläktade begrepp. Speciellt så utvecklar vi begreppet mycket svag tvåskalekonvergens med generaliseringar, och vi studerar en tillämpningav denna konvergenstyp där den används för att detektera förekomsten av heterogenitetsskalor.
2
Gathier, Benjamin. "Multiscale strength homogenization : application to shale nanoindentation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43049.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2008.Includes bibliographical references (p. 236-246).
Shales are one of the most encountered materials in sedimentary basins. Because of their highly heterogeneous nature, their strength prediction for oil and gas exploitation engineering has long time been an enigma. In this thesis, we propose a two-scale non-linear procedure for the homogenization of their yield design strength properties, based on the Linear Comparison Composite Theory. At Level 0, the intrinsic friction of shales is captured via a cohesive-frictional strength criterion for the clay particles (Drucker-Prager). Level I is composed of a porous clay phase and Level II incorporates silt and quartz grains. Homogenization yields either an elliptical or an hyperbolc strength criterion, depending on the packing density of the porous clay phase. These criteria are employed in an original reverse algorithm of indentation hardness to develop hardness-packing density scaling relations that allow a separation of constituent properties and volume fraction and morphology parameters, including interface conditions between the porous clay matrix and the (rigid) silt inclusions. The application of this algorithm to 11 shale samples from the GeoGenome project data base allows us to identify: (i) an invariant value of the solid hardness of clay particles, which is independent of clay mineralogy, porosity, etc.; and (ii) shale independent scaling relations of the cohesion and of the friction coefficient with the mean clay packing density, which provides some evidence that the elementary building block of shale is a clay polycrystal. The use of these scaling relations in the Level II-homogenization provides a first-order model for the prediction of the macroscopic strength properties of shale, based on only two parameters that delineate shale's macroscopic diversity: clay packing density and silt inclusion volume fraction.
by Benjamin Gathier.
S.M.
3
Covezzi, Federica <1990>. "Homogenization of nonlinear composites for multiscale analysis." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8608/1/covezzi_federica_tesi.pdf.
Full textAbstract:
A composite is a material made out of two or more constituents
(phases) combined together in order to achieve desirable mechanical
or thermal properties. Such innovative materials have been widely
used in a large variety of engineering fields in the past decades. The
design of a composite structure requires the resolution of a multiscale
problem that involves a macroscale (i.e. the structural scale)
and a microscale. The latter plays a crucial role in the determination
of the material behavior at the macroscale, especially when dealing
with constituents characterized by nonlinearities. For this reason, numerical
tools are required in order to design composite structures by
taking into account of their microstructure. These tools need to provide
an accurate yet efficient solution in terms of time and memory
requirements, due to the large number of internal variables of the
problem. This issue is addressed by different methods that overcome
this problem by reducing the number of internal variables. Within
this framework, this thesis focuses on the development of a new
homogenization technique named Mixed TFA (MxTFA) in order to
solve the homogenization problem for nonlinear composites. This
technique is based on a mixed-stress variational approach involving
self-equilibrated stresses and plastic multiplier as independent
variables on the Reference Volume Element (RVE). The MxTFA is developed
for the case of elastoplasticity and viscoplasticity, and it is
implemented into a multiscale analysis for nonlinear composites. Numerical
results show the efficiency of the presented techniques, both
at microscale and at macroscale level.
4
Johnsen, Pernilla. "Homogenization of Partial Differential Equations using Multiscale Convergence Methods." Licentiate thesis, Mittuniversitetet, Institutionen för matematik och ämnesdidaktik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-42036.
Full textAbstract:
The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of the research in the thesis is the homogenization results and, for the studied parabolic problems, adapted compactness results of multiscale convergence type.
5
CASTROGIOVANNI, ALFREDO. "Reduced Order Homogenization for Multiscale Analysis of Nonlinear Composites." Doctoral thesis, Università degli studi di Pavia, 2021. http://hdl.handle.net/11571/1447832.
Full textAbstract:
Heterogeneous materials are nowadays used in several fields of structural engineering.
Such materials, regarded as composites, have a heterogeneous microstructure
in which two or more constituents are combined in order to reach
improved mechanical properties. Most of the composites include constituents
characterized by a nonlinear behaviour, hence, it is important to consider the
inelastic phenomena arising at the microscale, to accurately predict the macroscopic
response of the heterogeneous material.
A modeling approach allowing for the heterogeneous nature of the composite to
be considered during the design process is provided by the Multiscale Analysis,
in which both the macroscopic scale and the microscopic scale are involved. At
the microscale, a Unit Cell, being a representaive sample of the heterogeneous
nonlinear material, is studied in order to derive the behaviour of an equivalent
homogeneous macroscopic material. In the scale transition process, usually regarded
as homogenization, efficient numerical tools are needed in order to reduce
the computational cost due to the large quantity of internal variables, coming
from the evaluation of the elastoplastic material models at the microscopic level.
Reduced Order Models (ROM) are introduced with the aim of lowering the number
of internal variables of the problem and to provide accurate solutions with
reasonable computational cost and time.
This thesis is mainly dedicated to the development of a ROM for the homogenization
of nonlinear heterogeneous materials; starting from the Hashin-Shtrikman
analytical homogenization scheme, a piecewise uniform distribution of the microscopic
quantities is assumed, and thus, the proposed ROM is referred as
PieceWise Uniform Hashin-Shtrikman (PWUHS) technique. In particular, the
PWUHS is developed for the solution of homogenization problems of nonlinear
composites and extended to Mises plasticity with linear hardening.
Numerical results demonstrate the accuracy of the proposed homogenization
scheme, which is compared to the well known PieceWise Uniform Transformation
Field Analysis (PWUTFA) in order to investigate the similarities and the
advantages of both reduced order models. PWUHS is implemented in the framework
of Multiscale Analysis for studying the response of auxetic composites and
numerical results are compared to the experimental counterpart to assess the
efficiency of the proposed multiscale scheme.
6
Arjmand, Doghonay. "Analysis and Applications of Heterogeneous Multiscale Methods for Multiscale Partial Differential Equations." Doctoral thesis, KTH, Numerisk analys, NA, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-160122.
Full textAbstract:
This thesis centers on the development and analysis of numerical multiscale methods for multiscale problems arising in steady heat conduction, heat transfer and wave propagation in heterogeneous media. In a multiscale problem several scales interact with each other to form a system which has variations over a wide range of scales. A direct numerical simulation of such problems requires resolving the small scales over a computational domain, typically much larger than the microscopic scales. This demands a tremendous computational cost. We develop and analyse multiscale methods based on the heterogeneous multiscale methods (HMM) framework, which captures the macroscopic variations in the solution at a cost much lower than traditional numerical recipes. HMM assumes that there is a macro and a micro model which describes the problem. The micro model is accurate but computationally expensive to solve. The macro model is inexpensive but incomplete as it lacks certain parameter values. These are upscaled by solving the micro model locally in small parts of the domain. The accuracy of the method is then linked to how accurately this upscaling procedure captures the right macroscopic effects. In this thesis we analyse the upscaling error of existing multiscale methods and also propose a micro model which significantly reduces the upscaling error invarious settings. In papers I and IV we give an analysis of a finite difference HMM (FD-HMM) for approximating the effective solutions of multiscale wave equations over long time scales. In particular, we consider time scales T^ε = O(ε−k ), k =1, 2, where ε represents the size of the microstructures in the medium. In this setting, waves exhibit non-trivial behaviour which do not appear over short time scales. We use new analytical tools to prove that the FD-HMM accurately captures the long time effects. We first, in Paper I, consider T^ε =O(ε−2 ) and analyze the accuracy of FD-HMM in a one-dimensional periodicsetting. The core analytical ideas are quasi-polynomial solutions of periodic problems and local time averages of solutions of periodic wave equations.The analysis naturally reveals the role of consistency in HMM for high order approximation of effective quantities over long time scales. Next, in paperIV, we consider T^ε = O(ε−1 ) and use the tools in a multi-dimensional settingto analyze the accuracy of the FD-HMM in locally-periodic media where fast and slow variations are allowed at the same time. Moreover, in papers II and III we propose new multiscale methods which substantially improve the upscaling error in multiscale elliptic, parabolic and hyperbolic partial differential equations. In paper II we first propose a FD-HMM for solving elliptic homogenization problems. The strategy is to use the wave equation as the micro model even if the macro problem is of elliptic type. Next in paper III, we use this idea in a finite element HMM setting and generalize the approach to parabolic and hyperbolic problems. In a spatially fully discrete a priori error analysis we prove that the upscaling error can be made arbitrarily small for periodic media, even if we do not know the exact period of the oscillations in the media.QC 20150216
Multiscale methods for wave propagation
7
Sviercoski, Rosangela. "Multiscale Analytical Solutions and Homogenization of n-Dimensional Generalized Elliptic Equations." Diss., The University of Arizona, 2005. http://hdl.handle.net/10150/194912.
Full textAbstract:
In this dissertation, we present multiscale analytical solutions, in the weak sense, to the generalized Laplace's equation in Ω ⊂ Rⁿ, subject to periodic and nonperiodic boundary conditions. They are called multiscale solutions since they depend on a coefficient which takes a wide possible range of scales. We define forms of nonseparable coefficient functions in Lᵖ(Ω) such that the solutions are valid for the periodic and nonperiodic cases. In the periodic case, one such solution corresponds to the auxiliary cell problem in homogenization theory. Based on the proposed analytical solution, we were able to write explicitly the analytical form for the upscaled equation with an effective coefficient, for linear and nonlinear cases including the one with body forces. This was done by performing the two-scale asymptotic expansion for linear and nonlinear equations in divergence form with periodic coefficient. We proved that the proposed homogenized coefficient satisfies the Voigt-Reiss inequality. By performing numerical experiments and error analyses, we were able to compare the heterogeneous equation and its homogenized approximation in order to define criteria in terms of allowable heterogeneity in the domain to obtain a good approximation. The results presented, in this dissertation, have laid mathematical groundwork to better understand and apply multiscale processes under a deterministic point of view.
8
Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.
Full textAbstract:
Dissertation for the Degree of Doctor of Philosophy in MathematicsFundação para a Ciência e a Tecnologia through the Carnegie Mellon | Portugal Program under Grant SFRH/BD/35695/2007, the Financiamento Base 20010 ISFL–1–297, PTDC/MAT/109973/2009 and UTA
9
Goncalves-Ferreira, Rita Alexandria. "Spectral and Homogenization Problems." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/83.
Full textAbstract:
In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases.
The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales
10
Nika, Grigor. "Multiscale analysis of emulsions and suspensions with surface effects." Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-dissertations/146.
Full textAbstract:
The better understanding of the behavior of emulsions and suspensions is important in many applications. In general, emulsions allow the delivery of insoluble agents to be uniformly distributed in a more efficient way. At the same time suspensions of rigid particles are used as “smart materialsâ€� as their properties can be changed by the interaction with a magnetic or electric field. In the first part of the talk we consider a periodic emulsion formed by two Newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape, in the presence of surface tension. We assume the droplets have fixed centers of mass and are only allowed to rotate. We are interested in the time-dependent, dilute case when the characteristic size of the droplets aε, of arbitrary shape, is much smaller than the period length ε. We obtain a Brinkman type of fluid flow for the critical size aε = O(ε3) as a replacement of the Stokes flow of the emulsion. Additionally, using Mosco convergence and semigroup theory we extend the convergence to the parabolic case. For the case when the droplets convect with the flow, it can be shown again using Mosco-convergence that, as the size of the droplets converges to zero faster than the distance between the droplets, the emulsion behaves in the limit like the continuous phase and no “strangeâ€� term appears. Moreover, we determine the rate of convergence of the velocity field for the emulsion to that of the velocity for the one fluid problem in both the H1 and L2 norms. Additionally, a second order approximation is determined in terms of the bulk and surface polarization tensors for the cases of uniform and non-uniform surface tension. The second part of the talk is devoted to the study of MR fluids. We consider a suspension of rigid magnetizable particles in a non-conducting, viscous fluid with an applied external magnetic field. Thus, we use the quasi-static Maxwell equations coupled with the Stokes equations to capture the magnetorheological effect. We upscale using two scale asymptotic expansions to obtain the effective equations consisting of a coupled nonlinear system in a connected phase domain as well as the new constitutive laws. The proposed model generalizes the model of Rosenweig by coupling the velocity of the fluid and the magnetic field intensity. Using the finite element method we compute the effective coefficients for the MR fluid. We analyze the resulting MR model for Poiseuille and Couette flows and compare with experimental data for validation.
11
Badillo, Almaraz Hiram. "Numerical modelling based on the multiscale homogenization theory. Application in composite materials and structures." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/83924.
Full textAbstract:
A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents.
The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs.
Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method.En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala.
12
Badillo, Almaraz Hiram. "Numerial modelling based on the multiscale homogenization theory. Application in composite materials and structures." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/83924.
Full textAbstract:
A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents.
The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs.
Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method.En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala.
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Shipley, Rebecca Julia. "Multiscale modelling of fluid and drug transport in vascular tumours." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:8f663f70-8d23-49ad-8348-1763359d8f62.
