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We consider a family of linearly elastic shells with thickness $2\varepsilon$ (where $\varepsilon$ is a small parameter). The shells are clamped along a portion of their lateral face, all having the same middle surface $S$, and may enter in…

Mathematical Physics · Physics 2016-11-23 Á. Rodríguez-Arós

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a…

Soft Condensed Matter · Physics 2025-07-02 Basile Audoly , Claire Lestringant , Hussein Nassar

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure,…

Analysis of PDEs · Mathematics 2024-03-08 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

We determine the asymptotic behavior of the solutions to the linear elastodynamic equations in a stratified medium comprising an alternation of possibly very stiff layers with much softer ones, when the thickness of the layers tends to…

Analysis of PDEs · Mathematics 2015-10-09 Michel Bellieud

A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov

In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed…

Analysis of PDEs · Mathematics 2016-12-28 Hayk Aleksanyan

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

Probability · Mathematics 2011-04-20 Martin Hairer , Charles Manson

The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the…

Analysis of PDEs · Mathematics 2018-07-25 Stefan Neukamm , Mario Varga

This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for…

Numerical Analysis · Mathematics 2023-08-08 Alessandra Aimi , Giulia Di Credico , Heiko Gimperlein

In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the…

Analysis of PDEs · Mathematics 2017-06-23 Adrien Semin , Bérangère Delourme , Kersten Schmidt

We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…

Analysis of PDEs · Mathematics 2021-09-14 David Wiedemann , Malte A. Peter

In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…

Analysis of PDEs · Mathematics 2019-02-01 Elisa Davoli , Rita Ferreira , Carolin Kreisbeck

Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental…

Classical Physics · Physics 2025-03-25 Davide Bigoni , Andrea Piccolroaz

In this paper we use the method of layer potentials to study $L^2$ boundary value problems in a bounded Lipschitz domain $\Omega$ for a family of second order elliptic systems with rapidly oscillating periodic coefficients, arising in the…

Analysis of PDEs · Mathematics 2009-10-23 Carlos Kenig , Zhongwei Shen

We consider a periodic, linear elastic laminate with a brittle crack, evolving along a prescribed path according to Griffith's criterion. We study the homogenized limit of this evolution, as the size of the layers vanishes. The limit…

Analysis of PDEs · Mathematics 2021-11-05 Matteo Negri

The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…

Analysis of PDEs · Mathematics 2021-08-03 Elisa Davoli , Carolin Kreisbeck

We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: {\em micro-macro}). The geometry we have in mind includes regions of…

Mathematical Physics · Physics 2010-03-23 T. van Noorden , A. Muntean

A phase field model is presented to investigate dislocation formation (coherency loss) and workhardening in two-phase binary alloys. In our model the elastic energy density is a periodic function of the shear and tetragonal strains, which…

Statistical Mechanics · Physics 2013-05-29 Akihiko Minami , Akira Onuki

We study the asymptotic behavior of thin heterogeneous elastoplastic plates in the framework of linearized elastoplasticity, focusing on the regime where the plate thickness vanishes much faster than the characteristic scale of the…

Analysis of PDEs · Mathematics 2026-05-14 Marin Bužančić , Igor Velčić , Josip Žubrinić