Abstract: We consider a homogenization problem for the linear elasticity system posed in a domain of the upper half-space, a part of its boundary being in contact with the plane. We assume that the surface is traction-free out of small regions, where we impose Winkler-Robin boundary conditions. The regions are at a distance between them. This condition links stresses and displacements by means of a symmetric and positive definite matrix-function and a reaction parameter that can be very large when. We address the convergence, as, of the solutions in the extreme cases where the averaged boundary condition on the plane is a Dirichlet or a Neumann one. A certain non-periodical distribution of the reaction regions is allowed. We also address the convergence of the associated spectral problems.

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