Homogenization via unfolding in periodic layer with contact
Georges Griso, Anastasia Migunova, Julia Orlik · Asymptotic Analysis · 2016
The elasticity problem for two domains separated by a heterogeneous layer of the thickness ε is considered. The layer has an ε -periodic structure, ε ≪ 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 ε -dependent periodic layer is performed. An asymptotic analysis with respect to ε → 0 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.