From atomistic systems to linearized continuum models for elastic materials with voids

Abstract

We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means of a recent geometric rigidity result in variable domains [27] and Γ-convergence tools, we rigorously derive effective linearized continuum models for elastically stressed solids with material voids in three-dimensional elasticity.

References in corpus (2)

• Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity
• Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces

Cited by in corpus (1)

• Geometric rigidity on Sobolev spaces with variable exponent and applications