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Understanding the perfusion of blood and drugs in tumours is fundamental to foreseeing the efficacy of treatment regimes and predicting tumour growth. In particular, the dependence of these processes on the tumour vascular structure is poorly established. The objective of this thesis is to derive effective equations describing blood, and drug perfusion in vascular tumours, and specifically to determine the dependence of these on the tumour vascular structure. This dependence occurs through the interaction between two different length scales - that which characterizes the structure of the vascular network, and that which characterizes the tumour as a whole. Our method throughout is to use homogenization as a tool to evaluate this interaction. In Chapter 1 we introduce the problem. In Chapter 2 we develop a theoretical model to describe fluid flow in solid tumours through both the vasculature and the interstitium, at a number of length scales. Ultimately we homogenize over a network of capillaries to form a coupled porous medium model in terms of a vascular density. Whereas in Chapter 2 it is necessary to specify the vascular structure to derive the effective equations, in Chapter 3 we employ asymptotic homogenization through multiple scales to derive the coupled equations for an arbitrary periodic vascular network. In Chapter 4, we extend this analysis to account for advective and diffusive transport of anticancer drugs delivered intravenously; we consider a range of reaction properties in the interstitium and boundary conditions on the vascular wall. The models derived in Chapters 2–4 could be applied to any drug type and treatment regime; to demonstrate their potential, we simulate the delivery of vinblastine in dorsal skinfold chambers in Chapter 5 and make quantitative predictions regarding the optimal treatment regime. In the final Chapter we summarize the main results and indicate directions for further work.
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Unnikrishnan, Vinu Unnithan. "Multiscale analysis of nanocomposite and nanofibrous structures." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1469.
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Edmans, Ben. "Non-linear finite element analysis of flexible pipes for deep-water applications." Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/11178.
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Flexible pipes are essential components in the subsea oil and gas industry, where they are used to convey fluids under conditions of extreme external pressure and (often) axial load, while retaining low bending stiffness. This is made possible by their complex internal structure, consisting of unbonded components that are, to a certain extent, free to move internally relative to each other. Due to the product's high value and high cost of testing facilities, much e ort has been invested in the development of analytical and numerical models for simulating flexible pipe behaviour, which includes bulk response to various loading actions, calculation of component stresses and use of this data for component fatigue calculations. In this work, it is proposed that the multi-scale methods currently in widespread use for the modelling of composite materials can be applied to the modelling of flexible pipe. This allows the large-scale dynamics of an installed pipe (often several kilometers in length) to be related to the behaviour of its internal components (with characteristic lengths in millimeters). To do this, a formal framework is developed for an extension of the computational homogenisation procedure that allows multiscale models to be constructed in which models at both the large and small scales are composed of different structural elements. Within this framework, a large-scale flexible pipe model is created, using a two-dimensional corotational beam formulation with a constitutive model representative of flexible pipe bulk behaviour, which was obtained by further development of a recently proposed formulation inspired by the analogy between the flexible pipe structural behaviour and that of plastic materials with non-associative flow rules. A three-dimensional corotational formulation is also developed. The model is shown to perform adequately for practical analyses. Next, a detailed finite element (FE) model of a flexible pipe was created, using shell finite elements, generalised periodic boundary conditions and an implicit solution method. This model is tested against two analytical flexible pipe models for several basic load cases. Finally, the two models are used to carry out a sequential multi-scale analysis, in which a set of simulations using the detailed FE model is carried out in order to find the most appropriate coefficients for the large-scale model.
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Yang, Weixuan. "Temperature-dependent homogenization technique and nanoscale meshfree particle methods." Diss., University of Iowa, 2007. http://ir.uiowa.edu/etd/147.
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Dondeti, Piyush Prashant. "Rate-Dependent Homogenization based Continuum Plasticity Damage Model for Dendritic Cast Aluminum Alloys." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1308245866.
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Flodén, Liselott. "G-Convergence and Homogenization of some Sequences of Monotone Differential Operators." Doctoral thesis, Mittuniversitetet, Institutionen för teknik och hållbar utveckling, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-8935.
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This thesis mainly deals with questions concerning the convergence of some sequences of elliptic and parabolic linear and non-linear operators by means of G-convergence and homogenization. In particular, we study operators with oscillations in several spatial and temporal scales. Our main tools are multiscale techniques, developed from the method of two-scale convergence and adapted to the problems studied. For certain classes of parabolic equations we distinguish different cases of homogenization for different relations between the frequencies of oscillations in space and time by means of different sets of local problems. The features and fundamental character of two-scale convergence are discussed and some of its key properties are investigated. Moreover, results are presented concerning cases when the G-limit can be identified for some linear elliptic and parabolic problems where no periodicity assumptions are made.
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Persson, Jens. "Homogenization of Some Selected Elliptic and Parabolic Problems Employing Suitable Generalized Modes of Two-Scale Convergence." Licentiate thesis, Mid Sweden University, Department of Engineering and Sustainable Development, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-11991.
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The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. Concerning the multiscaled parabolic problems, we find that the result of the homogenization depends on the behavior of the temporal scale functions. The temporal scale functions considered in the thesis may, in the sense explained in the text, be slow or rapid and in resonance or not in resonance with respect to the spatial scale function. The homogenization for the possibly non-periodic elliptic problems gives the same result as for the corresponding periodic problems but with the exception that the local gradient operator is everywhere substituted by a differential operator consisting of a product of the local gradient operator and matrix describing the geometry and which depends, effectively, parametrically on the global variable.
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Nandamuri, Sasank Sai. "A Multiscale Computational Study of the Mechanical Properties of the Human Stratum Corneum." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1458300092.
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Honorio, de Faria Tulio. "Modelling Concrete Behaviour At Early-Age : Multiscale Analysis And Simulation Of A Massive Disposal Structure." Thesis, Cachan, Ecole normale supérieure, 2015. http://www.theses.fr/2015DENS0045/document.
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La prédiction précise du comportement à long et court terme des structures en béton dans le domaine nucléaire est essentielle pour assurer des performances optimales (intégrité, capacité de confinement) pendant leur durée de vie. Dans le cas particulier des structures massives en béton, la chaleur produite au jeune âge par les processus d'hydratation ne peut pas s’évacuer rapidement, si bien que des températures élevées peuvent être atteintes et les gradients de température qui en résultent peuvent conduire à la fissuration, en fonction des conditions aux limites et contraintes internes auxquelles ces structures sont soumises. Les objectifs de cette étude sont (1) d'effectuer des simulations numériques afin de décrire et prédire le comportement thermo-chimio-mécanique au jeune âge d'une structure massive en béton dédiée au stockage de déchets en surface, et (2) de développer et appliquer des outils de changement d'échelle pour estimer rigoureusement, à partir de la composition du matériau, les propriétés physiques du béton nécessaires à une analyse au jeune âge. Une étude chimio-thermique visant à déterminer l'influence de la convection, du rayonnement solaire, du re-rayonnement et de la chaleur d'hydratation sur la réponse thermique de la structure est tout d’abord menée. Des recommandations pratiques concernant les températures de bétonnage sont fournies afin de limiter la température maximale atteinte au sein de la structure. Ensuite, au moyen d'une analyse mécanique, des stratégies de modélisation simplifiées et plus complexes (prenant en compte l’endommagement couplé au fluage) sont mises en œuvre pour évaluer des scénarios intégrant différentes conditions aux limites issues de l'analyse chimio-thermique précédente. Dans un second temps, une étude prenant en compte le caractère multi-échelle du béton est réalisée. Un modèle simplifié de cinétique d'hydratation du ciment est proposé. Les évolutions des fractions volumiques des différentes phases au niveau de la pâte de ciment peuvent être alors estimées. Par la suite des outils d’homogénéisation analytiques et numériques développés dans un cadre vieillissant sont présentés et appliqués pour estimer les propriétés mécaniques et thermiques des matériaux cimentaires. Les données d’entrée utilisées dans l'analyse structurelle sont finalement comparées avec les estimations obtenues dans l'analyse multiéchelle. Pour conclure, la stratégie proposée dans cette thèse vise à prédire le comportement des structures massives en béton à partir de la composition du béton au moyen d'une approche séquentielle: le comportement du béton est estimé via les outils de changement d’échelle, fournissant ainsi les données d'entrée pour l'analyse phénoménologique à l’échelle de la structureThe accurate prediction of the long and short-term behaviour of concrete structures in the nuclear domain is essential to ensure optimal performances (integrity, containment roperties) during their service life. In the particular case of massive concrete structures, at early age the heat produced by hydration reactions cannot be evacuated fast enough so that high temperatures may be reached and the resulting gradients of temperature might lead to cracking according to the external and internal restraints to which the structures are subjected. The goals of this study are (1) to perform numerical simulations in order to describe and predict the thermo-chemo-mechanical behaviour at early-age of a massive concrete structure devoted to nuclear waste disposal on surface, and (2) to develop and apply upscaling tools to estimate rigorously the key properties of concrete needed in an early-age analysis from the composition of the material. Firstly, a chemo-thermal analysis aims at determining the influence of convection, solar radiation, reradiation and hydration heat on the thermal response of the structure. Practical recommendations regarding concreting temperatures are provided in order to limit the maximum temperature reached within the structure. Then, by means of a mechanical analysis, simplified and more complex (i.e. accounting for coupled creep and damage) modelling strategies are used to assess scenarios involving different boundary conditions defined from the previous chemo-thermal analysis. Secondly, a study accounting for the multiscale character of concrete is performed. A simplified model of cement hydration kinetics is proposed. The evolution of the different phases at the cement paste level can be estimated. Then, analytical and numerical tools to upscale the ageing properties are presented and applied to estimate the mechanical and thermal properties of cementbased materials. Finally, the input data used in the structural analysis are compared with the estimations obtained in the multiscale analysis. To conclude, the entire strategy proposed in this thesis aims at predicting the behaviour of massive concrete structures from the composition of the concrete by means of a sequenced approach: concrete behaviour is estimated using the upscaling tools, providing then the input data to the phenomenological analysis at the structure level
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Madiot, François. "Méthodes éléments finis de type MsFEM pour des problèmes d'advection-diffusion." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1052/document.
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Ce travail a porté principalement sur le développement et l'étude de méthodes numériques de type éléments finis multi-échelles pour un problème d'advection diffusion multi-échelles dominé par l'advection. Deux types d'approches sont envisagées: prendre en compte l'advection dans la construction de l'espace d'approximation, ou appliquer une méthode de stabilisation. On commence par l'étude d'un problème d'advection diffusion, dominé par l'advection, dans un milieu hétérogène. On poursuit sur des problèmes d'advection-diffusion, sous le régime où l'advection domine, posés dans un domaine perforé. On se focalise ici sur la condition aux bords de type Crouzeix Raviart pour la construction des éléments finis multi-échelles. On considère deux situations différentes selon la condition prescrite au bord des perforations: la condition de Dirichlet homogène ou la condition de Neumann homogène. Cette étude repose sur une hypothèse de coercivité.Pour finir, on se place dans un cadre général où l'opérateur d'advection-diffusion est non coercif, possiblement dominé par l'advection. On propose une approche éléments finis basée sur une mesure invariante associée à l'opérateur adjoint. Cette approche est bien posée inconditionnellement en la taille du maillage. On la compare numériquement à une méthode standard de stabilisationThis work essentially deals with the development and the study of multiscale finite element methods for multiscale advection-diffusion problems in the advection-dominated regime. Two types of approaches are investigated: Take into account the advection in the construction of the approximation space, or apply a stabilization method. We begin with advection-dominated advection-diffusion problems in heterogeneous media. We carry on with advection-dominated advection-diffusion problems posed in perforated domains.Here, we focus on the Crouzeix-Raviart type boundary condition for the construction of the multiscale finite elements. We consider two different situations depending on the condition prescribed on the boundary of the perforations: the homogeneous Dirichlet condition or the homogeneous Neumann condition. This study relies on a coercivity assumption.Lastly, we consider a general framework where the advection-diffusion operator is not coercive, possibly in the advection-dominated regime. We propose a Finite Element approach based on the use of an invariant measure associated to the adjoint operator. This approach is unconditionally well-posed in the mesh size. We compare it numerically to a standard stabilization method
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Ginting, Victor Eralingga. "Computational upscaled modeling of heterogeneous porous media flow utilizing finite volume method." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/2242.
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In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.
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NAQVI, SAHRISH BATOOL. "Application of Homogenization Theory to the Flow Over and Through Micro-Structured, Porous and Elastic Surfaces." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1057992.
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This research is aimed to develop a homogenized model for practical applications of the fluid flow over and through the microstructured surfaces, which prescribed reliable estimates of the linear response of overall structures. The up-scaling method based on asymptotic theories is used to treat the fluid flow problems where various spatial scales (microscopic and macroscopic) are present. The goal of this work is to provide an in-expensive high-order homogenized framework for the flows over complex textures such as elastic and rigid rough surfaces, isotropic and orthotropic porous media, with periodic internal distributions, independent of the material properties and the constituent's geometrical arrangement in a reliable way. The framework includes effective conditions corrected up to the high-order as a replacement of the micro-textured surfaces, producing sizeable effects on the overlaying flow as compared to the classical Navier's conditions. These effective conditions contain parameters that are non-empirical and stems from the numerical solution of auxiliary Stokes-like problems. These conditions developed for different applications are tested on the classical problems such as Hiemenz stagnation point flow over a rough plate, Hiemenz stagnation point flow over isotropic and orthotropic porous bed, backward-facing step with porous step region, and flow over the permeable channel, to test the accuracy and working capability of the framework for different flow situations.
For simulation purposes, commercial software COMSOL academic version 5.4, open-source solver FreeFEM, and commercial software Star-CCM+ by are used. The outcomes of the model simulations are compared with exact simulations of our own and with literature. The overall results suggested that the homogenized model is computationally inexpensive compared to the feature-resolving simulations and can provide a quick design of drag-altering micro-textured surfaces. Moreover, the present model is flexible for further amendments to tackle complex engineered and industrial fluid flow problems.
