A homogenization result for weak membrane energies

Abstract

We prove a $\Gamma$-convergence result for space dependent weak membrane energies, that is for 'truncated quadratic potentials', that are quadratic below some threshold (depending on the pair of points that we are considering) and constant above. We prove that the limit surface energy density coincides with the one for spin systems, while the bulk energy density is not affected by the different levels of truncation and coincides with an purely elastic energy density.