Coupling rate-independent and rate-dependent processes: Existence results
- Rossi, Riccarda
- Thomas, Marita
2010 Mathematics Subject Classification
- 35A15 35A23 35A35 35G61 49J53 35Q74 74H20 74C05 74C10
- Rate-independent processes, gradient systems, inertia, energetic solutions, existence results, time-discretization, generalized standard solids
We address the analysis of an abstract system coupling a rate-independet process with a second order (in time) nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in visco-elastic solids with inertia, and to a recently proposed model for damage with plasticity.
- SIAM J. Math. Anal., 49 (2017), pp. 1419--1494.