Relevant bibliographies by topics / Multiscale homogenization

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Multiscale homogenization'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Multiscale homogenization"

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NGUYEN, VINH PHU, MARTIJN STROEVEN, and LAMBERTUS JOHANNES SLUYS. "MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS." Journal of Multiscale Modelling 03, no. 04 (December 2011): 229–70. http://dx.doi.org/10.1142/s1756973711000509.

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This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multiscale simulations are presented.
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Lukkassen, Dag, Annette Meidell, and Peter Wall. "Multiscale homogenization of monotone operators." Discrete & Continuous Dynamical Systems - A 22, no. 3 (2008): 711–27. http://dx.doi.org/10.3934/dcds.2008.22.711.

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Sokolov, Alexander Pavlovich, and Anton Yurievich Pershin. "Computer-Aided Design of Composite Materials Using Reversible Multiscale Homogenization and Graph-Based Software Engineering." Key Engineering Materials 779 (September 2018): 11–18. http://dx.doi.org/10.4028/www.scientific.net/kem.779.11.

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In this work, a new software for computer-aided design of composite materials with predefined thermomechanical properties is presented in case of incomplete input data. The mathematical basis of underlying computational method of the properties identification is a modified method of multiscale homogenization named reversible multiscale homogenization method. The system has a modular architecture and includes software implementation of the reversible multiscale homogenization method based on a new technique of construction of software implementations of complex computational methods. The latter was named «Graph-based software engineering» (GBSE) and is based on category and graph theories. The corresponding numerical and experimental results were obtained and compared. The expediency of GBSE approach is discussed for the case of the development of complex computational methods required when solving the applied problems of the design of new heterogeneous materials.
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Hedjazian, N., Y. Capdeville, and T. Bodin. "Multiscale seismic imaging with inverse homogenization." Geophysical Journal International 226, no. 1 (March 27, 2021): 676–91. http://dx.doi.org/10.1093/gji/ggab121.

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Summary Seismic imaging techniques such as elastic full waveform inversion (FWI) have their spatial resolution limited by the maximum frequency present in the observed waveforms. Scales smaller than a fraction of the minimum wavelength cannot be resolved, and only a smoothed, effective version of the true underlying medium can be recovered. These finite-frequency effects are revealed by the upscaling or homogenization theory of wave propagation. Homogenization aims at computing larger scale effective properties of a medium containing small-scale heterogeneities. We study how this theory can be used in the context of FWI. The seismic imaging problem is broken down in a two-stage multiscale approach. In the first step, called homogenized FWI (HFWI), observed waveforms are inverted for a smooth, fully anisotropic effective medium, that does not contain scales smaller than the shortest wavelength present in the wavefield. The solution being an effective medium, it is difficult to directly interpret it. It requires a second step, called downscaling or inverse homogenization, where the smooth image is used as data, and the goal is to recover small-scale parameters. All the information contained in the observed waveforms is extracted in the HFWI step. The solution of the downscaling step is highly non-unique as many small-scale models may share the same long wavelength effective properties. We therefore rely on the introduction of external a priori information, and cast the problem in a Bayesian formulation. The ensemble of potential fine-scale models sharing the same long wavelength effective properties is explored with a Markov chain Monte Carlo algorithm. We illustrate the method with a synthetic cavity detection problem: we search for the position, size and shape of void inclusions in a homogeneous elastic medium, where the size of cavities is smaller than the resolving length of the seismic data. We illustrate the advantages of introducing the homogenization theory at both stages. In HFWI, homogenization acts as a natural regularization helping convergence towards meaningful solution models. Working with fully anisotropic effective media prevents the leakage of anisotropy induced by the fine scales into isotropic macroparameters estimates. In the downscaling step, the forward theory is the homogenization itself. It is computationally cheap, allowing us to consider geological models with more complexity (e.g. including discontinuities) and use stochastic inversion techniques.
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Svanstedt, Nils. "Multiscale stochastic homogenization of monotone operators." Networks & Heterogeneous Media 2, no. 1 (2007): 181–92. http://dx.doi.org/10.3934/nhm.2007.2.181.

