Calculus of Variations and Geometric Measure Theory

A. Fiaschi

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

created by fiaschi on 13 Nov 2007
modified on 25 May 2009


Published Paper

Inserted: 13 nov 2007
Last Updated: 25 may 2009

Volume: 15
Pages: 245-278
Year: 2009


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.

Keywords: Young Measures, quasistatic evolution, rate-independent processes, elastic materials