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Articoli di riviste sul tema "Deformations (Mechanics) – Mathematical models"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 4 febbraio 2022

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1

Faddeev, Alexander O., Svetlana A. Pavlova, and Tatiana M. Nevdakh. "Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere." Engineering Technologies and Systems, no. 1 (March 29, 2019): 51–66. http://dx.doi.org/10.15507/2658-4123.029.201901.051-066.

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Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered. Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods o

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2

Petrushin, G. D., and A. G. Petrushina. "Determination of the area of mechanical hysteresis loop using mathematical models." Industrial laboratory. Diagnostics of materials 86, no. 5 (May 22, 2020): 59–64. http://dx.doi.org/10.26896/1028-6861-2020-86-5-59-64.

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A method of the hysteresis loop relates to the direct methods for determination of the energy dissipation and studying the inelasticity in the material. The method is based on the direct formation of the mechanical hysteresis loop by static loading and unloading of the sample and measuring of the corresponding deformations. The relative energy dissipation is defined as the ratio of the hysteresis loop area to the elastic energy corresponding to the maximum amplitude of strain. Construction of the hysteresis loop is performed on the installation «torsional pendulum for determination of the mech

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SACHSE, FRANK B., GUNNAR SEEMANN, MATTHIAS B. MOHR, and ARUN V. HOLDEN. "MATHEMATICAL MODELING OF CARDIAC ELECTRO-MECHANICS: FROM PROTEIN TO ORGAN." International Journal of Bifurcation and Chaos 13, no. 12 (December 2003): 3747–55. http://dx.doi.org/10.1142/s0218127403008910.

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Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models. In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reco

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Ivanov, Evgeny, Olaf Lechtenfeld, and Stepan Sidorov. "Deformed N = 8 Supersymmetric Mechanics." Symmetry 11, no. 2 (January 26, 2019): 135. http://dx.doi.org/10.3390/sym11020135.

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We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The corresponding models are deformations of the standard N = 8 mechanics models by a mass parameter m.

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Taghizadeh, D. M., and H. Darijani. "Mechanical Behavior Modeling of Hyperelastic Transversely Isotropic Materials Based on a New Polyconvex Strain Energy Function." International Journal of Applied Mechanics 10, no. 09 (November 2018): 1850104. http://dx.doi.org/10.1142/s1758825118501041.

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In this paper, the mechanical behavior of incompressible transversely isotropic materials is modeled using a strain energy density in the framework of Ball’s theory. Based on this profound theory and with respect to physical and mathematical aspects of deformation invariants, a new polyconvex constitutive model is proposed for the mechanical behavior of these materials. From the physical viewpoint, it is assumed that the proposed model is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber–matrix interaction where each of the

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6

Moerman, Kevin M., Behrooz Fereidoonnezhad, and J. Patrick McGarry. "Novel hyperelastic models for large volumetric deformations." International Journal of Solids and Structures 193-194 (June 2020): 474–91. http://dx.doi.org/10.1016/j.ijsolstr.2020.01.019.

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7

Bobkov, S. P., and I. V. Polishchuk. "Simulation and visualization of solid deformation upon impact." Vestnik IGEU, no. 2 (2020): 51–57. http://dx.doi.org/10.17588/2072-2672.2020.2.051-057.

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The use of adequate mathematical models to study the process of deformation of solids is an urgent issue for industrial engineering. It is known that under mechanical action the bodies are deformed and mechanical stresses arise in them, which, in turn, lead to destruction. Therefore, the simulation of deformation processes can be useful both in studying the issues of strength and reliability of equipment and for solving problems of fine grinding of solid fuels. Classical continuum models of continuum mechanics are useful for studying mechanical stresses in idealized environments and for bodies

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8

Consuegra, Franklin, Antonio Bula, Wilson Guillín, Jonathan Sánchez, and Jorge Duarte Forero. "Instantaneous in-Cylinder Volume Considering Deformation and Clearance due to Lubricating Film in Reciprocating Internal Combustion Engines." Energies 12, no. 8 (April 15, 2019): 1437. http://dx.doi.org/10.3390/en12081437.

