Asymptotic and numerical analysis for unilateral contact problem with Coulomb's friction between an elastic body and a thin elastic soft layer

We study the behavior of a device constituted of three bodies, one of them sliding with unilateral contact with non local Coulomb's friction on a thin layer, itself bounded to a rigid support. The Lame coefficients of the thin layer are assumed to vary with respect of epsilon. We show that when the thin layer disappears. its memory remains as a new contact law between the rigid support and the sliding body. Lastly, we give some numerical computation on a model device which evidences the theoritical results.