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Imkeller, Peter, N. Sri Namachchivaya, Nicolas Perkowski, and Hoong C. Yeong. "A Homogenization Approach to Multiscale Filtering." Procedia IUTAM 5 (2012): 34–45. http://dx.doi.org/10.1016/j.piutam.2012.06.005.

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Heida, Martin, Ralf Kornhuber, and Joscha Podlesny. "Fractal Homogenization of Multiscale Interface Problems." Multiscale Modeling & Simulation 18, no. 1 (January 2020): 294–314. http://dx.doi.org/10.1137/18m1204759.

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Yoshimura, Akinori, Anthony M. Waas, and Yoshiyasu Hirano. "Multiscale homogenization for nearly periodic structures." Composite Structures 153 (October 2016): 345–55. http://dx.doi.org/10.1016/j.compstruct.2016.06.002.

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Chen, Zhangxin. "Multiscale methods for elliptic homogenization problems." Numerical Methods for Partial Differential Equations 22, no. 2 (2006): 317–60. http://dx.doi.org/10.1002/num.20099.

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Sakata, Seiichiro, and Fumihiro Ashida. "Stochastic Microscopic Stress Analysis of a Composite Material via Multiscale Analysis Considering Microscopic Uncertainty." Key Engineering Materials 452-453 (November 2010): 277–80. http://dx.doi.org/10.4028/www.scientific.net/kem.452-453.277.

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This paper discusses a stochastic microscopic stress analysis of a composite material for a microscopic random variation. The stochastic stress analysis is performed via a stochastic homogenization and multiscale analysis. The homogenization method is employed for the multiscale analysis and the Monte-Carlo simulation or perturbation-based method can be employed for the stochastic analysis. In this paper, outline of the analysis and some numerical results are provided.
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Dissertations / Theses on the topic "Multiscale homogenization"

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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.

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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.
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Gathier, Benjamin. "Multiscale strength homogenization : application to shale nanoindentation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43049.

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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.
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Covezzi, Federica <1990&gt. "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.

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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.
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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.

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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.
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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.

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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.
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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.

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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
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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.

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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.
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Ferreira, Rita Alexandra Gonçalves. "Spectral and homogenization problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/7856.

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Dissertation for the Degree of Doctor of Philosophy in Mathematics
Fundação 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
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Goncalves-Ferreira, Rita Alexandria. "Spectral and Homogenization Problems." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/83.

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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
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Nika, Grigor. "Multiscale analysis of emulsions and suspensions with surface effects." Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-dissertations/146.

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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.
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Books on the topic "Multiscale homogenization"

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Bogdan, Vernescu, ed. Homogenization methods for multiscale mechanics. Singapore: World Scientific, 2010.

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M, Stuart A., ed. Multiscale methods: Averaging and homogenization. New York: Springer, 2008.

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Blanc, Xavier, and Claude Le Bris. Homogenization Theory for Multiscale Problems. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-21833-0.

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Berlyand, Leonid, and Volodymyr Rybalko. Getting Acquainted with Homogenization and Multiscale. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01777-4.

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Bailakanavar, Mahesh Raju. Space-Time Multiscale-Multiphysics Homogenization Methods for Heterogeneous Materials. [New York, N.Y.?]: [publisher not identified], 2013.

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1945-, Engquist Björn, Lötstedt Per, Runborg Olof, and Multiscale Methods in Science and Engineering (2004 : Uppsala, Sweden), eds. Multiscale methods in science and engineering. Berlin: Springer, 2005.

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Artz, Timothy Steven. Modeling Lifetime Performance of Ceramic Matrix Composites with Reduced Order Homogenization Multiscale Methods. [New York, N.Y.?]: [publisher not identified], 2022.

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Conference on Multiscale Problems in Science and Technology (2000 Dubrovnik, Croatia). Multiscale problems in science and technology: Challenges to mathematical analysis and perspectives. Berlin: Springer, 2002.

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1962-, Antonić N., ed. Multiscale problems in science and technology : challenges to mathematical analysis and perspectives : proceedings of the Conference on Multiscale Problems in Science and Technology, Dubrovnik, Croatia, 3-9 September 2000. Berlin: Springer, 2000.

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Coupled Systems: Theory, Models, and Applications in Engineering. Boca Raton: CRC Press, 2014.

