Calculus of Variations and Geometric Measure Theory

L. Kreutz - M. Friedrich - K. Zemas

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

created by kreutz on 12 May 2022
modified by zemas on 16 Apr 2023


Published Paper

Inserted: 12 may 2022
Last Updated: 16 apr 2023

Journal: Nonlinearity
Volume: 36
Number: 1
Pages: 50
Year: 2022
Doi: 10.1088/1361-6544/aca5de

ArXiv: 2202.05018 PDF


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 and \Gamma-convergence tools, we rigorously derive effective linearized continuum models for elastically stressed solids with material voids in three-dimensional elasticity.