MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract

Rossi, Riccarda

Beyond rate-independence: the coupling with viscosity and inertia

We consider a class of abstract systems in the unknowns $(u,z)$, where rate-independent evolution for $z$ is coupled with a rate-dependent, generalized gradient system in the variable $u$. Significant examples arise, for instance, in damage and delamination, where $z$ is the internal variable and $u$ the displacement, fulfilling the momentum equation with viscosity and, possibly, inertia. We propose a suitable notion of weak solution for these rate-independent/rate-dependent systems, reflecting their mixed character, and establish existence and approximation results.. We also address the stability of weak solutions with respect to variational convergence of the involved dissipation and energy functionals. Joint work with Marita Thomas (WIAS).