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Book chapters on the topic "Multiscale homogenization"

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Chung, Eric, Yalchin Efendiev, and Thomas Y. Hou. "Homogenization and numerical homogenization of linear equations." In Multiscale Model Reduction, 35–66. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20409-8_2.

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Chung, Eric, Yalchin Efendiev, and Thomas Y. Hou. "Homogenization and numerical homogenization of nonlinear equations." In Multiscale Model Reduction, 385–95. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20409-8_13.

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Engquist, Björn, and Olof Runborg. "Projection Generated Homogenization." In Multiscale Problems in Science and Technology, 129–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56200-6_4.

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Blanc, Xavier, and Claude Le Bris. "Homogenization in Dimension 1." In Homogenization Theory for Multiscale Problems, 61–98. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-21833-0_2.

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Rodríguez-Ramos, Reinaldo, Ariel Ramírez-Torres, Julián Bravo-Castillero, Raúl Guinovart-Díaz, David Guinovart-Sanjuán, Oscar L. Cruz-González, Federico J. Sabina, José Merodio, and Raimondo Penta. "Multiscale Homogenization for Linear Mechanics." In Constitutive Modelling of Solid Continua, 357–89. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31547-4_12.

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Desbrun, Mathieu, Roger D. Donaldson, and Houman Owhadi. "Modeling Across Scales: Discrete Geometric Structures in Homogenization and Inverse Homogenization." In Multiscale Analysis and Nonlinear Dynamics, 19–64. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2013. http://dx.doi.org/10.1002/9783527671632.ch02.

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Berlyand, Leonid, and Volodymyr Rybalko. "Introduction to Stochastic Homogenization." In Getting Acquainted with Homogenization and Multiscale, 85–101. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01777-4_8.

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Geers, M. G. D., V. G. Kouznetsova, and W. A. M. Brekelmans. "Computational homogenization." In Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics, 327–94. Vienna: Springer Vienna, 2010. http://dx.doi.org/10.1007/978-3-7091-0283-1_7.

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Blanc, Xavier, and Claude Le Bris. "Beyond the Diffusion Equation and Miscellaneous Topics." In Homogenization Theory for Multiscale Problems, 363–421. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-21833-0_6.

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Blanc, Xavier, and Claude Le Bris. "Numerical Approaches." In Homogenization Theory for Multiscale Problems, 257–362. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-21833-0_5.

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Conference papers on the topic "Multiscale homogenization"

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Cherkaev, E., S. Guenneau, H. Hutridurga, and N. Wellander. "Quasiperiodic Composites: Multiscale Reiterated Homogenization." In 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials). IEEE, 2019. http://dx.doi.org/10.1109/metamaterials.2019.8900926.

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Drago, Anthony S., Marek-Jerzy Pindera, Glaucio H. Paulino, Marek-Jerzy Pindera, Robert H. Dodds, Fernando A. Rochinha, Eshan Dave, and Linfeng Chen. "A Locally-Exact Homogenization Approach for Periodic Heterogeneous Materials." In MULTISCALE AND FUNCTIONALLY GRADED MATERIALS 2006. AIP, 2008. http://dx.doi.org/10.1063/1.2896777.

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Macri, Michael F., Andrew G. Littlefield, Joshua B. Root, and Lucas B. Smith. "Modeling Automatic Detection of Critical Regions in Composite Pressure Vessel Subjected to High Pressure." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84168.

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Composites can undergo micro damage leading to variations of the mechanical properties. The micro damage can be the result of high internal pressures and/or exposure to physical trauma. Modeling techniques, such as homogenization, are effective outside of these critical regions. However they break down in regions where the micro damage is occurring. To account for this, an algorithm has been developed to detect and implement a multiscale method on elements that observe a critical strain. The remaining model uses the homogenization method to simulate the composite. The elements surrounding the multiscale elements are adapted to act as a transition from multiscale to the homogenization. The multiscale approach is based on the partition of unity paradigm, allowing macro-scale computations to be performed with the micro-structural features explicitly considered. The model has been validated by comparing it to experimental results of a composite overwrapped steel tube section subjected to high internal pressures.
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Ke, L., and F. van den Meer. "Multiscale Modeling of Composite Laminates Delamination via Computational Homogenization." In VIII Conference on Mechanical Response of Composites. CIMNE, 2021. http://dx.doi.org/10.23967/composites.2021.040.

