In this joint work with Jean-Francois Babadjian and Gilles Francfort
we impart a variational structure upon the model of non-associative
plasticity, which is the reference model for soil and rock mechanics
and is usually considered not to be tractable from a variational
standpoint.
We prove the existence of a quasistatic evolution for such a model
under a natural capping assumption on the hydrostatic stresses and a
less natural mollification of the stress admissibility constraint. The
obtained elasto-plastic evolution is expressed for times that are
conveniently rescaled.