Calculus of Variations and Geometric Measure Theory

F. Solombrino

Quasistatic evolution problems for nonhomogeneous elastic plastic materials

created by solombrin on 17 Jul 2009
modified on 28 Sep 2013


Published Paper

Inserted: 17 jul 2009
Last Updated: 28 sep 2013

Journal: Journal of convex analysis
Volume: 16
Number: 1
Pages: 89-119
Year: 2009
Doi: jca16005


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 ofconvex 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.