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A new methodology for predicting the real instantaneous in-cylinder volume in the combustion chamber of a reciprocating internal combustion engine is implemented. The mathematical model developed as part of this methodology, takes into consideration the deformations due to pressure and inertial forces, via a deformation constant adjusted through ANSYS®, using a high-precision CAD model of a SOKAN SK-MDF300 engine. The deformation constant was obtained from the CAD model using the computational tool ANSYS® and the pressure data was obtained from the engine running at three regimes: 1500, 2500,

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9

Bulucea, Cornelia A., Constantin Brindusa, Doru A. Nicola, Nikos E. Mastorakis, Carmen A. Bulucea, and Philippe Dondon. "Evaluating through mathematical modelling the power equipment busbars electrodynamic strength under sudden short-circuit conditions." MATEC Web of Conferences 210 (2018): 02004. http://dx.doi.org/10.1051/matecconf/201821002004.

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The electrodynamic strength, as forces acting between the current-carrying electric circuits are exerted as long as the currents exist, and have the tendency of deformation and displacement of the circuits. In short-circuit regimes the strength in electrical equipment becomes severe. For instance, short-circuits highly affect power transformers connected to power transmission lines. The effects are also strong because of mechanical deformations occurring in the power transformer connection part. In line with this idea, in this paper it is made an analytical study upon the a.c. single-phase and

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10

Clifton, R. J., and F. P. Chiang. "Experimental Mechanics." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1279–81. http://dx.doi.org/10.1115/1.3143691.

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Mechanical failure of machine parts, structures, and microelectronic components has a strong negative impact on the safety, security, and productivity of our people. Prevention of these failures is a principal focus of solid mechanics, which uses analysis, experiment, and computation to provide the understanding necessary for failure reduction through improved design, fabrication, and inspection. Experimental mechanics plays a critical role in this effort since it provides the data base for the calculations and the means for testing the validity of proposed theoretical models of failure. Curre

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11

Zhao, S. Z., X. Y. Xu, and M. W. Collins. "The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 1: A review of models for arterial wall behaviour." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 212, no. 4 (April 1, 1998): 229–40. http://dx.doi.org/10.1243/0954411981534015.

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The structural response of a large artery is characteristically complex and includes the highly non-linear, history-dependent response of a nonhomogeneous anisotropic structure undergoing finite deformations. The mechanics of the arterial wall has been studied for nearly two centuries. The goals of such research range from the desire to have a basic knowledge and understanding of the mechanics and physiology of this complex structure to the need for data and methods for the design of arterial prostheses. In this paper, the models for arterial wall behaviour are critically reviewed. Firstly, th

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Vorobyov, V. S., E. L. Karelina, O. A. Bender, and K. V. Katalymova. "STATISTICAL MODELS OF PHYSIC-MECHANICAL CHARACTERISTICS OF ROADS IN THE AREA OF CULVERTS." Vestnik SibADI 15, no. 4 (September 12, 2018): 560–73. http://dx.doi.org/10.26518/2071-7296-2018-4-560-573.

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Introduction. Increased technical requirements for roads, associated with increasing axial loads, the intensity and speed of vehicles, with the actual technical condition of the roads number, engineering structures, including culverts, activation of federal and regional services to bring the parameters of road surfaces to the world standards, all listed parameters pose the task in developing the mathematical modeling methods of physical-mechanical characteristics of soils in the culverts area. Therefore, such methods allow to reduce economic costs and time for carrying out experimental researc

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Guzev, Mikhail, and Vladimir Makarov. "Principles of the non-Euclidian model application to the problem of dissipative mesocracking structures of highly compressed rock and massifs modelling." E3S Web of Conferences 56 (2018): 02001. http://dx.doi.org/10.1051/e3sconf/20185602001.

