相关论文: Convergence of two-scale expansions for elastic he…

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…

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This…

For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…

Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…

This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…

We use the notion of stochastic two-scale convergence to solve the problem of stochastic homogenization of the elastic plate in the bending regime.

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…

We analyse a problem of two-dimensional linearised elasticity for a two-component periodic composite, where one of the components consists of disjoint soft inclusions embedded in a rigid framework. We consider the case when the contrast…

We investigate a two-scale system featuring an upscaled parabolic dispersion-reaction equation intimately linked to a family of elliptic cell problems. The system is strongly coupled through a dispersion tensor, which depends on the…

Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…

We analyse the behaviour of thin composite plates whose material properties vary periodically in-plane and possess a high degree of contrast between the individual components. Starting from the equations of three-dimensional linear…

The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determinate this spectrum and the…

In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…

This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic…

We consider a diffusion equation with highly oscillatory coefficients that admits a homogenized limit. As an alternative to standard corrector problems, we introduce here an embedded corrector problem, written as a diffusion equation in the…

The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of…

We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…