A multiscale approach to the Neumann Sieve problem in dimensional reduction

This is a joint work with N. Ansini and C. I. Zeppieri. This talk is concerned with the characterization of the effective energy of weakly connected thin structures through a periodically distributed contact zone. We highlight the presence of three different regimes (depending on the mutual rate of convergence of the radii of the connecting zones and the thickness of the domain) and for each of them we derive the limit energy by a Gamma-convergence procedure. For each regime an interfacial energy term, depending on the jump of the deformation at the interface, appears in the limit representing the asymptotic memory of the sieve. We completely describe the interfacial energy densities by nonlinear capacitary type formulas.