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Yuan, Chongxi, and Xingchen Liu. "Fast Two-Scale Analysis via Clustering." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-68633.

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Abstract Both man-made and natural materials exhibit heterogeneous properties at smaller observation scales. The multiscale analysis allows the inclusion of fine-scale information in coarse-scale simulations. One of the commonly used methods is homogenization, replacing the detailed fine-scale structures with their locally homogeneous effective material properties. When fine-scale material structures are stationary, representative volume elements (RVE) are often identified for their effective material properties to be applied over the entire structure. However, in non-stationary material structures, it is inappropriate to assume a single representative material. In this case, homogenization is often required for every individual cell, resulting in significant increases in computational cost. We propose a stiffness-based clustering algorithm that reduces the total number of homogenization computations needed for multiscale analysis. Cells with similar effective stiffness tensors are clustered together such that only a single homogenization is required for each cluster. Specifically, the clustering algorithm is based on the novel concept of Eigenstiffness, which represents the relative directional stiffness of a given material structure. The rotation invariant property of Eigenstiffness allows material structure with similar intrinsic stiffness but different orientations to be clustered together, further decreasing the number of clusters required for the multiscale analysis. Without a priori knowledge of the accurate homogenized material properties, approximated elasticity tensors and Eigenstiffness estimated through FFT-based homogenization methods are used for rapid clustering. The effectiveness of the method is verified by numerical simulations on various multiscale structures, including Voronoi foams and fiber-reinforced composites.
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Kildishev, Alexander V., Zhaxylyk Kudyshev, Ludmila J. Prokopeva, Derek A. Olson, William D. Henshaw, Sawyer D. Campbell, and Douglas H. Werner. "Multiscale design of optical metafilms with bianisotropic homogenization (Conference Presentation)." In Metamaterials, Metadevices, and Metasystems 2018, edited by Nader Engheta, Mikhail A. Noginov, and Nikolay I. Zheludev. SPIE, 2018. http://dx.doi.org/10.1117/12.2320065.

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Chung, Peter, and Raju Namburu. "A Computational Framework for a Multiscale Continuum-Atomistic Homogenization Method." In 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-1655.

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Rezakhani, Roozbeh, Mohammed Alnaggar, and Gianluca Cusatis. "Multiscale Homogenization Modeling of Alkali-Silica-Reaction Damage in Concrete." In 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures. IA-FraMCoS, 2016. http://dx.doi.org/10.21012/fc9.285.

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OLAYA, MICHAEL N., and MARIANNA MAIARÙ. "HOMOGENIZATION METHODS FOR MULTISCALE PROCESS MODELING THROUGH FULL FACTORIAL DESIGN." In Proceedings for the American Society for Composites-Thirty Eighth Technical Conference. Destech Publications, Inc., 2023. http://dx.doi.org/10.12783/asc38/36605.

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Crucial to developing the next generation of high-performance composites are multiscale process models which have the capacity to predict in-service performance affecting residual stresses and deformations generated during manufacturing. Length scale and geometrical complexity of composites increase in tandem; thus, process models must rely upon methods for homogenization of the curing process. This work proposes a novel, high-fidelity computational approach which leverages finite element (FE) analysis at the microscale to predict effective composite properties at arbitrary cure and temperature states. The approach is applied to a high-fidelity representative volume element (RVE) and low-fidelity repeating unit cell (RUC) that models a 75% fiber volume fraction AS4-carbon fiber/epoxy composite microstructure. Elastic properties of the composite are characterized across several temperature and cure states for each FE model. Two classical closed-form composite homogenization approaches are also used to predict effective properties at each cure state. Predictions obtained by each method are compared against those of the RVE on a state-by-state and property-to-property basis.
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Najmon, Joel C., Homero Valladares, and Andres Tovar. "Multiscale Topology Optimization With Gaussian Process Regression Models." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-66758.

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Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.
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Reports on the topic "Multiscale homogenization"

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X. Frank Xu. Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs. Office of Scientific and Technical Information (OSTI), March 2010. http://dx.doi.org/10.2172/1036255.

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