Calculus of Variations and Geometric Measure Theory

L. Ambrosio - A. Lemenant - G. Royer Carfagni

A variational model for plastic slip and its regularization via Gamma-convergence.

created by lemenant on 06 Jul 2010
modified on 10 Feb 2015


Published Paper

Inserted: 6 jul 2010
Last Updated: 10 feb 2015

Journal: Journal of Elasticity
Year: 2010


A variational model is presented able to interpret the onset of plastic deformations, here modeled as displacement jumps occurring along slip surfaces of the crystalline lattices at constant yielding stress. The corresponding strain energy functional, leading to a free-discontinuity problem set in the space of SBV functions, is then approximated by a sequence of regularized elliptic functionals following the seminal work in Ambrosio-Tortorelli (1990) within the framework of Gamma-convergence. Comparisons between the results obtainable with the free-discontinuity model and its regularized approximation, in terms of stability of the pure elastic phase, irreversibility of plastic slip and response under unloading, are presented, in general, for the 2-D case of antiplane shear and exemplified, in particular, for the 1-D case.