Calculus of Variations and Geometric Measure Theory

A. Fiaschi

A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy

created by fiaschi on 31 Dec 2007
modified on 25 May 2009


Accepted Paper

Inserted: 31 dec 2007
Last Updated: 25 may 2009

Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Year: 2007


We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally we compare this solution with the one obtained with global minimization.

Keywords: Young Measures, quasistatic evolution, incremental problems, elastic materials