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New experimental results such as “zonal disintegration” around deep openings and “reversible deformations” of highly compressed rock samples cannot be described correctly from contemporary rock mechanics, which is based on the principals of classical Continuum Mechanics theory. A new approach to rock mechanics mathematical models consists of the application of non-Euclidian modelling to the problem of the description of anomalous experimental results. This leads to the formation of the “Geomechanics of Highly Compressed Rock and Rock Massifs” - a new branch of the existing theory of Geomechani

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14

Deng, Wubing, and Igor B. Morozov. "Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies." GEOPHYSICS 81, no. 4 (July 2016): D395—D404. http://dx.doi.org/10.1190/geo2015-0406.1.

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We have developed a macroscopic model for a two-phase medium (solid porous rock frame plus saturating pore fluid) with squirt flows based on Lagrangian continuum mechanics. The model focuses on improved physics of rock deformation, including explicit differential equations in time domain, causality, linearity, frequency-independent parameters with clear physical meanings, and an absence of mathematical internal or memory variables. The approach shows that all existing squirt-flow models can be viewed as microscopic models of viscosity for solid rock. As in existing models, the pore space is di

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Hvozd, Viktor, Eugene Tishchenko, Andriy Berezovskyi, and Stanislav Sidnei. "Research of Fire Resistance of Elements of Steel Frames of Industrial Buildings." Materials Science Forum 1038 (July 13, 2021): 506–13. http://dx.doi.org/10.4028/www.scientific.net/msf.1038.506.

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The article considers and analyses the methods by which it is possible to carry out research to determine the fire resistance of elements of steel frames of industrial buildings. It is determined that it is expedient to use the means of computational fluid dynamics, which has no limitations due to the high cost, complexity, environmental friendliness and complexity in comparison with real experiments. In order to conduct the most reliable computational experiments, mathematical models of temperature and mechanical reaction to the thermal effect of fire were created, taking into account the equ

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Okamoto, R. J., M. J. Moulton, S. J. Peterson, D. Li, M. K. Pasque, and J. M. Guccione. "Epicardial Suction: A New Approach to Mechanical Testing of the Passive Ventricular Wall." Journal of Biomechanical Engineering 122, no. 5 (May 30, 2000): 479–87. http://dx.doi.org/10.1115/1.1289625.

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The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular

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17

Krzysztof, Chelmiski. "On Noncoercive Models in the Theory of Inelastic Deformations with Internal Variables." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 81, S3 (2001): 595–96. http://dx.doi.org/10.1002/zamm.20010811575.

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Dubko, A. G., R. S. Osipov, Yu V. Bondarenko, and O. F. Bondarenko. "Electronic devices for studying mechanical properties of biological tissues." Технология и конструирование в электронной аппаратуре, no. 5-6 (2020): 40–47. http://dx.doi.org/10.15222/tkea2020.5-6.40.

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The paper shows the relevance of studying the mechanical properties of biological tissues and biocompatible materials for solving the problems of general and reconstructive surgery, transplantology, manual therapy, virtual simulation of surgical operations, robotic surgery, etc. The authors present basic information about biological tissue as an object of research and give a brief overview of the devices used for studying the mechanical characteristics of biological tissues. An experimental system for testing deformations of biological tissues and biocompatible materials during compression is

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19

Eremeyev, Victor A., Faris Saeed Alzahrani, Antonio Cazzani, Francesco dell’Isola, Tasawar Hayat, Emilio Turco, and Violetta Konopińska-Zmysłowska. "On existence and uniqueness of weak solutions for linear pantographic beam lattices models." Continuum Mechanics and Thermodynamics 31, no. 6 (September 13, 2019): 1843–61. http://dx.doi.org/10.1007/s00161-019-00826-7.

