Homogenization via unfolding in periodic layer with contact

The elasticity problem for two domains separated by a heterogeneous layer of the thickness e is considered. The layer has an e-periodic structure, e≪1, including a multiple cracks and the contact between the structural components. The inclusions are surrounded by cracks and can have rigid displacements. The contacts are described by the Signorini and Tresca-friction conditions. In order to obtain preliminary estimates, a modification of the Korn inequality for the e-dependent periodic layer is performed. An asymptotic analysis with respect to eRT0 is provided and the limit elasticity problem is obtained, together with the transmission condition across the interface. The periodic unfolding method is used to study the limit behavior.