  In this work we consider the elasticity problem for two domains separated by
a heterogeneous layer. The layer has an $\varepsilon-$periodic structure,
$\varepsilon\ll1$, including a multiple micro-contact between the structural
components. The components 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 modification of the Korn
inequality for the $\varepsilon-$dependent periodic layer is performed.
  An asymptotic analysis with respect to $\varepsilon \to 0$ is provided and
the limit problem is obtained, which consists of the elasticity problem
together with the transmission condition across the interface. The periodic
unfolding method is used to study the limit behavior.
