Matched asymptotic expansion method for an homogenized interface model

International audienceOur aim is to demonstrate the effectiveness of the matched asymptotic expansion method in obtaining a simpli ed model for the influence of small identical heterogeneities periodically distributed on an internal surface on the overall response of a linearly elastic body. The results of some numerical experiments corroborate the precise identi cation of the di fferent steps, in particular of the outer/inner regions with their normalized coordinate systems and the scale separation, leading to the model

Numerical validation of an Homogenized Interface Model

International audienceThe aim of this paper is to numerically validate the effectiveness of a matched asymptotic expansion formal method introduced in a pioneering paper by Nguetseng and Sànchez Palencia [1] and extended in [2], [3]. Using this method a simplified model for the influence of small identical heterogeneities periodically distributed on an internal surface to the overall response of a linearly elastic body is derived. In order to validate this formal method a careful numerical study compares the solution obtained by a standard method on a fine mesh to the one obtained by asymptotic expansion. We compute both the zero and the first order terms in the expansion. To efficiently compute the first order term we introduce a suitable domain decomposition method

Asymptotic expansions and domain decomposition

International audienceWe apply the domain decomposition method to linear elasticity problems for multi-materials where the heterogeneities are concentrated in a thin internal layer. In the first case the heterogeneities are small, identical and periodically distributed on an internal surface and in the second one all the thin, curved internal layer is made of an elastic material much more strong than the surrounding one. In the first case the domain decomposition is used to efficiently solve the non-standard transmission problems obtained by the asymptotic expansion method. In the second case a non-standard membrane transmission problem originates from a surface shell like energy.La méthode de décomposition de domaine est appliquée a des problèmes d'élasticité linéaire avec des hétérogénéités. Dans un premier cas il s'agit d'une couche fine contenant des hétérogénéités réparties de façon périodique, dans un second cas d'une couche interne constitué d'un matériau avec un module de Young beaucoup plus grand que celui du matériau qui l'entoure. Dans le premier cas la décomposition de domaine est utilisée pour résoudre efficacement un problème avec des conditions de transmission non standard obtenu par développement asymptotique, Dans le deuxième cas, une condition de type Vencell apparai

The matched asymptotic expansion for the computation of the effective behavior of an elastic structure with a thin layer of holes

International audienceIn the framework of matched asymptotic expansions we introduce a new efficient and robust method to approximate the behavior of a structure con- taining a thin layer with periodically distributed micro-holes. A surface (in 3d) or a line in (2d) on which particular jumping conditions are defined sub- stitutes for the initial problem

Some asymptotic models for a thin layer of heterogeneities in an elastic structure

International audienc

Mathematical and numerical modeling of plate dynamics with rotational inertia

International audienceWe give a presentation of the mathematical and numerical treatment of plate dynamics problems including rotational inertia. The presence of rotational inertia in the equation of motion makes the study of such problems interesting. We employ HCT finite elements for space discretization and the Newmark method for time discretization in FreeFEM++, and test such methods in some significant cases: a circular plate clamped all over its lateral surface, a rectangular plate simply supported all over its lateral surface, and an L-shaped clamped plate

Une méthode de résolution efficace pour un problème multi-échelle en élasticité

International audienceCette présentation décrit une méthode multi-échelle robuste et efficace qui combine développements asymptotiques raccordés et décomposition de domaines pour résoudre des problèmes d'élasticité avec un grand nombre d'hétérogénéités

Matched asymptotic expansion method for an homogenized interface model

International audienceOur aim is to demonstrate the effectiveness of the matched asymptotic expansion method in obtaining a simpli ed model for the influence of small identical heterogeneities periodically distributed on an internal surface on the overall response of a linearly elastic body. The results of some numerical experiments corroborate the precise identi cation of the di fferent steps, in particular of the outer/inner regions with their normalized coordinate systems and the scale separation, leading to the model