ESAIM: Control, Optimisation and Calculus of Variations

Research Article

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

Fiaschi, Alice

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

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.

(Received November 7 2007)

(Online publication April 26 2008)

Key Words:

  • Quasistatic evolution;
  • rate-independent processes;
  • elastic materials;
  • incremental problems;
  • Young measures

Mathematics Subject Classification:

  • 74B20;
  • 28A33;
  • 74G65;
  • 49J45
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