A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions

TL;DR

This paper develops a new plate theory model combining Kirchhoff's classical approach with Blake-Zisserman surface energies to analyze thin elastic films with soft inclusions and complex crack and fold structures.

Contribution

It introduces a novel Blake-Zisserman-Kirchhoff model for plates with soft inclusions, integrating surface energies at cracks, folds, and void boundaries.

Findings

Derivation of a new dimension reduction model for soft inclusion plates.

Inclusion of Blake-Zisserman surface energies in classical plate theory.

Application to thin films with complex crack and fold geometries.

Abstract

We consider a two phase elastic thin film with soft inclusions subject to bending dominated deformations. The soft (void) phase may comprise asymptotically small droplets within the elastic matrix. We perform a dimension reduction analysis and obtain a novel `Blake-Zisserman-Kirchhoff' model that combines Kirchhoff's classical plate theory with Blake-Zisserman type surface energy contributions at cracks, folds and the boundary of voids.