Calculus of Variations and Geometric Measure Theory

A. Braides - B. Cassano - A. Garroni - D. Sarrocco

Quasi-static damage evolution and homogenization: a case study of non-commutability

created by braidesa on 19 Sep 2013
modified on 02 Mar 2016


Published Paper

Inserted: 19 sep 2013
Last Updated: 2 mar 2016

Journal: Annales de l'Institut Henri Poincaré
Volume: 303
Pages: 309-328
Year: 2016
Doi: 10.1016/j.anihpc.2014.10.003


We illustrate a simple case of interaction between the processes of quasi-static evolution and homogenization. We consider a mixture of two one-dimensional elastic composites subject to damage (following the model of Francfort and Marigo). In this case we have a relaxation phenomenon: the limit of the variational evolutions with fixed space scale tends to a relaxed evolution which is not the evolution of the homogenized energies. We explicitly characterize the relaxed evolution as the one corresponding to a double-damage material (i.e., a homogeneous material with two possibility of damaged states and related dissipations).

Keywords: relaxation, Homogenization, composites, quasi-static evolution, damage, energetic solutions