Calculus of Variations and Geometric Measure Theory

G. Dal Maso - A. DeSimone - F. Solombrino

Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling

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


Published Paper

Inserted: 17 jul 2009
Last Updated: 28 sep 2013

Journal: Calc Var PDEs
Volume: 40
Number: 1-2
Pages: 125-181
Year: 2011
Doi: 10.1007/s00526-010-0336-0


Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in \cite{DM-DS} and \cite{DM-Sol}, the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.