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Xu, Rui. "Multiscale modeling of heterogeneous materials : application to Shape Memory Alloys." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0066.
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L’objectif principal de cette thèse est de développer des techniques de modélisation et de simulation multi-échelles avancées et efficaces pour les matériaux architecturés et composites à base d’Alliages à Mémoire de Forme (AMF). À cette fin, un modèle générique 3D multi-échelles pour les AMF architecturés est implémenté dans ABAQUS, où un modèle thermodynamique, proposé par Chemisky et al. [1], est adopté pour décrire le comportement constitutif local de l’AMF, et la méthode des éléments finis multi-échelles (EF2) pour réaliser l’interaction en temps réel entre le niveau microscopique et le niveau macroscopique. L’instabilité élastique des fibres au niveau microscopique est également étudiée efficacement dans ce cadre en introduisant la Méthode Asymptotique Numérique (MAN) et la Technique des Coefficients de Fourier à Variation Lente (TCFVL). Pour améliorer l’efficacité du calcul de l’approche simultanée à plusieurs échelles, dans laquelle d’énormes problèmes microscopiques sont résolus en ligne pour mettre à jour les contraintes macroscopiques, des méthodes de calcul multi-échelles basées sur les données sont proposées pour les structures composites. En découplant les échelles corrélées dans le cadre FE2, les problèmes microscopiques sont résolus hors ligne, tandis que le coût du calcul macroscopique en ligne est considérablement réduit. De plus, en formulant le schéma data-driven en contrainte et déformation généralisées, le calcul par la technique Structural-Genome-Driven est développé pour les structures composites à parois mincesThe main aim of this thesis is to develop advanced and efficient multiscale modeling and simulation techniques for Shape Memory Alloys (SMAs) composite and architected materials. Towards this end, a 3D generic multiscale model for architected SMAs is implemented in ABAQUS, where a thermodynamic model, proposed by Chemisky et al. [1], is adopted to describe the local constitutive behavior of the SMA, and the multiscale finite element method (FE2) to realize the real-time interaction between the microscopic and macroscopic levels. Microscopic fiber instability is also efficiently investigated in this framework by introducing the Asymptotic Numerical Method (ANM) and the Technique of Slowly Variable Fourier Coefficients (TSVFC). To improve the computational efficiency of the concurrent mulitscale approach, in which tremendous microscopic problems are solved online to update macroscopic stress, data-driven multiscale computing methods are proposed for composite structures. Decoupling the correlated scales in concurrent FE2 framework, microscopic problems are solved offline, while the online macroscopic computational cost is significantly reduced. Further, by formulating the data-driven scheme in generalized stress and strain, Structural-Genome-Driven computing is developed for thin-walled composite structures
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Nakhaei, Mohsen. "Layer-specific multiscale mechanical modeling of arterial structures with evolving fiber configurations." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEM014.
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Les tissus artériels sont constitués de réseaux de collagène et d'élastine diversement organisés et présentent un comportement anisotrope hautement non linéaire ainsi que la capacité de supporter de grandes déformations réversibles. Ces dernières s'accompagnent d'un réarrangement progressif des réseaux de fibres induit parle chargement. Dans cette thèse, l'important couplage entre la morphologie de la microstructure artérielle et sa réponse mécanique nous a motivé à développer un modèle multi-échelle détaillé de la paroi artérielle. Le cadre de la micromécanique des milieux continus a été utilisé dans une approche incrémentale pour calculer la contrainte, la déformation et les réorientations de fibres. Les extensions du problème d'inclusion de la matrice d'Eshelby permettent d'obtenir des expressions analytiques pour les tenseurs de concentration, qui relient le tenseur de vitesse de déformation macroscopique à la vitesse de déformation et à la vorticité moyennés sur les phases. Nous avons modélisé séparément le comportement de l'adventice et de la média, avant de proposer un modèle complet pour l'artère. De plus, le modèle de comportement multi-échelle a été implémenté dans une formulation éléments finis non linéaire, afin de réaliser des calculs de structure sur l'artère. Le modèle a été validé par différents ensembles de données expérimentales sur des échantillons artériels de différentes espèces. Les résultats montrent que le modèle est capable d'estimer la contribution de chaque tunique dans la réponse macroscopique du tissu pour différents chargements et peut prédire avec précision à la fois la réponse macroscopique et la cinématique microscopique des fibresArterial tissues are made of variously organized collagen and elastin networks and exhibit a highly nonlinear anisotropic behavior with the ability to sustain large reversible strains and to undergo a load-induced progressive morphological rearrangement of the microstructure. In the present study motivated by these specificities of arterial mechanics, we developed a detailed multi-scale model of the arterial wall. The framework of finite strain continuum micromechanics was employed in an incremental approach to compute stress, strain, and fiber reorientations. The extensions of Eshelby’s matrix-inclusion problem allowed for deriving analytical expressions for the concentration tensors, which relate the macroscopic strain rate tensor to phase-averaged strain rate and vorticity. The model accounts for the universal patterns across different scales in the two mechanically significant layers of arteries, namely the adventitia and the media. Furthermore, the multi-scale constitutive model was implemented in a non-linear finite element formulation to solve the structural model of the artery. The model was validated against different experimental data sets on arterial samples from different species. The results show that the model is able to estimate the contribution of each component into the macroscopic response of the tissue for different loading and can predict both the macroscopic response and microscopic fiber kinematics accurately. We submit that such model would help in predicting the evolution of the mechanical tissue response overtime during, for instance, remodeling and growth or damage
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Galvis, Rodriguez Andres Felipe. "Análise multiescala de falha dinâmica em materiais policristalinos usando o método dos elementos de contorno." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265901.
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Orientador: Paulo SolleroDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: Este trabalho apresenta uma análise numérica de falha dinâmica em materiais policristalinos usando modelagem multiescala. O problema foi descrito em duas escalas, a escala micro ou mesoescala e a escala atômica. A estrutura policristalina (mesoescala) é gerada usando o diagrama de Voronoi com diferentes níveis de tamanho de grão homogêneo. As equações constitutivas para materiais anisotrópicos são apresentadas segundo o tipo de estrutura atômica do material, considerando a orientação cristalina aleatória e as propriedades do material rotacionadas um ângulo aleatório no plano para cada grão. O campo de deslocamentos na mesoescala é calculado usando o Método dos Elementos de Contorno de Reciprocidade Dual para materiais anisotrópicos, considerando as forças de corpo no domínio do tempo. A fratura intergranular é estudada com a Modelagem Multiescala de Zonas Coesivas, incluindo zonas coesivas nas interfaces. Para a análise da escala atômica é preciso o gradiente de deformação efetivo utilizando a homogeneização de Hill-Mandel, e o tensor de tensão efetivo usando o potencial de Lennar-Jones e o primeiro tensor de Piola-Kirchhoff na zona coesiva empregando o campo de deslocamentos da mesoescala. A regra de Cauchy-Born define que todos os átomos contidos na zona coesiva têm um gradiente de deformação constante, sendo preciso utilizar apenas uma célula atômica unitária em cada zona coesiva, reduzindo o tempo de processamento computacional da simulação. Conhecidas as propriedades efetivas na zona coesiva, as forças coesivas que definem a separação do material são calculadas na mesoescala com o tensor de tensão efetivo e a geometria da estrutura. A separação do material e a propagação da trinca são definidas pelas forças coesivas ao longo de cada passo de tempo
Abstract: This work presents a numerical analysis of dynamic failure in polycrystaline materials using multiscale modeling. The problem was describe by two scales, the micro or mesoscale and the atomistic scale. The polycrystalline structure (mesoscale) is generated using the Voronoi diagram with different levels of grain size homogenization. The constitutive equations for anisotropic materials are presented depending of the type of atomic structure, considering random crystal and material properties orientation. The displacement field of the mesoscale is calculate using the Dual Reciprocity Boundary Element Method for anisotropic materials, considering the body forces in the time domain. The intergranular fracture is studied with the Multiscale Cohesive Zone Model, including cohesive zones in the interfaces. To analise the atomistic scale, is require the effective deformation gradient using the Hill-Mandel homogenization, and the effective stress tensor employing the Lennard-Jones potential and the first Piola-Kirchhoff tensor in the cohesive zone using the displacement field from the mesoscale. The Cauchy-Rule defines that all atoms inside the cohesive zone have a constant deformation gradient, then is just require the use of a unit atomic cell in each cohesive zone, reducing the computational load of the simulation. With the known effective properties in the cohesive zone, the cohesive forces that define the material separation are determined in the mesoscale with the effective stress tensor and the geometry of the structure. The material separation and crack propagation are define by the cohesive forces through each time step
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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Silva, Uziel Paulo da. "Emprego do método de homogeneização assintótica no cálculo das propriedades efetivas de estruturas ósseas." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/82/82131/tde-17042015-153207/.
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Ossos são sólidos não homogêneos com estruturas altamente complexas que requerem uma modelagem multiescala para entender seu comportamento eletromecânico e seus mecanismos de remodelamento. O objetivo deste trabalho é encontrar expressões analíticas para as propriedades elástica, piezoelétrica e dielétrica efetivas de osso cortical modelando-o em duas escalas: microscópica e macroscópica. Utiliza-se o Método de Homogeneização Assintótica (MHA) para calcular as constantes eletromecânicas efetivas deste material. O MHA produz um procedimento em duas escalas que permite obter as propriedades efetivas de um material compósito contendo uma distribuição periódica de furos cilíndricos circulares unidirecionais em uma matriz piezoelétrica linear e transversalmente isotrópica. O material da matriz pertence à classe de simetria cristalina 622. Os furos estão centrados em células de uma matriz periódica de secções transversais quadradas e a periodicidade é a mesma em duas direções perpendiculares. O compósito piezoelétrico está sob cisalhamento antiplano acoplado a um campo elétrico plano. Os problemas locais que surgem da análise em duas escalas usando o MHA são resolvidos por meio de um método da teoria de variáveis complexas, o qual permite expandir as soluções correspondentes em séries de potências de funções elípticas de Weierstrass. Os coeficientes das séries são determinados das soluções de sistemas lineares infinitos de equações algébricas. Truncando estes sistemas infinitos até uma ordem finita de aproximação, obtêm-se fórmulas analíticas para as constantes efetivas elástica, piezoelétrica e dielétrica, que dependem da fração de volume dos furos e de um fator de acoplamento eletromecânico da matriz. Os resultados numéricos obtidos a partir destas fórmulas são comparados com resultados obtidos pelas fórmulas calculadas via método de Mori-Tanaka e apresentam boa concordância. A boa concordância entre todas as curvas obtidas via MHA sugere que a expressão correspondente da primeira aproximação fornece uma fórmula muito simples para calcular o fator de acoplamento efetivo do compósito. Os resultados são úteis na mecânica de osso.Bones are inhomogeneous solids with highly complex structures that require multiscale modeling to understand its electromechanical behavior and its remodeling mechanisms. The objective of this work is to find analytical expressions for the effective elastic, piezoelectric, and dielectric properties of cortical bone by modeling it on two scales: microscopic and macroscopic. We use Asymptotic Homogenization Method (AHM) to calculate the effective electromechanical constants of this material. The AHM yields a two-scale procedure to obtain the effective properties of a composite material containing a periodic distribution of unidirectional circular cylindrical holes in a linear transversely isotropic piezoelectric matrix. The matrix material belongs to the symmetry crystal class 622. The holes are centered in a periodic array of cells of square cross sections and the periodicity is the same in two perpendicular directions. The piezoelectric composite is under antiplane shear deformation together with in-plane electric field. Local problems that arise from the two-scale analysis using the AHM are solved by means of a complex variable method, which allows us to expand the corresponding solutions in power series of Weierstrass elliptic functions. The coefficients of these series are determined from the solutions of infinite systems of linear algebraic equations. Truncating the infinite systems up to a finite, but otherwise arbitrary, order of approximation, we obtain analytical formulas for effective elastic, piezoelectric, and dielectric properties, which depend on both the volume fraction of the holes and an electromechanical coupling factor of the matrix. Numerical results obtained from these formulas are compared with results obtained by the Mori-Tanaka approach and show good agreement. The good agreement between all curves obtained via AHM suggests that the corresponding expression of first approximation provides a very simple formula to calculate the effective coupling factor of the composite. The results are useful in bone mechanics.
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Quintela, Bárbara de Melo. "Implementação computacional paralela da homogeneização por expansão assintótica para análise de problemas mecânicos em 3D." Universidade Federal de Juiz de Fora (UFJF), 2011. https://repositorio.ufjf.br/jspui/handle/ufjf/3536.
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FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais
A Homogeneização por Expansão Assintótica (HEA) é uma técnica multiescala empregada ao cálculo de propriedades efetivas de meios contínuos com estrutura periódica. As principais vantagens desta técnica são a redução do tamanho do problema a resolver e a possibilidade de se empregar uma propriedade homogeneizada que guarda informações da microestrutura heterogênea. Quando associada ao Método dos Elementos Finitos (MEF), a HEA demanda o emprego de malhas que permitam a imposição de condições de contorno periódicas – sendo portanto necessário especificar tal particularidade quando da geração dos modelos em MEF. Tais modelos representam as células periódicas, que são volumes representativos do meio heterogêneo e, em alguns casos, apresentam uma complexidade geométrica e física que torna imprescindível o emprego de malhas com alto grau de refinamento – levando a um custo computacional significativo. Este trabalho tem por objetivo a obtenção de um programa em Elementos Finitos para a aplicação da HEA à Elasticidade em 3D, empregando técnicas de programação paralela. Foram desenvolvidas versões do programa em 2D: uma sequencial em C e duas paralelas empregando OpenMP e CUDA. Foi implementado com sucesso o programa HEA3D em uma versão sequencial, em linguagem FORTRAN e uma paralela, empregando OpenMP. Para validação dos programas, foram analisadas células periódicas bifásicas e os resultados apresentaram boa concordância com valores experimentais e numéricos disponíveis na literatura. A versão paralela obteve expressivos ganhos de desempenho, com acelerações de desempenho de até 5.3 vezes em relação a versão sequencial.
