Calculus of Variations and Geometric Measure Theory

F. Solombrino

Quasistatic evolution for plasticity with softening: the spatially homogeneous case

created by solombrin on 17 Jul 2009
modified on 28 Sep 2013


Published Paper

Inserted: 17 jul 2009
Last Updated: 28 sep 2013

Journal: Discrete Contin. Dyn. Syst. Ser. A.
Volume: 27
Number: 3
Pages: 1189-1217
Year: 2010
Doi: 10.3934/dcds.2010.27.1189


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.