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In this work we consider the elasticity problem for two domains separated by a heterogeneous layer. The layer has an $\varepsilon-$periodic structure, $\varepsilon\ll1$, including a multiple micro-contact between the structural components.…

Analysis of PDEs · Mathematics 2015-11-25 Georges Griso , Anastasia Migunova , Julia Orlik

In this paper we investigate rods made of nonlinearly elastic, composite--materials that feature a micro-heterogeneous prestrain that oscillates (locally periodic) on a scale that is small compared to the length of the rod. As a main result…

Analysis of PDEs · Mathematics 2019-10-15 Robert Bauer , Stefan Neukamm , Mathias Schäffner

We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…

Numerical Analysis · Mathematics 2021-12-28 Fanyi Yang , Xiaoping Xie

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the…

Numerical Analysis · Mathematics 2015-03-11 Leonardo A. Poveda , Sebastian Huepo , Victor M. Calo , Juan Galvis

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…

Mathematical Physics · Physics 2015-12-31 A. Bacigalupo , L. Morini , A. Piccolroaz

In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…

Mathematical Physics · Physics 2014-03-17 Patrizio Neff , Ionel-Dumitrel Ghiba , Markus Lazar , Angela Madeo

For plane strain linear elasticity, given any anisotropic elasticity tensor $\mathbb{C}_{\rm aniso}$, we determine a best approximating isotropic counterpart $\mathbb{C}_{\rm iso}$. This is not done by using a distance measure on the space…

Analysis of PDEs · Mathematics 2025-01-01 Jendrik Voss , Panos Gourgiotis , Peter Lewintan , Adam Sky , Patrizio Neff

We prove, under some assumptions, the existence of correctors for the stochastic homoge-nization of of " viscous " possibly degenerate Hamilton-Jacobi equations in stationary ergodic media. The general claim is that, assuming knowledge of…

Analysis of PDEs · Mathematics 2017-04-26 Pierre Cardaliaguet , Panagiotis Souganidis

The paper deals with optimization of the acoustic band gaps computed using the homogenized model of strongly heterogeneous elastic composite which is constituted by soft inclusions periodically distributed in stiff elastic matrix. We employ…

Computational Physics · Physics 2020-02-14 Jaroslav Vondřejc , Eduard Rohan , Jan Heczko

This paper derives an explicit formula for the effective diffusion tensor by using the solutions to some effective cell problems after homogenizing Road effective boundary conditions (EBCs). The concept of Road EBCs was proposed recently by…

Analysis of PDEs · Mathematics 2020-10-26 Zhonggan Huang

Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…

Materials Science · Physics 2015-06-04 Konstantin Volokh

In this note, we propose a formal framework accounting for the sensitivity of a function of the domain with respect to the addition of a thin ligament. To set ideas, we consider the model setting of elastic structures, and we approximate…

Optimization and Control · Mathematics 2019-12-30 Charles Dapogny

We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…

Numerical Analysis · Mathematics 2025-05-07 Ruchi Guo , Xu Zhang

This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the…

Analysis of PDEs · Mathematics 2019-07-24 Changkun Wei , Jiaqing Yang , Bo Zhang

The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…

Classical Physics · Physics 2025-01-16 Luca Viviani , Davide Bigoni , Andrea Piccolroaz

This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…

Numerical Analysis · Mathematics 2020-08-11 Anh-Khoa Vo , Ekeoma Rowland Ijioma , Nhu-Ngoc Nguyen

Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…

Soft Condensed Matter · Physics 2025-11-17 Jehoon Moon , Gisoo Lee , Jaehee Lee , Hansohl Cho

Homogenization in linear elliptic problems usually assumes coercivity of the accompanying Dirichlet form. In linear elasticity, coercivity is not ensured through mere (strong) ellipticity so that the usual estimates that render…

Analysis of PDEs · Mathematics 2019-02-20 Marc Briane , Gilles A. Francfort

We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the…

Numerical Analysis · Mathematics 2007-09-10 Mechkour Houari

Homogenization in terms of multiscale limits transforms a multiscale problem with $n+1$ asymptotically separated microscales posed on a physical domain $D \subset \mathbb{R}^d$ into a one-scale problem posed on a product domain of dimension…

Numerical Analysis · Mathematics 2020-06-03 V. Kazeev , I. Oseledets , M. Rakhuba , Ch. Schwab