The Asymptotic Expansion Homogenization (AEH) is a multiscale technique applied to estimate the effective properties of heterogeneous media with periodical structure. The main advantages of this technique are the reduction of the problem size to be solved and the ability to employ an homogenized property that keeps information from the heterogeneous microstructure. In association with the Finite Element Method (FEM), the AEH requires the application of periodic boundary conditions, which must be taken into account during the generation of FE meshes. Such models represent periodic cells, which are representative volumes for heterogeneous media and, in some cases, present a geometric and physics complexity that demands refined meshes, leading to a significant computational cost. The aim of this work is to develop a parallel program that applies both FEM and AEH to estimate the elasticity properties of 3D bodies. A sequential version of the 2D program using C, and parallel versions using OpenMP and CUDA were implemented. A sequential version of the program, called HEA3D, was successfully implemented using FORTRAN. Also, a parallel version of the code was implemented using OpenMP. The validation of the codes consisted of comparisons of the numerical results obtained, with numerical and experimental data available in the literature, showing good agreement. Significant speedups were obtained by the parallel version of the code, achieving speedups up to 5.3 times over its sequential version.
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Xiong, Hao. "Modélisation multiscalaire de matériaux granulaires en application aux problèmes d'ingénierie géotechnique." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAI096/document.
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Les matériaux granulaires présentent une large gamme de lois de comportement lorsqu'ils sont soumis à différents chemins de chargement. Le développement de modèles constitutifs permettant de rendre compte de ces caractéristiques a été une préoccupation constante de nombreux chercheurs depuis des décennies. Parmi les différentes options possibles, les approches par changement d’échelle semblent prometteuses. Dans ces approches, le modèle constitutif est formulé en reliant les propriétés macroscopiques du matériau aux propriétés micro-structurelles correspondantes.Cette thèse propose un modèle micromécanique tridimensionnel (le modèle H-3D) prenant en compte une échelle intermédiaire (méso-échelle). Il permet ainsi de décrire de manière naturelle un grand nombre de caractéristiques constitutives des matériaux granulaires non cohésifs. La comparaison entre essais expérimentaux et simulations numériques révèle la capacité prédictive de ce modèle. En particulier, des simulations réalisées avec différentes pressions de confinement et différents rapports de vide initiaux ont permis de démontrer la capacité du modèle à rendre compte quantitativement de l'état critique sans nécessiter d’équation spécifique et de paramètre d'état critique. Le modèle est également analysé à l’échelle microscopique, où l'évolution de certains paramètres microscopiques clés est présentée.Une approche multi-échelle 3D est ensuite présentée afin d’étudier le comportement mécanique d'un échantillon macroscopique constitué d'un assemblage granulaire, en tant que problème aux conditions limites. Le cœur de cette approche est un couplage multi-échelle, où la méthode des éléments finis est utilisée pour résoudre le problème aux conditions limites et le modèle H-3D est utilisé pour calculer la loi de comportement à l’échelle d’un volume élémentaire représentatif. Cette approche fournit un moyen pratique de relier les observations macroscopiques avec les mécanismes microscopiques intrinsèques. Des conditions de chargement biaxiaux en déformations planes sont appliquées pour simuler le phénomène de localisation des déformations. Une série de tests est effectuée, où différents motifs de rupture sont observés et analysés. Un système de bande de cisaillement apparaît naturellement dans un spécimen initialement homogène. En définissant la zone de la bande de cisaillement, les mécanismes microstructuraux sont étudiés séparément à l'intérieur et à l'extérieur de celle-ci. En outre, une analyse directionnelle de travail du second ordre est effectuée en appliquant des petits incréments de contrainte à différents états de contrainte-déformation sur des chemins de chargement biaxiaux drainés. Le travail de second ordre normalisé, introduit comme un indicateur d’instabilité du système, est analysé non seulement à l’échelle macroscopique mais aussi à l’échelle microscopique.Enfin, une analyse du travail de second ordre appliquée à des problèmes géotechniques et utilisant l'approche multi-échelle développée dans cette thèse est présentée. L'approche multi-échelle est utilisée afin de simuler des problèmes aux conditions limites homogènes et non homogènes, offrant ainsi la possibilité d’interpréter et de comprendre les micro-mécanismes qui à l’origine des phénomènes de rupture dans les problèmes géotechniques. Cette approche multi-échelle utilise un schéma numérique d’intégration dynamique-explicite afin de pouvoir étudier la rupture post-pic sans avoir à recourir à des outils mathématiques trop sophistiqués. Ainsi, en changeant le type de condition de chargement de déplacement à contrainte lorsque le système atteint son état limite, son effondrement se traduit par une augmentation soudaine de l'énergie cinétique découlant de la différence entre les travaux internes et externes du second ordreGranular materials exhibit a wide spectrum of constitutive features when submitted under various loading paths. Developing constitutive models which succeed in accounting for these features has been challenged by scientists for decades. A promising direction for achieving this can be the multi-scale approach. Through this approach, the constitutive model is formulated by relating material’s macroscopic properties to their corresponding microstructure properties.This thesis proposes a three-dimensional micro-mechanical model (the so-called 3D-H model) taking into account an intermediate scale (meso-scale) which makes it possible to describe a variety of constitutive features in a natural way. The comparison between experimental tests and numerical simulations reveals the predictive capability of this model. Particularly, several simulations are carried out with different confining pressures and initial void ratios, based on the fact that the critical state is quantitatively described without requiring any critical state formulations and parameter. The model is also analyzed from a microscopic view, wherein the evolution of some key microscopic parameters is investigated.Then, a 3D multi-scale approach is presented to investigate the mechanical behavior of a macroscopic specimen consisting of a granular assembly, as a boundary value problem. The core of this approach is a multiscale coupling, wherein the finite element method is used to solve a boundary value problem and the 3D-H model is employed to build the micro constitutive relationship used at a representative volume element scale. This approach provides a convenient way to link the macroscopic observations with intrinsic microscopic mechanisms. Plane-strain biaxial loading conditions are selected to simulate the occurrence of strain localization. A series of tests are performed, wherein distinct failure patterns are observed and analyzed. A system of shear band naturally appears in a homogeneous setting specimen. By defining the shear band area, microstructural mechanisms are separately investigated inside and outside the shear band. Moreover, a second-order work directional analysis is performed by applying strain probes at different stress-strain states along drained biaxial loading paths. The normalized second order work introduced as an indicator of an unstable trend of the system is analyzed not only on the macroscale but also on the microscale.Finally, a second order work analysis in application to geotechnical problems by using the aforementioned multiscale approach is presented. The multiscale approach is used to simulate a homogeneous and a non-homogeneous BVP, opening a road to interpret and understand the micro mechanisms hiding behind the occurrence of failure in geotechnical issues. This multiscale approach utilizes an explicit-dynamic integral method so that the post-peak failure can be investigated without requiring over-sophisticated mathematical ingredients. Thus, by switching the loading method from a strain control to a stress control at the limit state, the collapse of the system can be reflected in an abrupt increase of kinetic energy, stemming from the difference between both internal and external second-order works
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Vargas, Sabrina Mascarenhas. "Estimativa das propriedades elásticas do esmalte dentário humano via homogeneização computacional." Universidade Federal de Juiz de Fora, 2016. https://repositorio.ufjf.br/jspui/handle/ufjf/1773.
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Visto que o esmalte dentário é um tecido não inervado e avascular, que está constantemente sob a in uência de carregamento cíclico (funcional ou parafuncional) e que o mesmo não tem capacidade de regeneração, torna-se importante o estudo sobre as propriedades mecânicas desse tecido. Possui uma microestrutura única, que o faz apresentar propriedades mecânicas excelentes, porém o mesmo se apresenta frágil, com pouca capacidade de suportar deformação plástica antes da sua fratura. Alguns testes experimentais de indentação tentam entender o comportamento mecânico desse compósito, porém a complexidade desse comportamento e as diferenças de técnicas fazem com que os módulos de elasticidade para a hidroxiapatita, a matriz orgânica e o módulo efetivo do esmalte dentário tenham resultados muito variados na literatura. O mesmo se dá para as simulações multiescala de modelos para o esmalte dentário. Diante disso, esse estudo tem como o objetivo utilizar a modelagem multi-escala em 2D para a determinação dos tensores de propriedades mecânicas efetivas do esmalte dentário, através da técnica de homogeneização por expansão assintótica (HEA). Dentre as conclusões do trabalho têm-se que: 1- O esmalte dentário pode ser representado por um meio homogêneo equivalente, uma célula unitária representativa repetitiva; 2- Os modelos propostos nesse estudo têm comportamento ortotrópico; 3- Embora haja limitações relacionadas às simpli cações mecânicas e geométricas adotadas, os resultados obtidos encorajam aplicações mais realistas e estudos mais aprofundados acerca da microestrutura do material em questão.
Whereas tooth enamel is not an innervated neither vascular tissue which is constantly under the in uence of cyclical loading (functional or parafuncional) and that its tissue has no capacity for regeneration, it becomes important to study the mechanical properties of the enamel. It has an unique microstructure, which makes it exhibit excellent mechanical properties, but it appears fragile, with little ability to withstand plastic deformation prior to fracture. Some experimental indentation tests attempt to understand the mechanical behavior of this composite, but the complexity of its behavior and the di erent techniques imply in the modulus of elasticity for the hydroxyapatite, the organic matrix and the e ective modulus of dental enamel showing very di erent results in the literature. The same occurs for multiscale simulations of dental enamel models. Thus, this study aims 2D multi-scale modeling by Asymptotic Expansion Homogenization (AEH) technic to determine the mechanical properties e ective tensor of dental enamel. The conclusions of this study shows: 1- The enamel can be represented by an equivalent homogeneous medium, a repetitive representative unit cell; 2- The models proposed in this study present orthotropic behavior; 3- Although there are some limitations due to the mechanical and geometric simpli cations adopted, the results suggest more realistic applications and further studies on the microstructure of the material in question.
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Hellman, Fredrik. "Numerical Methods for Darcy Flow Problems with Rough and Uncertain Data." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-318589.
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We address two computational challenges for numerical simulations of Darcy flow problems: rough and uncertain data. The rapidly varying and possibly high contrast permeability coefficient for the pressure equation in Darcy flow problems generally leads to irregular solutions, which in turn make standard solution techniques perform poorly. We study methods for numerical homogenization based on localized computations. Regarding the challenge of uncertain data, we consider the problem of forward propagation of uncertainty through a numerical model. More specifically, we consider methods for estimating the failure probability, or a point estimate of the cumulative distribution function (cdf) of a scalar output from the model. The issue of rough coefficients is discussed in Papers I–III by analyzing three aspects of the localized orthogonal decomposition (LOD) method. In Paper I, we define an interpolation operator that makes the localization error independent of the contrast of the coefficient. The conditions for its applicability are studied. In Paper II, we consider time-dependent coefficients and derive computable error indicators that are used to adaptively update the multiscale space. In Paper III, we derive a priori error bounds for the LOD method based on the Raviart–Thomas finite element. The topic of uncertain data is discussed in Papers IV–VI. The main contribution is the selective refinement algorithm, proposed in Paper IV for estimating quantiles, and further developed in Paper V for point evaluation of the cdf. Selective refinement makes use of a hierarchy of numerical approximations of the model and exploits computable error bounds for the random model output to reduce the cost complexity. It is applied in combination with Monte Carlo and multilevel Monte Carlo methods to reduce the overall cost. In Paper VI we quantify the gains from applying selective refinement to a two-phase Darcy flow problem.
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Poulet, Pierre-Alexis. "Effet de la variabilité microstructurale sur le comportement d’un composite UD verre/PA11 : de la caractérisation expérimentale à la modélisation multi-échelle." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEM050/document.
