相关论文: Quantitative stochastic homogenization of nonlinea…
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…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. Under the…
A reduced order asymptotic homogenization based multiscale technique which can capture damage and inelastic effects in composite materials is proposed. This technique is based on two scale homogenization procedure where eigen strain…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an…
We analyze a mesoscopic model of a shear stress material with a three dimensional slab geometry, under an external quasistatic deformation of a simple shear type. Relaxation is introduced in the model as a mechanism by which an unperturbed…
Knowledge of the state of plastic deformation in metallic structures is vital to prevent failure. This is why non-destructive acoustic tests based on the measurement of first order elastic constants have been developed and intensively used.…
We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented…
Investigation of inhomogeneities has wide applications in different areas of mechanics including the study of composite materials. Here, we analytically study an arbitrarily-shaped isotropic inhomogeneity embedded in a finite-sized…
Floquet-Bloch wave asymptotics is used to homogenize the in-plane mechanical response of a periodic grillage of elastic Rayleigh rods, possessing a distributed mass density, together with rotational inertia. The grid is subject to…
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, "viscous" Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be…
A method for the homogenization of 3-D periodic elastic composites is presented. It allows for the evaluation of the averaged overall frequency dependent dynamic material constitutive tensors relating the averaged dynamic field variable…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
We examine the buckling shape and critical compression of confined inhomogeneous composite sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of the sheet, the density of the substrate, and the…