A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies

SISSA, via Beirut 2-4, 34014 Trieste, Italy; fiaschi@sissa.it

Received: 7 November 2007

Abstract

Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes on a suitable probability space.