Two phase models for elastic membranes with soft inclusions

Abstract

We derive an effective membrane theory in the thin film limit within a two phase material model for a specimen consisting of an elastic matrix and soft inclusions. The soft inclusions may lead to the formation of cracks within the elastic matrix and the corresponding limiting models are described by Griffith type fracture energy functionals. We also provide simplified proofs of relaxation results for bulk materials.

arXiv comment23 pages. In v2 we correct a mistake in the computation of the $\Gamma$-limit in the membrane limit. We also make some changes here and there to improve the presentation