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Abstract In this paper, we discuss well-posedness of the boundary-value problems arising in some “gradient-incomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class of metamaterials whose microstructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy density depends on displacements and only on some specific partial derivatives among those constituting displacements first and second gradients. So, unli

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20

Shen, Li-Jun. "Fractional derivative models for viscoelastic materials at finite deformations." International Journal of Solids and Structures 190 (May 2020): 226–37. http://dx.doi.org/10.1016/j.ijsolstr.2019.10.025.

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Paggi, M., S. Kajari-Schröder, and U. Eitner. "Thermomechanical deformations in photovoltaic laminates." Journal of Strain Analysis for Engineering Design 46, no. 8 (September 13, 2011): 772–82. http://dx.doi.org/10.1177/0309324711421722.

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Recent experimental results based on the digital image correlation technique (U. Eitner, M. Köntges, R. Brendel, Solar Energy Mater. Solar Cells, 2010, 94, 1346–1351) show that the gap between solar cells embedded into a standard photovoltaic laminate varies with temperature. The variation of this gap is an important quantity to assess the integrity of the electric connection between solar cells when exposed to service conditions. In this paper, the thermo-elastic deformations in photovoltaic laminates are analytically investigated by developing different approximate models based on the multil

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22

Bdeiwi, Houda, Andrea Ciarella, Andrew Peace, and Marco Hahn. "Model structure effect on static aeroelastic deformation of the NASA CRM." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 9 (January 18, 2019): 4167–83. http://dx.doi.org/10.1108/hff-07-2018-0352.

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Purpose This paper aims to present a computational aeroelastic capability based on a fluid–structure interaction (FSI) methodology and validate it using the NASA Common Research Model (CRM). Focus is placed on the effect of the wind tunnel model structural features on the static aeroelastic deformations. Design/methodology/approach The FSI methodology couples high-fidelity computational fluid dynamics to a simplified beam representation of the finite element model. Beam models of the detailed CRM wind tunnel model and a simplified CRM model are generated. The correlation between the numerical

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Choksi, R., G. Del Piero, I. Fonseca, and D. Owen. "Structured Deformations as Energy Minimizers in Models of Fracture and Hysteresis." Mathematics and Mechanics of Solids 4, no. 3 (September 1999): 321–56. http://dx.doi.org/10.1177/108128659900400304.

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Deng, Wubing, and Igor B. Morozov. "Mechanical interpretation and generalization of the Cole-Cole model in viscoelasticity." GEOPHYSICS 83, no. 6 (November 1, 2018): MR345—MR352. http://dx.doi.org/10.1190/geo2017-0821.1.

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The mechanical basis of the popular Cole-Cole rheological model in viscoelasticity is investigated by using Lagrangian mechanics with nonlinear energy dissipation. The Cole-Cole model is usually viewed as a convenient way to fit the observed frequency-dependent attenuation and velocity-dispersion spectra, but its time-domain and numerical formulations are complex and contradict standard physical principles. For example, time-domain modeling of Cole-Cole media requires special mathematical tools such as fractional derivatives, convolutional integrals, and/or memory variables. Nevertheless, we f

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Kislitsyn, V. D., K. A. Mokhireva, V. V. Shadrin, and A. L. Svistkov. "Research and Modeling of Viscoelastic Behavior of Elastomeric Nanocomposites." PNRPU Mechanics Bulletin, no. 2 (December 15, 2021): 76–87. http://dx.doi.org/10.15593/perm.mech/2021.2.08.

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The paper presents results of studying mechanical properties of polymer composites depending on types of filler particles (granular - carbon black, nanodiamonds; layered - graphene plates; fibrous - single-walled nanotubes). These nanofillers differ greatly from each other in their structure and geometry. A significant difference in behavior of nanocomposites was revealed even with little introduction of particles into the elastomer. The highest level of reinforcement of the matrix was obtained when single-wall nanotubes and detonation nanodiamonds were used as fillers. The viscoelastic proper

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Okuno, A., and H. B. Kingsbury. "Dynamic Modulus of Poroelastic Materials." Journal of Applied Mechanics 56, no. 3 (September 1, 1989): 535–40. http://dx.doi.org/10.1115/1.3176123.

