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 (Friedrich et al 2021 arXiv:2107.10808) and Γ-convergence tools, we rigorously derive effective linearized continuum models for elastically stressed solids with material voids in three-dimensional elasticity.