Homogenization of an elastic material with inclusions in frictionless contact

The homogenization method is applied to the problem of elastic deformations of an array of holes, or pores, filled with softer inclusions and imbedded in a stiffer matrix. The contact of the inclusions with the matrix is assumed to be frictionless and is modeled by Signoriniʹs condition. A priori estimates are established for solutions to the problem with χ that permit passing to the homogenization limit ϵ → 0. The limit problem is identified, and the two-scale convergence of the solutions to the unique limit solution is proven.