Calculus of Variations and Geometric Measure Theory

G. Dal Maso - F. Solombrino

Quasistatic evolution for Cam-Clay plasticity: 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: Netw. Heterog. Media
Volume: 5
Pages: 97-132
Year: 2010
Doi: 10.3934/nhm.2010.5.97


We study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of 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 strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where viscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.