Calculus of Variations and Geometric Measure Theory

F. Solombrino

Quasistatic evolution in perfect plasticity for general heterogeneous materials.

created by solombrin on 14 Mar 2012
modified on 17 May 2015


Published Paper

Inserted: 14 mar 2012
Last Updated: 17 may 2015

Journal: Arch. Rat. Mech. Anal.
Volume: 212
Number: 1
Pages: 283-330
Year: 2014
Doi: 10.1007/s00205-013-0703-z


Inspired by some recents developments in the theory of small-strain heterogeneous elastoplasticity, we both revisit and generalize the formulation of the quasistatic evolutionary problem in perfect plasticity given by Francfort and Giacomini in \cite{FG}. We show that their definition of the plastic dissipation measure is equivalent to an abstract one, where it is defined as the supremum of the dualities between the deviatoric parts of admissible stress fields and the plastic strains. By means of this abstract definition, a viscoplastic approximation and variational techniques from the theory of rate-independent processes give the existence of an evolution statisfying an energy-dissipation balance and consequently Hill's maximum plastic work principle for an abstract and very large class of yield conditions.