Equilibrium configurations for nonhomogeneous linearly elastic materials with surface discontinuities

TL;DR

This paper establishes a compactness and semicontinuity framework for minimisation problems in nonhomogeneous linear elasticity with surface discontinuities, extending previous results to more general materials and boundary conditions.

Contribution

It generalizes a prior compactness theorem to include nonhomogeneous materials and surface discontinuities in linear elasticity problems.

Findings

Proves a new compactness theorem for nonhomogeneous elastic materials.

Extends existence results for minimisers in elasticity with surface discontinuities.

Provides mathematical tools for analyzing complex elastic structures.

Abstract

We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to show existence of minimisers for the Dirichlet problem for the (homogeneous) Griffith energy.