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We consider a one-dimensional totally asymmetric exclusion process on a ring with extended inhomogeneities, consisting of several segments with different hopping rates. Depending upon the underlying inhomogeneity configurations and for…

Statistical Mechanics · Physics 2015-02-26 Tirthankar Banerjee , Niladri Sarkar , Abhik Basu

A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…

Applied Physics · Physics 2018-11-26 Rosaria Del Toro , Andrea Bacigalupo , Marco Paggi

In this paper we describe efficient methods of generation of representative volume elements (RVEs) suitable for producing the samples for analysis of effective properties of composite materials via and for stochastic homogenization. We are…

Numerical Analysis · Mathematics 2014-11-18 Vladimir Salnikov , Daniel Choi , Philippe Karamian-Surville

This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In…

Analysis of PDEs · Mathematics 2025-02-11 Akira Ishikawa , Karel Svadlenka

Heterogeneity is classified in five categories---topologic, geometric, kinematic, static, and constitutive---and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments…

Soft Condensed Matter · Physics 2019-01-23 Matthew R. Kuhn

This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…

Soft Condensed Matter · Physics 2018-10-29 O. Rokoš , M. M. Ameen , R. H. J. Peerlings , M. G. D. Geers

In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule…

Analysis of PDEs · Mathematics 2016-04-11 M. Heida , B. Schweizer

We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…

Applied Physics · Physics 2018-03-14 Armand Wirgin

Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…

Analysis of PDEs · Mathematics 2016-06-13 Brian Seguin

Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…

Graphics · Computer Science 2020-10-27 Bin Wang , Yuanmin Deng , Paul Kry , Uri Ascher , Hui Huang , Baoquan Chen

In the present contribution we establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy…

Numerical Analysis · Mathematics 2014-09-04 Antoine Gloria , Felix Otto

Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been…

In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…

Analysis of PDEs · Mathematics 2025-12-02 Amartya Chakrabortty , Georges Griso , Julia Orlik

Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective…

Numerical Analysis · Mathematics 2022-06-07 Kaushik Bhattacharya , Burigede Liu , Andrew M. Stuart , Margaret Trautner

Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and…

Analysis of PDEs · Mathematics 2023-07-21 Changqing Ye , Eric T. Chung , Junzhi Cui

We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…

Numerical Analysis · Mathematics 2015-09-07 Claude Le Bris , Frederic Legoll , William Minvielle

We investigate the implications of a given symmetry of a random microstructure on the obtained effective tensor and its fluctuation in the context of thermal conductivity, and study strategies for enforcing these symmetries in…

Computational Engineering, Finance, and Science · Computer Science 2025-11-07 Binh Huy Nguyen , Matti Schneider

Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel,…

Disordered Systems and Neural Networks · Physics 2011-12-06 Xiaoming Mao , Paul M. Goldbart , Xiangjun Xing , Annette Zippelius

In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure…

Analysis of PDEs · Mathematics 2017-01-16 Martin Heida , Sergiy Nesenenko

We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macro-energy density.…

Computational Engineering, Finance, and Science · Computer Science 2024-09-23 Vien Minh Nguyen-Thanh , Lu Trong Khiem Nguyen , Timon Rabczuk , Xiaoying Zhuang