We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the varia- tional framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corre- sponding incremental problems is not justified from the mechanical point of view. Thus, we analyse a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.

A vanishing viscosity approach to quasistatic evolution in plasticity with softening

De Simone, Antonio;
2008

Abstract

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the varia- tional framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corre- sponding incremental problems is not justified from the mechanical point of view. Thus, we analyse a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.
2008
Settore MAT/05 - Analisi Matematica
Variational formulation; existence; systems; microstructures; equations; models
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/84197
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