Effective computation of the asymptotic expansion for a small inclusion in elastic media
Résumé
This paper presents a new method to compute the influence of a small inclusion of arbitrary shape in elastic media. Conventional homogenization techniques, while effective in many applications, fail to provide accurate predictions because of the averaged values used. A model based on the technique of asymptotic expansions is then proposed. At each order we provide corrective terms modeling the influence of the inclusion using techniques of scaling and multi-scale asymptotic expansions. Expansions are constructed for the Poisson and linear elasticity two-dimensional problems.
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