# American Institute of Mathematical Sciences

August  2010, 27(3): 1189-1217. doi: 10.3934/dcds.2010.27.1189

## Quasistatic evolution for plasticity with softening: The spatially homogeneous case

 1 SISSA, Via Beirut 2-4 34014 Trieste, Italy

Received  January 2009 Revised  January 2010 Published  March 2010

The spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.
Citation: Francesco Solombrino. Quasistatic evolution for plasticity with softening: The spatially homogeneous case. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 1189-1217. doi: 10.3934/dcds.2010.27.1189
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