Homogenization and corrector results of elliptic problems with Signorini boundary conditions in perforated domains

This paper is devoted to the asymptotic behavior and some corrector-type results of an elastic deformation problem with highly oscillating coefficients posed in a domain periodically perforated with holes of four different sizes. On the boundary of the holes, a class of Signorini boundary condition is imposed; while a Dirichlet boundary condition is prescribed on the exterior boundary. For the critical-sized holes, the homogenization process via periodic unfolding method reveals two new terms at the limit, a reference cell average term and a strange term depending on the capacity of the holes and the negative part of the limit function. Meanwhile, the remaining cases provide either a Dirichlet limit problem or some nonnegative spreading effect at the limit.