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Dans le domaine des transports, l’allègement des structures est une préoccupation de l’industrie moderne. À cet effet, les matériaux composites unidirectionnels à matrice polymère sont de plus en plus utilisés pour des applications structurelles. Pour mener à bien cette transition technologique, les campagnes expérimentales laborieuses et onéreuses sont progressivement réduites, laissant la place à une caractérisation “numérique“ supplétive et ciblée. C’est dans ce contexte que s’inscrit ce travail de thèse. Le matériau considéré est un composite à matrice thermoplastique (le Polyamide 11) et à renforts unidirectionnels de fibres de verre. Sous sollicitations mécaniques, la variabilité microstructurale, à l’échelle des constituants, engendre des contraintes multi-axiales importantes qu’il est nécessaire d’évaluer. C’est notamment le cas dans les zones où la matrice est confinée par le renfort. Étudier l’échelle microscopique se révèle primordial pour comprendre et simuler les mécanismes de déformation spécifiques à la matrice thermoplastique.En première partie, une campagne expérimentale est réalisée sur le polymère thermoplastique massif. Des éprouvettes axisymétriques entaillées sont sollicitées en traction monotone et suivies in situ en tomographie aux rayons X. Un phénomène de cavitation est observé. Les grandeurs macroscopiques (ouverture d’entaille, réduction diamétrale. . .) mais aussi microscopiques (évolution des cavités considérées en cluster et individuellement)sont analysées de manières qualitative et quantitative.Un modèle Éléments Finis poro-viscoplastique est ensuite proposé et calibré afin de prendre en compte les mécanismes spécifiques de déformation et d’endommagement du polymère observés expérimentalement. La seconde partie est consacrée à l’étude numérique du matériau composite unidirectionnel. La représentation de la microstructure réelle est permise par la génération de cellules périodiques aléatoires et représentatives(vis-à-vis de descripteurs morphologiques). Des calculs micromécaniques sont alors menés et permettent d’accéder aux mécanismes de déformation, aux grandeurs locales et au comportement mécanique du composite (en élasticité linéaire et au-delà). Une attention particulière est portée à la représentativité des grandeurs calculées. Enfin, une démarche multi-échelle est proposée. Une homogénéisation numérique par un milieu de substitution permet de réaliser des calculs de structure tandis qu’une relocalisation sur certains points critiques donne accès aux grandeurs localesIn the field of transport, research for reducing the weight of structures is a continuing preoccupation for the industry. For this reason, polymer matrix composite materials are being used increasingly for structural applications. To succeed with this technological transition numerical modelling plays a significant role as cumbersome and costly experimental campaigns are being limited. This is the background to this thesis work.The material considered is composed of a thermoplastic resin (Polyamide 11) with a unidirectional glass fibre reinforcement. Under mechanical loadings, the microsctructural variability, at the constituent length scale, leads to important multi-axial stresses that need to be evaluated. This is notably true in zones where the matrix is particularly confined. Studying the microscopic scale is of paramount importance in order to understand and simulate specific strain mechanisms of the thermoplastic resin.In the first part, an experimental campaign has been conducted on the plain thermoplastic polymer. Axisymetric notched specimens were tested under uniaxial monotonous tension and monitored with in-situ X-ray synchrotron computed tomography. A cavitation phenomenon has been observed. Not only macroscopic quantities (notch opening displacement, reduction in diameter…) but also microscopic (evolution of voids considered as a cluster or individually) have been analyzed both quantitatively and qualitatively. A finite element model is subsequently proposed and calibrated to take into account the specific strain deformations and damage experimentally observed with this polymer.The second part is dedicated to a numerical study of the unidirectional composite material. A representation of the real microstructure has been tackled with the generation of virtual random and periodic cells in a way that nevertheless is truely morphologically representative. Micromechanics computations have been carried out and give access to strain mechanisms, to local quantities and to the composite material behaviour (in linear elasticity and beyond). Special attention is paid to the representativeness of the computed quantities. Finally, a multiscale approach is proposed. Structural computations have been possible due to a numerical homogenization based on an homogeneous equivalent medium whilst a relocalisation gives access to local quantities in critical zones of the structure
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Rasoulzadeh, Mojdeh. "Modèles non locaux des écoulements en milieux poreux et fracturés multi-échelles." Thesis, Vandoeuvre-les-Nancy, INPL, 2011. http://www.theses.fr/2011INPL025N/document.
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La thèse concerne les modèles de l'écoulement dans les milieux fracturés multiéchelles qui prouvent l'effet de mémoire à chaque échelle. Les processus analysés dans ces milieux est auto-similaire. Nous avons analysé l'équation de diffusion à toutes les échelles et appliqué la méthode d'homogénéisation asymptotique avec l'objectif de construire le modèle macroscopique moyenne sur toutes les échelles d'hétérogénéité. Un système fermé des équations récursives pour les noyaux d’échange effectif est obtenu. La solution analytico-numérique de ce système est développé. Nous avons montré une convergence des résultats obtenus pour le nombre des différentes échelles d'un comportement limite stable. Le problème limite pour les noyaux est obtenus pour un nombre relativement élevé d'échelles. En plus, nous avons analysé l'écoulement dans une immergée dans le réservoir poreux à différents nombres de Reynolds. Les équations de Navier-Stokes sont résolu par la méthode asymptotique à deux échelles avec l'objectif d'obtenir l'équation de la moyenne sur l'ouverture de fracture en présence d'afflux à travers les limites et pour la géométrie irrégulière des mursThe thesis concerns the models of flow in multiscale fractured media which prove the memory effect at each scale. The analyzed process in these media is self-similar. The necessary and sufficient condition of self-similarity has been proposed so that it is possible to analyze the behavior of media for any number of scales. We analyzed the diffusion equation at each scale and applied the asymptotic homogenization method with the objective to construct the macroscopic model averaged over all scales of heterogeneity. A system of closed recurrent equations for the effective exchange kernels was obtained. The procedure of analytico-numerical solution of this system was developed. We showed a convergence of the results obtained for various numbers of scales to a stable limit behavior. The limit problem for the effective kernels from the recurrent equations obtained for a relatively large number of scales. In addition we analyzed the flow in a single fracture and circular channel immersed in porous reservoir at various Reynolds numbers. The Navier-Stokes equations was solved by the method of two-scale asymptotic method with the objective to obtain the flow equation averaged over the fracture aperture in the presence of inflow through the limits and irregular geometry of walls
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Lhadi, Safaa. "Modélisation mécanique des tissus biologiques : application à la croissance des tumeurs solides et à la reconstruction multiéchelles des propriétés élastiques de la cuticule d'arthropode." Thesis, Strasbourg, 2015. http://www.theses.fr/2015STRAD030/document.
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De nos jours, l’enjeu de la mécanobiologie ne cesse de grandir. On s’intéresse à la description des problèmes biophysiques d’un point de vue mécanique avec des approches multiéchelles. Dans ce travail, nous proposons d’étudier deux exemples mettant en évidence le rôle important de la mécanique sur des processus purement biologiques. 1) La croissance tumorale dans son stade avasculaire : nous proposons un modèle continu où le tissu tumoral est considéré capable de croître et de se déformer tout en obéissant aux lois de conservation. Nous proposons ensuite pour étudier l’effet des propriétés mécaniques du microenvironnement -où réside la tumeur- sur le développement tumoral d’intégrer certaines conditions aux interfaces tumeur/microenvironnement. 2) La reconstruction des propriétés élastiques de la cuticule d’arthropode : nous proposons un modèle multiéchelles de son comportement mécanique fondé sur la structure hiérarchique établie dans la littérature. Pour remédier à la sous-estimation du modèle des propriétés élastiques de la cuticule, nous proposons d’inclure les interfaces à certaines échelles qui pourraient améliorer la transmission des efforts aux constituants multiéchelles du composite (cuticule) et donc améliorer les propriétés élastiques macroscopiques de ce dernierNowadays, the challenge of mechanobiology keeps growing. We are interested in the description of biophysical problems from a mechanical point of view with multiscale approaches.In the present study, we propose to study two examples highlighting the substantial role of mechanics on purely biological processes. 1) Tumor growth in the avascular stage: we propose a continuous model where tumor tissue is considered able to grow and to deform while obeying to conservation laws. Then, we propose to study the effect of the mechanical properties of the microenvironment- where lives the tumor- on the tumor development by integration of certain interfaces conditions tumor/microenvironment. 2) Reconstruction of the elastic properties of the arthropod cuticle: we propose a multiscale model of its mechanical behavior based on the hierarchical structure established in the literature. To remedy the under-estimation of the cuticle elastic properties of the model, we propose to include the interfaces to some scales that could improve the transmission of forces to the multiscale components of the composite (cuticle) and thus improve their macroscopic elastic properties
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Liu, Mingyong. "Optimization of electromagnetic and acoustic performances of power transformers." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS256/document.
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Le travail présenté dans ce mémoire s’intéresse à la prédiction des vibrations d'un noyau de transformateur multicouche, constitué d'un assemblage de tôles ferromagnétiques. Le problème couplé magnéto-mécanique est résolu par une approche séquentielle progressive : la résolution magnétique est suivie d'une résolution mécanique. Un modèle multi-échelle simplifié 3D décrivant les anisotropies magnétiques et magnétostrictives, et considérant les non-linéarités magnétiques et de magnétostriction, est utilisé comme loi de comportement du matériau. La structure du noyau du transformateur est modélisée en 2D. Une technique d'homogénéisation permet de tenir compte du comportement anisotrope de chaque couche afin de définir un comportement moyen pour chaque élément du maillage éléments finis.. Des mesures expérimentales sont ensuite effectuées, permettant d’une part la validation des lois de comportement matériau utilisées, et d’autres part des modèles de comportement structurel statique, du comportement structurel dynamique et de l'estimation du bruit. Différents matériaux et différentes géométries de prototypes de transformateurs sont considérés pour ce travail. Des optimisations structurelles sont finalement proposées grâce à des simulations numériques s’appuyant sur le modèle développé, afin de réduire les vibrations et les émissions de bruit du noyau du transformateurThis thesis deals with the prediction of the vibration of a multi-layer transformer core made of an assembly of electrical sheets. This magneto-mechanical coupled problem is solved by a stepping finite element method sequential approach: magnetic resolution is followed by mechanical resolution. A 3D Simplified Multi-Scale Model (SMSM) describing both magnetic and magnetostrictive anisotropies is used as the constitutive law of the material. The transformer core structure is modeled in 2D and a homogenization technique is implemented to take the anisotropic behavior of each layer into consideration and define an average behavior at each element of the finite element mesh. Experimental measurements are then carried out, allowing the validation of the material constitutive law, static structural behavior, dynamic structural behavior, and the noise estimation. Different materials geometries are considered for this workStructural optimizations are finally achieved by numerical simulation for lower vibration and noise emission of the transformer cores
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Van, Den Eijnden Bram. "Modélisation multi-échelle du comportement hydro-méchanique des roches argileuses." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAI034/document.
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Les études de faisabilité concernant le stockage géologique profond des déchets radioactifs ont conduit un intérêt accru concernant la modélisation géomécanique de la roche hte. En France, une roche hte potentielle est l'argilite du Callovo-Oxfordien du site de Meuse/Haute Marne. Etant donné que le principe de stockage géologique profond repose fortement sur la capacité de confinement de la formation hte, sa faible perméabilité est d'une importance clé. La perméabilité étant dépendante de la microstructure du matériau et de son évolution sous chargement, le comportement couplé hydro-mécanique de l'argilite est important. En effet, des modifications mécaniques sont induites par le creusement de la galerie d'entreposage, générant une zone endommagée (EDZ), pouvant conduire une modification de la perméabilité dans le voisinage de la galerie. Dans les matériaux microstructure complexe comme l'argilite du Callovo-Oxfordien, le comportement macroscopique trouve son origine dans l'interaction des constituants micro-mécaniques. En plus du couplage entre le comportement hydraulique et mécanique, un couplage entre les échelles micro et macro existe. Par le biais de l'élaboration d'un cadre d'homogénéisation du couplage hydro-mécanique, une approche de modélisation deuxéchelles est développée dans ce travail, dans laquelle la relation constitutive macroscopique découle directement du comportement à l'échelle microscopique. Un modèle existant du couplage hydro-mécanique, reposant sur l'identification de grains et d'espaces poreux intergranulaires à l'échelle micro est adopté comme point de départ. Ce modèle repose sur une homogénéisation numérique du comportement à la petite échelle afin d'obtenir à l'échelle macroscopique la réponse en contrainte et de transport du fluide interstitiel. Ce modèle est basé sur un VER périodique qui permet de déduire le comportement macroscopique local de l'argilite. En réponse, en un point d'intégration macro donné, à un incrément de la déformation et du gradient de pression, la réponse du VER permet d'exprimer l'incrément de contrainte et de flux associé, constituant de fait un équivalent numérique de la relation constitutive. Les problèmes aux conditions limites macro et micro sont traités simultanément par la méthode élément fini. Pour obtenir les opérateurs tangents consistants à l'échelle macro, la méthode d'homogénéisation par condensation statique des opérateurs tangeants micro est étendu au cas avec couplage hydro-mécanique. L'implémentation du modèle double échelle et la mise en uvre des développements théoriques d'homogénéisation ont été effectués dans le code élément fini Lagamine (Université de Liège). Pour la modélisation de la localisation de la déformation à l'échelle macro, qui, dans un formalisme de milieu continu classique, souffre de la dépendance au maillage, l'approche double-échelle a été utilisée dans un formalisme de milieu enrichi de type milieu de second gradient pour matériau poreux saturé. Les capacités du modèle homogénéisé numériquement, utilisé dans un cadre de milieu de second gradient, sont ensuite démontrées par des simulations d'essais dométriques et d'essais de compression biaxiaux. L'approche se confirme être un moyen puissant pour modéliser l'anisotropie initiale et induite du comportement mécanique et du comportement hydraulique. Pour la modélisation du comportement de l'argilite du Callovo-Oxfordien, des VER sont construits en tenant compte des travaux de caractérisation de la géométrie des inclusions microscopiques et des résultats expérimentaux d'essais macroscopiques.La loi de comportement homogénéisée numériquement ainsi calibrée est utilisée dans des simulations de creusement de galerie jusqu'à des niveaux d'endommagement générant une localisation de la déformation.Ces calculs montrent à la fois la pertinence et l'applicabilité du concept double échelle pour l'évaluation du comportement hydromécanique des EDZ dans un contexte du stockage des déchets radioactifsFeasibility studies for deep geological radioactive waste disposal facilities have led to an increased interest in the geomechanical modelling of its host rock. In France, a potential host rock is the Callovo-Oxfordian claystone. The low permeability of this material is of key importance, as the principal of deep geological disposal strongly relies on the sealing capacity of the host formation. The permeability being coupled to the mechanical material state, hydromechanical coupled behaviour of the claystone becomes important when mechanical alterations are induced by gallery excavation in the so-called excavation damaged zone (EDZ). In materials with microstructure such as the Callovo-Oxfordian claystone [Robinet et al., 2012], the macroscopic behaviour has its origin in the interaction of its mi- cromechanical constituents. In addition to the coupling between hydraulic and mech- anical behaviour, a coupling between the micro (material microstructure) and macro will be made. By means of the development of a framework of computational homo- genization for hydromechanical coupling, a doublescale modelling approach is formu- lated, for which the macroscale constitutive relations are derived from the microscale by homogenization. An existing model for the modelling of hydromechanical coupling based on the distinct definition of grains and intergranular pore space [Frey, 2010] is adopted and modified to enable the application of first order computational homogenization for obtaining macroscale stress and fluid transport responses. This model is used to constitute a periodic representative elementary volume (REV) that allows the rep- resentation of the local macroscopic behaviour of the claystone. As a response to deformation loading, the behaviour of the REV represents the numerical equivalent of a constitutive relation at the macroscale. For the required consistent tangent operators, the framework of computational homogenization by static condensation [Kouznetsova et al., 2001] is extended to hy- dromechanical coupling. The theoretical developments of this extension are imple- mented in the finite element code Lagamine (Li` ege) as an independent constitutive relation. For the modelling of localization of deformation, which in classical FE meth- ods suffers from the well-known mesh dependency, the doublescale approach of hy- dromechanical coupling is combined with a local second gradient model [Collin et al., 2006] to control the internal length scale of localized deformation. By accepting the periodic boundary conditions as a regularization of the microscale deformation, the use of the multiscale model in combination with the local second gradient model can be used for modelling localization phenomena in HM-coupled settings with material softening. The modelling capacities of the approach are demonstrated by means of simula- tions of oedometer tests and biaxial compression tests. The approach is demonstrated to be a powerful way to model anisotropy in the mechanical as well as the hydraulic behaviour of the material both in the initial material state and as an effect of hy- dromechanical alterations. For the application to the modelling of Callovo-Oxfordian claystone, microstructural REVs are calibrated to geometrical characteristics of the inclusion that form the microstructure under consideration and to macroscale ex- perimental results of the mechanical behaviour. The calibrated constitutive relation is used in the simulation of gallery excavation processes. These computations give a proof of concept of the doublescale assessment of the hydromechanical behaviour of the excavation damaged zones around galleries in the context of nuclear waste disposal
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Barkaoui, Abdelwahed. "Modélisation multiéchelle du comportement mécano-biologique de l’os humain : de l’ultrastructure au remodelage osseux." Thesis, Orléans, 2012. http://www.theses.fr/2012ORLE2086/document.