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A simple mathematical formula is proposed to predict the fluid damping effects in poroelastic materials. Biot’s poroelasticity equations are solved to obtain the response of poroelastic materials undergoing harmonic tension-compression and bending deformation. Complex moduli of poroelastic material are explored from the response functions on basis of mathematical models. It is shown that the effects of material parameters, geometrical parameters, and flow boundary conditions on the fluid damping are predicted by simple mathematical formulas. Numerical results are presented and compared with th

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Spagnuolo, Mario, and Ugo Andreaus. "A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling." Mathematics and Mechanics of Solids 24, no. 1 (February 5, 2018): 258–80. http://dx.doi.org/10.1177/1081286517737000.

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In this paper, we give a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities. The main scope of this work is to present the different methods of analysis available for describing the possible equilibrium forms and the motions of elastic beams. For the sake of completeness, we start by giving an overview of the nonlinear theories introduced for approaching this argument and then we account for the variational principles and deformation energies introduced for modelling beams undergoing large deforma

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Krysko, A. V., J. Awrejcewicz, K. S. Bodyagina, M. V. Zhigalov, and V. A. Krysko. "Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials." Acta Mechanica 232, no. 9 (June 26, 2021): 3441–69. http://dx.doi.org/10.1007/s00707-021-03010-8.

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AbstractIn this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of

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Piekarska, W., M. Kubiak, Z. Saternus, S. Stano, and T. Domański. "Numerical Prediction Of Deformations In Laser Welded Sheets Made Of X5CrNi18-10 Steel." Archives of Metallurgy and Materials 60, no. 3 (September 1, 2015): 1965–72. http://dx.doi.org/10.1515/amm-2015-0334.

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AbstractThe work concerns the numerical modelling of coupled thermal and mechanical phenomena occurring in the laser beam welding process. Commercial Abaqus FEA engineering software is adopted to numerical computations in order to perform a comprehensive analysis of thermo-mechanical phenomena. Created in Fortran programming language additional numerical subroutines are implemented into Abaqus solver, used to describe the power intensity distribution of the movable laser beam heat source. Temperature dependent thermomechanical properties of X5CrNi18-10 steel are adopted in the numerical analys

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Giacomini, Alessandro, and Marcello Ponsiglione. "Non-interpenetration of matter for SBV deformations of hyperelastic brittle materials." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 138, no. 5 (October 2008): 1019–41. http://dx.doi.org/10.1017/s0308210507000121.

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We prove that the Ciarlet–Nečas non-interpenetration of matter condition can be extended to the case of deformations of hyperelastic brittle materials belonging to the class of special functions of bounded variation (SBV), and can be taken into account for some variational models in fracture mechanics. In order to formulate such a condition, we define the deformed configuration under an SBV map by means of the approximately differentiable representative, and we prove some connected stability results under weak convergence. We provide an application to the case of brittle Ogden materials.

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Velmisov, Petr A., Yuliya A. Tamarova, and Yuliya V. Pokladova. "Investigation of the dynamic stability of bending-torsional deformations of the pipeline." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 1 (March 31, 2021): 72–81. http://dx.doi.org/10.15507/2079-6900.23.202101.72-81.

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Nonlinear mathematical models are proposed that describe the dynamics of a pipeline with a fluid flowing in it: a) the model of bending-torsional vibrations with two degrees of freedom; b) the model describing flexural-torsional vibrations taking into account the nonlinearity of the bending moment and centrifugal force; c) the model that takes into account joint longitudinal, bending (transverse) and torsional vibrations. All proposed models are described by nonlinear partial differential equations for unknown strain functions. To describe the dynamics of a pipeline, the nonlinear theory of a

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Buffa, Franco, Andrea Causin, Antonio Cazzani, Sergio Poppi, Giannina Sanna, Margherita Solci, Flavio Stochino, and Emilio Turco. "The Sardinia Radio Telescope: A comparison between close-range photogrammetry and finite element models." Mathematics and Mechanics of Solids 22, no. 5 (December 23, 2015): 1005–26. http://dx.doi.org/10.1177/1081286515616227.

