Calculus of Variations and Geometric Measure Theory

R. Rossi - M. Thomas

From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination

created by rossi on 31 May 2017


Submitted Paper

Inserted: 31 may 2017
Last Updated: 31 may 2017

Year: 2017


We revisit the weak, energetic-type existence results obtained in a previous paper of ours for a system for rate-independent, brittle delamination between two visco-elastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of visco-elastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the Mosco-convergence of the functionals involved in the energetic formulation of the system. We apply this approximation result in two different situations: Firstly, to pass from a nonlinearly elastic to a linearly elastic, brittle model on the time-continuous level, and secondly, to pass from a time-discrete to a time-continuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, super-quadratic regularization of the bulk energy. The latter approach is beneficial if the model also accounts for the evolution of temperature.