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L’os est un matériau vivant avec une structure hiérarchique complexe qui lui confère des propriétés mécaniques remarquables. L’os subit perpétuellement des contraintes mécaniques et physiologiques, ainsi sa qualité et sa résistance à la fracture évoluent constamment au cours du temps à travers le processus de remodelage osseux. La qualité osseuse est non seulement définie par la densité minérale osseuse mais également par les propriétés mécaniques ainsi que la microarchitecture. Dans le cadre de la présente thèse, on a développé une modélisation multiéchelle unifiée couplant à la fois les activités cellulaires au comportement mécanique de l'os tenant compte des différents niveaux hiérarchiques de l'os: de l’ultrastructure au remodelage osseux. Ce modèle permet d’étudier le comportement mécano-bibliologique de l’os et de prédire ses propriétés mécaniques apparentes à différentes échelles allant du nanoscopique au macroscopique en fonction des constituants élémentaires de l'os. Pour atteindre cet objectif, une démarche en quatre phases a été adoptée. La première phase consiste à décrire les constituants élémentaires de l’os. La deuxième phase avait pour objectif la modélisation multiéchelle de l'ultrastructure osseuse constituée de trois échelles nanoscopiques (microfibrille, fibrille et fibre) par la méthode des éléments finis et des réseaux de neurones. La troisième phase correspond à la modélisation des échelles micro-macroscopiques de l’os cortical (lamelle, ostéon, os cortical) en utilisant comme paramètres d’entrée les propriétés de la fibre déterminées dans la deuxième phase. Enfin, dans la dernière phase, on a développé un modèle mécano-biologique du remodelage osseux permettant de simuler le processus d'adaptation osseuse tenant compte explicitement des activités biologiques des cellules osseuses. Les propriétés mécaniques prédites par nos algorithmes multiéchelles ont servi pour alimenter le modèle de remodelage. Ce modèle a été implémenté au code de calcul d’éléments finis ABAQUS/Standard à travers sa routine utilisateur UMAT. Finalement, le modèle EF mécano-biologique multiéchelle du remodelage osseux a été appliqué pour simuler différents scénarii de remodelage sur des fémurs humains (2D et 3D). Différents facteurs ont été ainsi analysés tels que l'âge, le genre, l'amplitude des activités physiques, etc. Les résultats obtenus sont conformes (qualitativement) avec les observations cliniques et cohérents avec les différentes études expérimentales. En conclusion: (i) Les modèles unifiés ainsi développés (modèle multiéchelle, modèle mécano-biologique de remodelage osseux) contribuent à l'analyse fine du comportement de l'os humain. (ii) L'application des algorithmes a permis d'effectuer des essais virtuels pour analyser les effets combinés de nombreux facteurs caractérisant la qualité osseuseBone is a living material with a complex hierarchical structure which entails exceptional mechanical properties. Bone undergoes permanent mechanical and physiological stresses, thus its quality and fracture toughness are constantly evolving over time through the process of bone remodeling. Bone quality is not only defined by bone mineral density but also by the mechanical properties and microarchitecture. The current thesis offers a multiscale modeling approach unifying the cell activity to the mechanical behavior, taking into consideration the hierarchical levels of bone, from the ultrastructure to bone remodeling. This model permits to study the mechanobiological behavior and to predict the mechanical properties of the bone at different scales from nano to macro depending on the elementary constituents of bone. To achieve the objective of the current work, an approach of four phases was adopted. The first phase is to describe the basic components of the bone. The second phase concerns the multiscale modeling of the three nanoscopic levels of bone ultrastructure (microfibril, fibril and fiber) by the finite element method and neural networks. The third phase aims to model the micro-macroscopic structures of cortical bone (lamella, osteon, cortical bone) using the fiber properties predicted from the second phase as input parameters. In the last phase, a mechano-biological model of bone remodeling was achieved to simulate the process of bone adaptation explicitly considering the biological activities of bone cells. Mechanical properties predicted by our multiscale algorithms were used to feed the remodeling model. This model has been implemented into the ABAQUS/Standard finite elements code as a user subroutine. Finally, the finite element mechano-biological multiscale model of bone remodeling was applied to simulate different scenarios on human femurs (2D and 3D). Hence, different factors such as: age, gender, physical activities, etc were analyzed. The obtained results are conformed (qualitatively) to clinical observations and consistent with the various experimental studies. In summary, (i) the models portrayed here (multiscale model, mechanical-biological model of bone remodeling) contribute by their unified approach to the realistic modeling of the response of human bone. (ii) The application of the algorithms permits to perform virtual experiments to scrutinize the combined effects of numerous factors dictating the bone quality
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Nierenberger, Mathieu. "Mécanique multiéchelles des parois vasculaires : expérimentation, imagerie, modélisation." Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00966831.
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Les perspectives d'évolution des techniques chirurgicales sont de plus en plus demandeuses de modèles permettant de prédire déplacements et contraintes au sein des tissus. De tels modèles permettent par exemple de mieux focaliser un traitement sur une zone de tissu affectée par une pathologie. L'un des principaux obstacles posés par la plupart des modèles existants adaptés à la description du comportement mécanique des tissus vivants concerne la difficulté de mesure de leurs paramètres. Il en résulte une difficulté à les déterminer, ainsi qu'à comprendre leur influence. L'adoption d'une modélisation multiéchelles permet d'apporter une réponse satisfaisante à ce problème. En effet, elle autorise la prise en compte et lacombinaison de phénomènes simples qui ont lieu à différentes échelles, et fait ainsi intervenir des paramètres physiques et mesurables. Dans l'étude proposée, nous nous focalisons sur le comportement mécanique des parois des veines en pont, qui peuvent parvenir à rupture lors d'un choc appliqué à la tête. Nous proposons pour commencer des observations par microscopie optique, microtomographie X et microscopie confocale biphotonique visant à caractériser la structure de la paroi vasculaire à différentes échelles. Un essai mécanique est combiné à l'une des observations. Nous proposons ensuite une nouvelle modélisation multiéchelles du comportement mécanique de cette paroi vasculaire. Cette modélisation combine des modèles simples à trois échelles et reproduit ainsi le comportement mécanique global de la paroi vasculaire. Pour finir, le modèle est intégré à une modélisation par éléments finis afin de permettre l'étude de géométries complexes.
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Lougou, Komla Gaboutou. "Méthodes multi-échelles pour la modélisation des vibrations de structures à matériaux composites viscoélastiques." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0044/document.
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Dans cette thèse, des techniques d’homogénéisation multi-échelles sont proposées pour l’analyse des vibrations des matériaux composites viscoélastiques. Dans la première partie, la Méthode Asymptotique à Deux Echelles (MADE) est proposée pour la modélisation des vibrations des longues structures sandwichs viscoélastiques répétitives. Pour ce type de structures les pulsations amorties correspondant aux modes propres de vibration sont regroupées en paquets bien distincts. La MADE décompose le problème initial de grande taille en deux problèmes de petites tailles. Le premier est défini sur quelques cellules de base et le second est une équation différentielle d’amplitude à coefficients complexes. La résolution de ces problèmes permet de déterminer les propriétés amortissantes correspondant aux modes de début et de fin de paquet de la structure tout en évitant la discrétisation de toute la structure. Pour les structures dont les coeurs ont un module d’Young dépendant de la fréquence, le problème non linéaire formulé sur les cellules de bases est résolu par l’approche diamant. Les modèles ADF et à dérivées fractionnaires ont été considérés dans les tests numériques. En utilisant la MADE, on évite la discrétisation de toute la structure, ce qui permet donc de réduire considérablement le temps de calcul ainsi que l’espace mémoire CPU nécessaires. L’approche proposée a été validée en comparant les résultats à ceux de la simulation éléments finis basée sur la discrétisation de toute la structure, et utilisant l’approche diamant. Dans la seconde partie de cette thèse, la méthode des éléments finis multi-échelles (EF2) a été développée pour le calcul des propriétés modales des structures à matériaux hétérogènes viscoélastiques en terme de fréquences amorties et amortissements modaux. Dans le principe de l’approche EF2, le problème de vibration est formulé à deux échelles : l’échelle de la structure globale (échelle macroscopique) et l’échelle d’un VER minutieusement choisi (échelle microscopique). Le problème à résoudre à l’échelle microscopique est un problème non linéaire alors que le problème à résoudre à l’échelle macroscopique est un problème linéaire. La non linéarité à l’échelle microscopique est introduite par la dépendance en fréquence du module d’Young des matériaux des phases viscoélastiques. Le problème non linéaire ainsi généré à l’échelle microscopique est résolu grâce à la MAN et ses outils de différentiation automatique réalisés sous Matlab, Fortran et C++. Un outil numérique, générique, robuste, peu coûteux en temps de calcul et espace mémoire CPU, de résolution des problèmes de vibrations non amorties des structures composites viscoélastique est ainsi mis en place. Le modèle viscoélastique à module constant ainsi que des modèles à modules dépendant de la fréquence notamment le modèle ADF et le modèle à dérivées fractionnaires ont été considérés pour les tests numériques de validation. Les comparaisons avec les résultats ABAQUS ont confirmé l’efficacité du code propos é. Le modèle est ensuite utilisé pour le calcul des propriétés amortissantes des structures sandwichs viscoélastiques à coeur composite. Les capacités de la nouvelle approche à concevoir des structures sandwichs viscoélastiques à coeur composite et à haut pouvoir amortissant ont été testées avec succès à travers l’étude de l’influence des différents paramètres des inclusions sur les propriétés amortissantes d’une structure sandwich viscoélastique à coeur compositeIn this thesis, multiscale homogenization techniques are proposed for vibration analysis of structures with viscoelastic composite materials. In the first part, the Double Scale Asymptotic Method is proposed for vibration modeling of large repetitive viscoelastic sandwich structures. For this kind of structures, la eigenfrequencies are closely located in well separated packets. The DSAM splits the initial problem of large size into two problems of relatively small sizes. The first problem is posed on few basic cells, and the second one is an amplitude equation with complex coefficients. The resolution of these equations permits to compute the damping properties that correspond to the beginning and the end of every packets of eigenmodes. In case of structure with frequency dependent Young modulus in the core, the diamant approach is used to solve the nonlinear problem posed on basic cells. The ADF and fractional derivative models are considered in numerical tests. By using the DSAM, one avoid the discretization of the whole structure, and the computation time and needed CPU memory are thus reduced. The proposed method is validated by comparing its results with those of the direct finite element method using the diamant approach. In the second part of this thesis, the multiscale finite element method (FE2) is proposed for computation of modal properties (resonant frequency and modal loss factors) of structures with composite materials. In the principle of the (FE2) method, the vibration problem is formulated at two scales: the scale of the whole structure (macroscopic scale) and the scale of a Representative Volume Element (RVE) considered as the microscopic scale. The microscopic problem is a nonlinear one and the macroscopic problem is linear. The nonlinearity at the microscopic scale is introduced by the frequency dependence of the Young modulus of the viscoelastic phases. This nonlinear problem is solved by the Asymptotic Numerical Method and its automatic differentiation tools realizable in Matlab, Fortran or C++. From this approach, numerical tool that is generic, flexible, robust and inexpensive in term of CPU time and memory is proposed for vibration analysis of viscoelastic structures. The constant Young modulus and frequency dependent Young modulus are considered in validation tests. The results of numerical simulation with ABAQUS are used are reference. The model is then used to compute the modal properties of sandwich structure with viscoelastic composite core. To test the capacities of the proposed approach to design sandwich viscoelastic structure with high damping properties, the influence of parameters of the inclusions are studied
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Wangermez, Maxence. "Méthode de couplage surfacique pour modèles non-compatibles de matériaux hétérogènes : approche micro-macro et implémentation non-intrusive." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASN001.