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The Sardinia Radio Telescope (SRT), located near Cagliari (Italy), is the world’s second largest fully steerable radio telescope endowed with an active-surface system. Its primary mirror has a quasi-parabolic shape with a diameter of 64 m. The configuration of the primary mirror surface can be modified by means of electro-mechanical actuators. This capability ensures, within a fixed range, the balancing of the deformation caused, for example, by loads such as self-weight, thermal effects and wind pressure. In this way, the difference between the ideal shape of the mirror (which maximizes its p

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Ostanina, T. V., A. I. Shveykin, and P. V. Trusov. "The grain structure refinement of metals and alloys under severe plastic deformation: experimental data and analysis of mechanisms." PNRPU Mechanics Bulletin, no. 2 (December 15, 2020): 85–111. http://dx.doi.org/10.15593/perm.mech/2020.2.08.

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Wide opportunities of using fine-grained materials as structural and functional materials with advanced physical and mechanical properties have proved the importance of improving the existing technology and creating new processing methods and treatment conditions for such ma-terials. At the same time, a preliminary theoretical analysis using mathematical models gives an opportunity to significantly reduce the cost of such experimental studies. Thus, it is necessary to develop multilevel models of polycrystalline metals and alloys based on crystal plasticity with the description of structure, d

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Forest, Samuel, and Karam Sab. "Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models." Mathematics and Mechanics of Solids 25, no. 7 (August 1, 2017): 1429–49. http://dx.doi.org/10.1177/1081286517720844.

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Germain’s general micromorphic theory of order [Formula: see text] is extended to fully non-symmetric higher-order tensor degrees of freedom. An interpretation of the microdeformation kinematic variables as relaxed higher-order gradients of the displacement field is proposed. Dynamical balance laws and hyperelastic constitutive equations are derived within the finite deformation framework. Internal constraints are enforced to recover strain gradient theories of grade [Formula: see text]. An extension to finite deformations of a recently developed stress gradient continuum theory is then presen

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Glaesener, Raphaël N., Claire Lestringant, Bastian Telgen, and Dennis M. Kochmann. "Continuum models for stretching- and bending-dominated periodic trusses undergoing finite deformations." International Journal of Solids and Structures 171 (October 2019): 117–34. http://dx.doi.org/10.1016/j.ijsolstr.2019.04.022.

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Barari, A., M. Omidvar, D. D. Ganji, and Abbas Tahmasebi Poor. "An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics." Mathematical Problems in Engineering 2008 (2008): 1–13. http://dx.doi.org/10.1155/2008/394103.

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Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and

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McGinty, R. D., T. B. Rhyne, and S. M. Cron. "Analytical Solution for the Stresses Arising in +/− Angle Ply Belts of Radial Tires." Tire Science and Technology 36, no. 4 (December 1, 2008): 244–74. http://dx.doi.org/10.2346/1.2999704.

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Abstract (sommario):

Abstract Stresses arising in the belts of radial ply tires, particularly those at the belt edge, are known to be critical to tire durability. Belt edge stresses are commonly calculated using finite element (FE) methods that provide estimates of the levels but do not necessarily give significant insight into the underlying mechanics. In contrast, analytical models can provide physical insight into the mechanisms affecting tire durability but are currently incomplete due to the challenges faced in obtaining closed-form mathematical solutions. Nevertheless, analytical solutions remain important t

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38

Sivtsev, N. S., and V. V. Tarasov. "Numerical Study of Stress-Strain State of Workpiece in Contact Problem of Surface Mandrel Drilling." Science & Technique 20, no. 3 (June 3, 2021): 259–67. http://dx.doi.org/10.21122/2227-1031-2021-20-3-259-267.

