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Communicated by P. G. CiarletOur aim is to demonstrate the effectiveness of the matched asymptotic expansion method in obtaining a simplified 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 several numerical experiments corroborate the precise identification of the different steps, in particular of the outer/inner regions with their normalized coordinate systems and the scale separation, leading to the model.