65J15 Equations with nonlinear operators (do not use 65Hxx)
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Keywords
- Gamma convergence (1)
- approximate incremental problems (1)
- approximation (1)
- damage (1)
- debonding (1)
- energetic solution (1)
- energetic solutions (1)
- magnetostriction (1)
- martensitic transformation (1)
- plasticity (1)
Project
- C18 (2)
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- C (2)
Energetic solutions to rate-independent processes are usually constructed via time-incremental minimization problems. In this work we show that all energetic solutions can be approximated by incremental problems if we allow approximate minimizers, where the error in minimization has to be of the order of the time step. Moreover, we study sequences of problems where the energy functionals have a Gamma limit.
A general abstract approximation scheme for rate-independent processes in the
energetic formulation is proposed and its convergence is proved under various
rather mild data qualifications. The abstract theory is illustrated on several
examples: plasticity with isotropic hardening, damage, debonding,
magnetostriction, and two models of martensitic transformation in
shape-memory alloys.