Abstract
A rate-independent evolution problem is considered for which the stored energy density depends on the gradient of the displacement. The stored energy density does not have to be quasiconvex and is assumed to exhibit linear growth at infinity; no further assumptions are made on the behaviour at infinity. We analyse an evolutionary process with positively $1$-homogeneous dissipation and time-dependent Dirichlet boundary conditions.
Highlights
In this contribution, we analyse a rate-independent mesoscopic process governed by time-dependent Dirichlet boundary conditions
A characteristic feature of the problem is that the stored energy has linear growth at infinity
Crystalline materials can often be characterised via energy minimisation; for plastically deformed crystals, Ortiz and Repetto [13] provide a setting in which dislocation structures can be described by a nonconvex minimisation problem
Summary
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