Averaged reaction for nonlinear boundary conditions on a grill-type Winkler foundation

We consider a homogenization problem for the elasticity operator posed in a bounded domain of the half-space, a part of its boundary being in contact with the plane. This surface is traction-free out of “small regions”, where we impose nonlinear Winkler-Robin boundary conditions containing “large reaction parameters”. Non-periodical distribution of these regions is allowed provided that they have the same area. We show the convergence of solutions towards those of the homogenized problems depending on the relations between the parameters distance, sizes, and reaction.