Calculus of Variations and Geometric Measure Theory

V. Crismale - G. Lazzaroni - R. Rossi

On the visco-plastic approximation of a rate-independent coupled elastoplastic damage model

created by rossi on 20 Nov 2023



Inserted: 20 nov 2023

Year: 2023

ArXiv: 2311.10186 PDF


In this paper we study a rate-independent system for the propagation of damage and plasticity. To construct solutions we resort to approximation in terms of viscous evolutions, where viscosity affects both damage and plasticity with the same rate. The main difficulty arises from the fact that the available estimates do not provide sufficient regularity on the limiting evolutions to guarantee that forces and velocities are in a duality pairing, hence we cannot use a chain rule for the driving energy. Nonetheless, via careful techniques we can characterize the limiting rate-independent evolution by means of an energy-dissipation balance, which encodes the onset of viscous effects in the behavior of the system at jumps.