Coupling rate-independent and rate-dependent processes: Existence results

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Date
2015
Volume
2123
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We address the analysis of an abstract system coupling a rate-independent 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.

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Keywords
Rate-independent processes, gradient systems, inertia, energetic solutions, existence results, time-discretization, generalized standard solids
Citation
Rossi, R., & Thomas, M. (2015). Coupling rate-independent and rate-dependent processes: Existence results (Vol. 2123). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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