Calculus of Variations and Geometric Measure Theory
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G. Dal Maso - A. DeSimone - M. G. Mora

Quasistatic evolution problems for linearly elastic - perfectly plastic materials

created by dalmaso on 10 Dec 2004
modified by mora on 13 Dec 2006

[BibTeX]

Published Paper

Inserted: 10 dec 2004
Last Updated: 13 dec 2006

Journal: Arch. Ration. Mech. Anal.
Volume: 180
Pages: 237-291
Year: 2006

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 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.


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