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Journal of Convex Analysis 16 (2009), No. 1, 089--119
Copyright Heldermann Verlag 2009

Quasistatic Evolution Problems for Nonhomogeneous Elastoplastic Materials

Francesco Solombrino
SISSA, Via Beirut 2-4, 34014 Trieste, Italy

The paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

Keywords: Quasistatic evolution, measurable compact convex multifunctions, rate-independent processes, perfect plasticity, Prandtl-Reuss plasticity, shear bands, one-dimensional problems, variational problems in BD.

MSC: 74C05; 74G65, 49J45, 47J20, 35Q72

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