Full textAbstract:
Un des objectifs prioritaires des industries aéronautiques est la réduction de la masse des structures, tout en permettant l'amélioration de leurs performances. Ceci passe notamment par l'utilisation de matériaux composites et le recours croissant à la simulation numérique, permettant la minimisation du nombre d'essais physiques et l'optimisation des structures.L'enjeu de ces travaux est de pouvoir calculer précisément, sur des matériaux architecturés, l'influence de la microstructure, modélisée par exemple directement par tomographie, sur la tenue de pièces complètes. Pour prendre en compte à la fois l'ensemble de la pièce et les effets de son chargement, une approche global/local multiéchelle semble adaptée tant du point de vue des méthodes de calcul que des modèles matériaux utilisés.Pour répondre à cette problématique, une méthode de couplage entre des modèles qui décrivent une même structure, mais à des échelles différentes, a été développée. Elle repose sur une séparation micro-macro des quantités d’interface, dans la zone de raccord surfacique entre les deux modèles. Pour faciliter son utilisation dans les bureaux d’étude, une technique de résolution itérative non-intrusive est également présentée. Elle permet de mettre en œuvre la méthode de couplage proposée dans un environnement logiciel industriel qui utilise bien souvent des codes éléments finis commerciaux fermés. La méthode est systématiquement comparée à d'autres méthodes de couplage de la littérature et la qualité des solutions est quantifiée par comparaison à une solution de référence obtenue par un calcul direct à l'échelle fine.Les principaux résultats sont encourageants dans la mesure où ils montrent, dans des cas d'étude représentatifs bidimensionnels et tridimensionnels, sous des hypothèses d’élasticité linéaire, des solutions cohérentes avec les théories de l’homogénéisation au premier et second ordre. De fait, les solutions obtenues sont systématiquement de meilleure qualité avec la méthode proposée qu'avec les méthodes de la littérature, non-adaptées à des cas de couplage pour modèles non-compatibles.Finalement, les perspectives sont multiples en raison des différentes alternatives de la méthode qui, dans un contexte industriel, pourrait offrir un véritable outil d'analyse visant à introduire un modèle local décrit à l'échelle fine dans un modèle global macroscopique homogénéiséOne of the priority objectives of the aeronautics industry is to reduce the mass of structures while improving their performances. This involves the use of composite materials and the increasing use of digital simulation to optimize structures.The major challenge of this project is to be able to accurately calculate the local variations of the microstructure - for instance detected by tomography and directly modelled from tomogram - on the behavior of an architectured material part. In order to take into account the whole structure and its load effects, a multi-scale approach seems to be a natural choice. Indeed, the related models to the part and its microstructure might use different formalisms according to each scale.In this context, a coupling formulation was proposed in order to replace, in a non-intrusive way, a part of a homogenized macroscopic finite-element model by a local one described at a microscopic level. It is based on a micro-macro separation of interface quantities in the coupling area between the two models. To simplify its use in design offices, a non-intrusive iterative resolution procedure has also been proposed. It allows the implementation of the proposed coupling method in an industrial software environment that often uses closed commercial finite element codes. Different mechanical problems under linear elasticity assumption are proposed. The proposed method is systematically compared with other coupling methods of the literature and the quality of the solutions is quantified compared to a reference one obtained by direct numerical simulation at a fine scale.The main results are promising as they show, for representatives test cases under linear elasticity assumption in two and three-dimensions, solutions that are consistent with first- and second-order homogenization theories. The solutions obtained with the proposed method are systematically the best approximations of the reference solution whereas the methods of the literature are less accurate and shown to be unsuitable to couple non-compatible models.Finally, there are many perspectives due to the different alternatives of the method which could become, in an industrial context, a real analytic tool that aims to introduce a local model described at a fine scale, into a homogenized macroscopic global one
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Kinvi-Dossou, Gbèssiho Raphaël. "Étude de la résistance à l’impact et de l’endommagement des composites stratifiés à matrice Elium acrylique : caractérisation expérimentale et modélisation numérique multi-échelle." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0249/document.
Full textAbstract:
Face aux défis environnementaux actuels, les industriels ont mis en œuvre de nouveaux matériaux recyclables et permettant une réduction significative de la masse. Le développement de la résine thermoplastique Elium par ARKEMA s’inscrit dans cette problématique. L’utilisation de cette résine pour la fabrication de pièces composites qui peuvent être sujettes à des dommages d’impact, nécessite au préalable des études, dans le but de comprendre leurs mécanismes de ruine sous ce type de sollicitation. Ainsi, la présente thèse propose une contribution à l’analyse multi-échelle de la tenue à l’impact des composites stratifiés à base de la résine Elium. Une étude expérimentale préliminaire a permis de confirmer la meilleure résistance à l’impact des composites à matrice Elium acrylique, comparativement à celles des composites thermodurcissables conventionnels. Ensuite, les performances à l’impact des composites stratifiés ont été améliorées par l’introduction de copolymères à blocs dans la matrice. Ces derniers sont capables de former des micelles de tailles nanométriques et ainsi d’améliorer la ténacité de la matrice acrylique. Les effets de l’énergie d’impact, de la température et de la composition en nanocharges sur la réponse du matériau composite ont été analysés. Afin de proposer un outil d’aide à la prédiction de la réponse à l’impact des matériaux fibres de verre/Acrylique, deux stratégies de modélisation ont été retenues. La première modélisation (macroscopique) considère le pli tissé du stratifié comme un matériau homogène tandis que la seconde (mésoscopique) utilise une description géométrique de l’ondulation et de l’entrecroisement des torons noyés dans la résine Elium. Ces deux modèles considèrent des zones cohésives à l’interface entre les plis adjacents pour simuler le délaminage interlaminaire. Des essais de délaminage (expérimentaux et numériques) ont permis d’alimenter le modèle d’endommagement de l’interface interplis. D’autre part, des essais de caractérisation du comportement mécanique et de l’endommagement du matériau couplés à l’homogénéisation multi-échelle des matériaux par la Mécanique du Génome de Structure ont permis d’identifier les paramètres du modèle macroscopique. A l’échelle mésoscopique, le modèle géométrique a été réalisé grâce au logiciel Texgen. Ce logiciel permet d’obtenir une description approchée mais réaliste de l’ondulation des torons de fibres. La même description a servi à l’homogénéisation numérique multi-échelle des stratifiés étudiés. La simulation numérique de l’impact basse vitesse a été effectuée au moyen du logiciel d’éléments finis ABAQUS/Explicit. Les modèles de comportement du matériau ont été implémentés via la routine utilisateur VUMAT. Les résultats obtenus offrent une bonne corrélation avec les données expérimentalesIn the race for light materials able of meeting modern environmental challenges, an acrylic resin (Elium) has been developed. Elium is a thermoplastic resin able to replace thermosetting matrices, which are widespread nowadays in the industrial world. The present study aims to evaluate the impact resistance and to understand the failure mechanisms of composite laminates based on acrylic matrix under impact loading. We provide a contribution to the multiscale analysis of the impact resistance of laminated composite.First, the impact resistance and the damage tolerance of the acrylic resin based composites were compared with those of conventional composites. Then, the impact performance of the laminated composites has been enhanced by adding copolymer blocks to the liquid acrylic resin. These copolymers are able to form micelles of nanometer sizes, which lead to the improvement of both the acrylic matrix fracture toughness and the impact resistance. The effects of the impact energy, temperature, and composition in nano-copolymers have also been investigated.In order to provide a numerical tool for the prediction of the impact response of the glass fiber/Acrylic laminates, two strategies have been analyzed. The first one, performed at the macroscopic scale, considers the woven ply of the laminate as homogeneous material, and the second one (at the mesoscopic scale), deals with a realistic geometrical description of the yarns undulation. Both models use cohesive zones at the interface between the adjacent plies, to simulate the delamination. For this purpose, experimental and numerical delamination tests were performed to feed the inter-ply damage model. Mechanical tests for material characterization were also performed on specimens in order to identify the ply-damage model parameters. The Mechanics of Structure Genome (MSG) and a finite element based micromechanics approaches were then conducted to evaluate the effective thermomechanical properties of the yarns and the plain woven composite laminate. The realistic topological and morphological textures of the composite were accounted through Texgen software. These numerical impact simulations were performed using the finite element software ABAQUS/Explicit. Both models were implemented through a user material subroutine VUMAT. The obtained results appear in a good agreement with the experimental data and confirm the relevance of the proposed approach
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Moreau, Antoine. "Calcul des propriétés homogénéisées de transfert dans les matériaux poreux par des méthodes de réduction de modèle : Application aux matériaux cimentaires." Thesis, La Rochelle, 2022. http://www.theses.fr/2022LAROS024.
Full textAbstract:
Cette thèse propose de coupler deux outils préexistant pour la modélisation mathématique en mécanique : l’homogénéisation périodique et la réduction de modèle, afin de modéliser la corrosion des structures de béton armé exposées à la pollution atmosphérique et au sel marin. Cette dégradation est en effet difficile à simuler numériquement, eu égard la forte hétérogénéité des matériaux concernés, et la variabilité de leur microstructure. L’homogénéisation périodique fournit un modèle multi-échelle permettant de s’affranchir de la première de ces deux difficultés. Néanmoins, elle repose sur l’existence d’un volume élémentaire représentatif (VER) de la microstructure du matériau poreux modélisé. Afin de prendre en compte la variabilité de cette dernière, on est amenés à résoudre en temps réduit les équations issues du modèle multi-échelle pour un grand nombre VER. Ceci motive l’utilisation de la méthode POD de réduction de modèle. Cette thèse propose de recourir à des transformations géométriques pour transporter ces équations sur la phase fluide d’un VER de référence. La méthode POD ne peut, en effet, pas être utilisée directement sur un domaine spatial variable (ici le réseau de pores du matériau). Dans un deuxième temps, on adapte ce nouvel outil à l’équation de Poisson-Boltzmann, fortement non linéaire, qui régit la diffusion ionique à l’échelle de la longueur de Debye. Enfin, on combine ces nouvelles méthodes à des techniques existant en réduction de modèle (MPS, interpolation ITSGM), pour tenir compte du couplage micro-macroscopique entre les équations issues de l’homogénéisation périodiqueIn this thesis, we manage to combine two existing tools in mechanics: periodic homogenization, and reduced-order modelling, to modelize corrosion of reinforced concrete structures. Indeed, chloride and carbonate diffusion take place their pores and eventually oxydate their steel skeleton. The simulation of this degradation is difficult to afford because of both the material heterogenenity, and its microstructure variability. Periodic homogenization provides a multiscale model which takes care of the first of these issues. Nevertheless, it assumes the existence of a representative elementary volume (REV) of the material at the microscopical scale. I order to afford the microstructure variability, we must solve the equations which arise from periodic homogenization in a reduced time. This motivates the use of model order reduction, and especially the POD. In this work we design geometrical transformations that transport the original homogenization equations on the fluid domain of a unique REV. Indeed, the POD method can’t be directly performed on a variable geometrical space like the material pore network. Secondly, we adapt model order reduction to the Poisson-Boltzmann equation, which is strongly nonlinear, and which rules ionic electro diffusion at the Debye length scale. Finally, we combine these new methods to other existing tools in model order reduction (ITSGM interpolatin, MPS method), in order to couple the micro- and macroscopic components of periodic homogenization
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Kinvi-Dossou, Gbèssiho Raphaël. "Étude de la résistance à l’impact et de l’endommagement des composites stratifiés à matrice Elium acrylique : caractérisation expérimentale et modélisation numérique multi-échelle." Electronic Thesis or Diss., Université de Lorraine, 2018. http://www.theses.fr/2018LORR0249.
