Numerical validation of an homogenized interface model

• Complete numerical study of a matched asymptotic expansion method using the first two terms of the expansion.
• Validation of the method.
• Implementation of the zeroth and first order terms.
• Original algorithm for solving the first order problem by a domain decomposition type algorithm.
• Numerical tests which show the efficiency of the proposed method.

The 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 Sánchez Palencia (1985) [1] and extended in Geymonat et al. (2011) [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.