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Abstract (sommario):

In recent years, the economic factor has played an increasingly important role in the selection of technologies for manufacturing machine parts with specified values of normalized parameters of geometric accuracy and quality of working surfaces. As applied to surface plastic deformation processes, this is noticeably manifested in the search for effective friction control methods in the “tool – workpiece” pair, which ultimately determines the distribution pattern and the magnitude of stresses and strains in the workpiece and the tool. It is not possible to obtain a rigorous analytical solution

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39

Jafari Bidhendi, Amirhossein, and Rami K. Korhonen. "A Finite Element Study of Micropipette Aspiration of Single Cells: Effect of Compressibility." Computational and Mathematical Methods in Medicine 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/192618.

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Abstract (sommario):

Micropipette aspiration (MA) technique has been widely used to measure the viscoelastic properties of different cell types. Cells experience nonlinear large deformations during the aspiration procedure. Neo-Hookean viscohyperelastic (NHVH) incompressible and compressible models were used to simulate the creep behavior of cells in MA, particularly accounting for the effect of compressibility, bulk relaxation, and hardening phenomena under large strain. In order to find optimal material parameters, the models were fitted to the experimental data available for mesenchymal stem cells. Finally, thr

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40

Hsu, Tze-Chi, and William R. D. Wilson. "Refined Models for Hydrodynamic Lubrication in Axisymmetric Stretch Forming." Journal of Tribology 116, no. 1 (January 1, 1994): 101–9. http://dx.doi.org/10.1115/1.2927023.

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Abstract (sommario):

Two mathematical models for axisymmetric stretch forming with a spherical punch are developed. The models combine a finite element representation of the sheet deformation with a hydrodynamic lubrication model. In one model the influence of sheet bending stiffness is taken into account while in the other only the membrane stiffness is considered. Comparison of the predictions of the models with the film thickness measurements of Hector and Wilson indicates that the inclusion of elastic effects is important in predicting lubricant film thickness. The results of the bending model are in particula

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41

Dosaev, Marat, Vitaly Samsonov, and Vladislav Bekmemetev. "Comparison between 2D and 3D Simulation of Contact of Two Deformable Axisymmetric Bodies." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 2 (April 26, 2020): 123–33. http://dx.doi.org/10.1515/ijnsns-2018-0157.

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Abstract (sommario):

AbstractA portable pneumatic video-tactile sensor for determining the local stiffness of soft tissue and the methodology for its application are considered. The expected range of local elastic modulus that can be estimated by the sensor is 100 kPa–1 MPa. The current version of the device is designed to determine the characteristics of tissues that are close in mechanical properties to the skin with subcutis and muscles. A numerical simulation of the contact between the sensor head and the soft tissue was performed using the finite-element method. Both 2D and 3D models were developed. Results o

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42

Snoeijer, J. H., A. Pandey, M. A. Herrada, and J. Eggers. "The relationship between viscoelasticity and elasticity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (November 2020): 20200419. http://dx.doi.org/10.1098/rspa.2020.0419.

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Abstract (sommario):

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models f

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43

Gao, X. L., X. N. Jing, and G. Subhash. "Two new expanding cavity models for indentation deformations of elastic strain-hardening materials." International Journal of Solids and Structures 43, no. 7-8 (April 2006): 2193–208. http://dx.doi.org/10.1016/j.ijsolstr.2005.03.062.

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44

Oden, J. T., T. L. Lin, and J. M. Bass. "A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder." Tire Science and Technology 16, no. 1 (January 1, 1988): 18–43. http://dx.doi.org/10.2346/1.2148795.

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Abstract (sommario):

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

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45

Volkov, Ivan, Leonid Igumnov, and Denis Shishulin. "Evaluating long-term strength of structures." Thermal Science 23, Suppl. 2 (2019): 477–88. http://dx.doi.org/10.2298/tsci19s2477v.