Full textAbstract:
Face aux défis environnementaux actuels, les industriels ont mis en œuvre de nouveaux matériaux recyclables et permettant une réduction significative de la masse. Le développement de la résine thermoplastique Elium par ARKEMA s’inscrit dans cette problématique. L’utilisation de cette résine pour la fabrication de pièces composites qui peuvent être sujettes à des dommages d’impact, nécessite au préalable des études, dans le but de comprendre leurs mécanismes de ruine sous ce type de sollicitation. Ainsi, la présente thèse propose une contribution à l’analyse multi-échelle de la tenue à l’impact des composites stratifiés à base de la résine Elium. Une étude expérimentale préliminaire a permis de confirmer la meilleure résistance à l’impact des composites à matrice Elium acrylique, comparativement à celles des composites thermodurcissables conventionnels. Ensuite, les performances à l’impact des composites stratifiés ont été améliorées par l’introduction de copolymères à blocs dans la matrice. Ces derniers sont capables de former des micelles de tailles nanométriques et ainsi d’améliorer la ténacité de la matrice acrylique. Les effets de l’énergie d’impact, de la température et de la composition en nanocharges sur la réponse du matériau composite ont été analysés. Afin de proposer un outil d’aide à la prédiction de la réponse à l’impact des matériaux fibres de verre/Acrylique, deux stratégies de modélisation ont été retenues. La première modélisation (macroscopique) considère le pli tissé du stratifié comme un matériau homogène tandis que la seconde (mésoscopique) utilise une description géométrique de l’ondulation et de l’entrecroisement des torons noyés dans la résine Elium. Ces deux modèles considèrent des zones cohésives à l’interface entre les plis adjacents pour simuler le délaminage interlaminaire. Des essais de délaminage (expérimentaux et numériques) ont permis d’alimenter le modèle d’endommagement de l’interface interplis. D’autre part, des essais de caractérisation du comportement mécanique et de l’endommagement du matériau couplés à l’homogénéisation multi-échelle des matériaux par la Mécanique du Génome de Structure ont permis d’identifier les paramètres du modèle macroscopique. A l’échelle mésoscopique, le modèle géométrique a été réalisé grâce au logiciel Texgen. Ce logiciel permet d’obtenir une description approchée mais réaliste de l’ondulation des torons de fibres. La même description a servi à l’homogénéisation numérique multi-échelle des stratifiés étudiés. La simulation numérique de l’impact basse vitesse a été effectuée au moyen du logiciel d’éléments finis ABAQUS/Explicit. Les modèles de comportement du matériau ont été implémentés via la routine utilisateur VUMAT. Les résultats obtenus offrent une bonne corrélation avec les données expérimentalesIn the race for light materials able of meeting modern environmental challenges, an acrylic resin (Elium) has been developed. Elium is a thermoplastic resin able to replace thermosetting matrices, which are widespread nowadays in the industrial world. The present study aims to evaluate the impact resistance and to understand the failure mechanisms of composite laminates based on acrylic matrix under impact loading. We provide a contribution to the multiscale analysis of the impact resistance of laminated composite.First, the impact resistance and the damage tolerance of the acrylic resin based composites were compared with those of conventional composites. Then, the impact performance of the laminated composites has been enhanced by adding copolymer blocks to the liquid acrylic resin. These copolymers are able to form micelles of nanometer sizes, which lead to the improvement of both the acrylic matrix fracture toughness and the impact resistance. The effects of the impact energy, temperature, and composition in nano-copolymers have also been investigated.In order to provide a numerical tool for the prediction of the impact response of the glass fiber/Acrylic laminates, two strategies have been analyzed. The first one, performed at the macroscopic scale, considers the woven ply of the laminate as homogeneous material, and the second one (at the mesoscopic scale), deals with a realistic geometrical description of the yarns undulation. Both models use cohesive zones at the interface between the adjacent plies, to simulate the delamination. For this purpose, experimental and numerical delamination tests were performed to feed the inter-ply damage model. Mechanical tests for material characterization were also performed on specimens in order to identify the ply-damage model parameters. The Mechanics of Structure Genome (MSG) and a finite element based micromechanics approaches were then conducted to evaluate the effective thermomechanical properties of the yarns and the plain woven composite laminate. The realistic topological and morphological textures of the composite were accounted through Texgen software. These numerical impact simulations were performed using the finite element software ABAQUS/Explicit. Both models were implemented through a user material subroutine VUMAT. The obtained results appear in a good agreement with the experimental data and confirm the relevance of the proposed approach
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Bhagat, Atul Ramesh. "Homogenization and multiscale modeling of carbon/carbon composite." Thesis, 2017. http://localhost:8080/xmlui/handle/12345678/7275.
Full text
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Jhurani, Chetan Kumar. "Multiscale modeling using goal-oriented adaptivity and numerical homogenization." 2009. http://hdl.handle.net/2152/6545.
Full textAbstract:
Modeling of engineering objects with complex heterogeneous material
structure at nanoscale level has emerged as an important research problem. In
this research, we are interested in multiscale modeling and analysis of mechanical
properties of the polymer structures created in the Step and Flash Imprint
Lithography (SFIL) process. SFIL is a novel imprint lithography process designed
to transfer circuit patterns for fabricating microchips in low-pressure
and room-temperature environments. Since the smallest features in SFIL are
only a few molecules across, approximating them as a continuum is not completely
accurate. Previous research in this subject has dealt with coupling
discrete models with continuum hyperelasticity models. The modeling of the
post-polymerization step in SFIL involves computing solutions of large nonlinear
energy minimization problems with fast spatial variation in material properties. An equilibrium configuration is found by minimizing the energy of
this heterogeneous polymeric lattice.
Numerical solution of such a molecular statics base model, which is
assumed to describe the microstructure completely, is computationally very
expensive. This is due to the problem size – on the order of millions of degrees
of freedom (DOFs). Rapid variation in material properties, ill-conditioning,
nonlinearity, and non-convexity make this problem even more challenging to
solve.
We devise a method for efficient approximation of the solution. Combining
numerical homogenization, adaptive finite element meshes, and goaloriented
error estimation, we develop a black-box method for efficient solution
of problems with multiple spatial scales. The purpose of this homogenization
method is to reduce the number of DOFs, find locally optimal effective material
properties, and do goal-oriented mesh refinement. In addition, it smoothes
the energy landscape.
Traditionally, a finite element mesh is designed after obtaining material
properties in different regions. The mesh has to resolve material discontinuities
and rapid variations. In our approach, however, we generate a sequence
of coarse meshes (possibly 1-irregular), and homogenize material properties on
each coarse mesh element using a locally posed constrained convex quadratic
optimization problem. This upscaling is done using Moore-Penrose pseudoinverse
of the linearized fine-scale element stiffness matrices, and a material independent
interpolation operator. This requires solution of a continuous-time Lyapunov equation on each element. Using the adjoint solution, we compute
local error estimates in the quantity of interest. The error estimates also drive
the automatic mesh adaptivity algorithm. The results show that this method
uses orders of magnitude fewer degrees of freedom to give fast and approximate
solutions of the original fine-scale problem.
Critical to the computational speed of local homogenization is computing
Moore-Penrose pseudoinverse of rank-deficient matrices without using
Singular Value Decomposition. To this end, we use four algorithms, each
having different desirable features. The algorithms are based on Tikhonov
regularization, sparse QR factorization, a priori knowledge of the null-space
of the matrix, and iterative methods based on proper splittings of matrices.
These algorithms can exploit sparsity and thus are fast.
Although the homogenization method is designed with a specific molecular
statics problem in mind, it is a general method applicable for problems
with a given fine mesh that sufficiently resolves the fine-scale material properties.
We verify the method using a conductivity problem in 2-D, with chessboard
like thermal conductivity pattern, which has a known homogenized
conductivity. We analyze other aspects of the homogenization method, for
example the choice of norm in which we measure local error, optimum coarse
mesh element size for homogenizing SFIL lattices, and the effect of the method
chosen for computing the pseudoinverse.text
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Bailakanavar, Mahesh Raju. "Space-Time Multiscale-Multiphysics Homogenization Methods for Heterogeneous Materials." Thesis, 2013. https://doi.org/10.7916/D89S1Z89.
Full textAbstract:
We present a unified, homogenization framework for computational analysis of heterogeneous materials consisting of multiple length scales, multiple time scales and coupled-multiple physics. The research efforts also addresses the technological issues associated with modeling the morphological details of microstructures with randomly distributed inclusions. The Random Sequential Adsorption (RSA) algorithm is improved to accurately and effectively model the morphological details of materials with randomly distributed inclusions. The proposed algorithm is more robust; computational efficient and versatile in comparison to the existing methods. A temporal homogenization scheme is developed and integrated with the previously developed spatial homogenization theory for fatigue life analysis of heterogeneous materials. The unified space-time multiscale homogenization model is validated for fatigue life prediction of elevated temperature Ceramic Matrix Composites (CMCs). In the final phase of the research a mathematical model for coupled moisture diffusion-mechanical deformation is developed. This model is integrated with the spatial homogenization framework to analyze problems consisting of multiple length scales and coupled-multiple physics. The unified multiscale-multiphysics model is validated for evaluating the degradation of physical and mechanical properties of short glass fiber and carbon fiber filled thermoplastic material systems.
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PERRIN, ELEONORE. "Multiscale poroelastic modeling of bone." Doctoral thesis, 2018. http://hdl.handle.net/11573/1208669.
Full textAbstract:
Total Hip Arthroplasty is nowadays one of the most performed orthopedic surgery and is
representing a major health and economic issue. Bone is a complex material showing a
hierarchical and porous structure, but also a natural ability to remodel itself thanks to
specific cells, which are sensitive to fluid flows. Based on these characteristics, a
multiscale numerical model has been developed within this thesis in order to simulate the
bone response under external mechanical solicitations. The developed model relies on the
homogenization technique for periodic structures based on an asymptotic expansion. It
simulates cortical bone as a homogeneous structure. The first application of the
developed model is the case of the loading of a finite volume of bone, allowing for the
determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid
boundary conditions (impermeable walls and atmospheric pressure), the analysis of the
corresponding structural response provides an overview of the fluid contribution to the
poroelastic behavior, impacting the stiffness of the considered material. To validate the
developed model, both a numerical and an experimental validation are realized. The
numerical validation consists in the variation of parameters such as material properties or
boundary conditions to estimate the accuracy of the model tendencies. Regarding the
experimental validation, a cubic trabecular bone sample, extracted from a human hip and
put under a compressive load, has been used. Increasing the load applied on the top of
the bone specimen, the displacement is extracted, allowing to computation of the
equivalent strain-stress curve. The equivalent stiffness of the bone specimen calculated
numerically is then compared with the one from the experiments. A good agreement
between the curves attests the validity of the developed numerical model, accounting for
both the solid matrix and fluid contributions.
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Chen, Chen. "Multiscale modelling of continuum and discrete dynamics in materials with complicated microstructure." Thesis, 2015. http://hdl.handle.net/2440/98116.
Full textAbstract:
Homogenization and other multiscale modelling techniques empower scientist and engineers to build efficient macroscale mathematical models for simulating materials with complicated microstructure. But the modelling methodology rarely systematically derives the boundary conditions for macroscale model. This thesis aims to systematically derive boundary conditions for macroscale models without heuristic arguments. I start by building a smooth macroscale model for a one-dimensional discrete diffusion system with rapidly varying microscale diffusivity, finite scale separation, and Dirichlet boundary conditions. I apply both centre manifold theory and homogenization theory to build the macroscale model. Both theories find same macroscale model. I then apply modern dynamical system theory to derive macroscopic boundary conditions for this class of diffusion problems. The results suggest a specific Robin boundary condition is a good choice for the macroscale model. I extend my methodology to a linear two-strand diffusion problem. My method finds macroscale boundary conditions for the microscale two-strand problem with different classes of microscale boundary conditions such as specified flux and mixed microscale boundary conditions. The two-strand problem has a more complicated eigen structure than the single strand problems but my method performs well. I also show this method is suitable for continuous problems, such as a class of continuous heterogeneous wave partial differential equations. Furthermore, I apply this technique to wave equations with periodic elasticities and densities and with arbitrary periodicity and number of strands. The algebra in these problem is tedious so I extensively implement computer algebra to find the corresponding macroscale models and boundary conditions. Finally, I consider nonlinearity by analysing the macroscale modelling and the derivation of macroscale boundary conditions for a nonlinear heat exchanger. The proposed technique provides a systematic tool for deriving macroscale boundary conditions for multiscale models. In comparison with heuristically proposed boundary conditions, my derived boundary conditions improve the accuracy of multiscale models in physical science and engineering.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2015.
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Tamer, Atakan. "Probabilistic Determination of Thermal Conductivity and Cyclic Behavior of Nanocomposites via Multi-Phase Homogenization." Thesis, 2013. http://hdl.handle.net/1911/72046.
Full textAbstract:
A novel multiscale approach is introduced for determining the thermal conductivity of polymer nanocomposites (PNCs) reinforced with single-walled carbon nanotubes (SWCNTs), which accounts for their intrinsic uncertainties associated with dispersion, distribution, and morphology. Heterogeneities in PNCs on nanoscale are identified and quantified in a statistical sense, for the calculation of effective local properties. A finite element method computes the overall macroscale properties of PNCs in conjunction with the Monte Carlo simulations. This Monte Carlo Finite Element Approach (MCFEA) allows for acquiring the randomness in spatial distribution of the nanotubes throughout the composite. Furthermore, the proposed MCFEA utilizes the nanotube content, orientation, aspect ratio and diameter inferred from their statistical information.
Local SWCNT volume or weight fractions are assigned to the finite elements (FEs), based on various spatial probability distributions. Multi-phase homogenization techniques are applied to each FE to calculate the local thermal conductivities. Then, the Monte Carlo simulations provide the statistics on the overall thermal conductivity of the PNCs. Subsequently, dispersion characteristics of the nanotubes are assessed by incorporating nanotube agglomerates. In this regard, a multi-phase homogenization method is developed for enhanced accuracy and effectiveness. The effect of the nanotube orientation in a polymer is studied for the cases where the SWCNTs are randomly oriented as well as longitudinally aligned.
The influence of voids existing in the polymer is investigated on the thermal conductivity, to capture the uncertainties in PNCs more extensively. Further, a unique damage evaluation model is proposed to assess the degradation of PNCs when subjected to thermal cycling. The growth in void content is represented with a Weibull-based equation, to quantify the deterioration of the thermal and mechanical properties of PNCs under thermal fatigue. In addition, the MCFEA considers the interface resistance of the carbon nanotubes as one of the key factors in the thermal conductivity of nanocomposites.
Parametric studies are performed comprehensively. The numerical results obtained are compared with available analytical techniques at hand and with the data from pertinent independent experimental studies. It is found that the proposed MCFEA is capable of estimating the thermal conductivity with good accuracy.