Published Paper

Inserted: 20 nov 2023
Last Updated: 14 dec 2024

Journal: SIAM J. Math. Anal.
Volume: 56
Number: 6
Pages: 7940-7988
Year: 2024
Doi: 10.1137/23M1620429

Abstract:

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.