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Abstract (sommario):

The issue of evaluating strength and service life is discussed as applied to structures, the exploitation properties of which are characterized by multi-parametric nonstationary thermal mechanical effects. The main requirements to mathematical models of the related processes are formulated. In the framework of mechanics of damaged media, a mathematical model describing processes of inelastic deformation and damage accumulation due to creep is developed. The mechanics of damaged media model consists of three interconnected parts: relations defining inelastic behavior of the material accounting

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46

Wijata, Adam, Jan Awrejcewicz, Jan Matej, and Michał Makowski. "Mathematical model for two-dimensional dry friction modified by dither." Mathematics and Mechanics of Solids 22, no. 10 (June 2, 2016): 1936–49. http://dx.doi.org/10.1177/1081286516650483.

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Abstract (sommario):

A new dynamic two-dimensional friction model is developed that is based on the bristle theory. Actually, it is the Reset Integrator Model converted into a two-dimensional space. Usually, two-dimensional friction models are in fact one-dimensional models that are rotated into a slip velocity direction. However, this common approach cannot be applied to the bristle model. That is why the idea of a two-dimensional bristle is presented. The bristle’s deformation is described using polar coordinates. The carried-out numerical simulation of a planar oscillator has proved that the new model correctly

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47

Man, Xiaolin, and Colby C. Swan. "A Mathematical Modeling Framework for Analysis of Functional Clothing." Journal of Engineered Fibers and Fabrics 2, no. 3 (September 2007): 155892500700200. http://dx.doi.org/10.1177/155892500700200302.

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Abstract (sommario):

In the analysis and design of functional clothing systems, it is helpful to quantify the effects of a system on a wearer's physical performance capabilities. Toward this end, a clothing modeling framework for quantifying the mechanical interactions between a given clothing system design and a specific wearer performing defined physical tasks is proposed. The modeling framework consists of three interacting modules: (1) a macroscale fabric mechanics/dynamics model; (2) a collision detection and contact correction module; and (3) a human motion module. In the proposed framework, the macroscopic

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48

Stempin, Paulina, and Wojciech Sumelka. "Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects." Computational Mechanics 68, no. 3 (March 13, 2021): 697–708. http://dx.doi.org/10.1007/s00466-021-01987-6.

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Abstract (sommario):

AbstractIn this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric study on the influence of length scale and order of fractional continua for different boundary conditions demonstrates, how the non-locality affects the static bending response of the

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49

Szekely, Julian. "Mathematical Modeling in Materials Science and Engineering." MRS Bulletin 19, no. 1 (January 1994): 11–13. http://dx.doi.org/10.1557/s0883769400038793.

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Abstract (sommario):

During the past two decades, mathematical modeling has been gaining acceptance as a legitimate part of materials science and engineering. However, as common to all relatively new disciplines, we still lack a realistic perspective regarding the uses, limitations, and even the optimal methodologies of mathematical modeling techniques.The term “mathematical modeling” covers a broad range of activities, including molecular dynamics, other atomistic scale systems, continuum fluid and solid mechanics, deformation processing, systems analysis, input-output models, and lifecycle analyses. The common p

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50

Han, Rui, and Jinju Chen. "A modified Sneddon model for the contact between conical indenters and spherical samples." Journal of Materials Research 36, no. 8 (April 28, 2021): 1762–71. http://dx.doi.org/10.1557/s43578-021-00206-5.

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Abstract (sommario):

AbstractIndentation techniques have proven to be effective to characterize the mechanical properties of materials. For the elastic deformation, the commonly used models are Hertz model and Sneddon model. However, neither of them works for indenting the spherical samples using the pyramid or conical indenter. Therefore, one modified Sneddon model has been developed to determine the Young’s modulus of spherical samples from indentation results. In this study, the effects of sample diameter and indenter angles on indentation tests were investigated by finite element method (FEM). The empirical co

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