Two phase models for elastic membranes with soft inclusions

TL;DR

This paper develops a two-phase membrane model for elastic materials with soft inclusions, capturing crack formation and fracture energies, and provides simplified proofs for relaxation in bulk materials.

Contribution

It introduces a new effective membrane theory for thin films with soft inclusions and describes crack formation using Griffith type fracture energies.

Findings

Derives an effective membrane model for two-phase materials.

Models crack formation within elastic matrices due to soft inclusions.

Provides simplified proofs for relaxation results in bulk materials.

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.