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March  2010, 5(1): 97-132. doi: 10.3934/nhm.2010.5.97

Quasistatic evolution for Cam-Clay plasticity: The spatially homogeneous case

Gianni Dal Maso 1, and  Francesco Solombrino 2,

1. 

SISSA, via Bonomea 265, 34136 Trieste, Italy
2. 

SISSA, Via Beirut 2-4, 34151 Trieste, Italy

Received  July 2009 Revised  December 2009 Published  February 2010

We study the spatially uniform case of the quasistatic evolution in Cam-Clay plasticity, a relevant example of small strain nonassociative elastoplasticity. Introducing a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity; the slow dynamics, when the stress evolves smoothly on the yield surface and plastic flow is produced; the fast dynamics, which may happen only in the softening regime, when viscous solutions exhibit a jump determined by the heteroclinic orbit of an auxiliary system. We give an iterative procedure to construct a viscous solution.
Keywords: vanishing viscosity limit, rate independent dissipative processes, quasistatic evolution, singular perturbations of ODEs., Cam-Clay plasticity, nonassociative plasticity, softening behavior, pressure-sensitive yield criteria.
Mathematics Subject Classification: 74C05, 74L10, 49L25, 34E1.
Citation: Gianni Dal Maso, Francesco Solombrino. Quasistatic evolution for Cam-Clay plasticity: The spatially homogeneous case. Networks and Heterogeneous Media, 2010, 5 (1) : 97-132. doi: 10.3934/nhm.2010.5.97
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