Archive for Rational Mechanics and Analysis

, Volume 180, Issue 2, pp 237–291

Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials

  • Gianni Dal Maso
  • Antonio DeSimone
  • Maria Giovanna Mora
Article

DOI: 10.1007/s00205-005-0407-0

Cite this article as:
Maso, G., DeSimone, A. & Mora, . Arch. Rational Mech. Anal. (2006) 180: 237. doi:10.1007/s00205-005-0407-0

Abstract

The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This approach provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gianni Dal Maso
    • 1
  • Antonio DeSimone
    • 1
  • Maria Giovanna Mora
    • 1
  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly