Networks and Heterogeneous Media (NHM)

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

Pages: 97 - 132, Volume 5, Issue 1, March 2010      doi:10.3934/nhm.2010.5.97

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Gianni Dal Maso - SISSA, via Bonomea 265, 34136 Trieste, Italy (email)
Francesco Solombrino - SISSA, Via Beirut 2-4, 34151 Trieste, Italy (email)

Abstract: 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:  Cam-Clay plasticity, softening behavior, nonassociative plasticity, pressure-sensitive yield criteria, quasistatic evolution, rate independent dissipative processes, vanishing viscosity limit, singular perturbations of ODEs.
Mathematics Subject Classification:  74C05, 74L10, 49L25, 34E10.

Received: July 2009;      Revised: December 2009;      Available Online: February 2010.