Homogenization in gradient plasticity

Abstract

This paper yields a two-scale homogenization result for a rate-independent elastoplastic system. The presented model is a generalization of the classical model of linearized elastoplacticity with hardening, which is extended by a gradient term of the plastic variables. The associated stored elastic energy density has periodically oscillating coefficients, where the period is scaled by e > 0 . The additional gradient term of the plastic variables z is contained in the elastic energy with a prefactor e? (? = 0) . We derive different limiting models for e ? 0 in dependence of &gamma ;. For ? > 1 the limiting model is the two-scale model derived in [MielkeTimofte07], where no gradient term was present. For ? = 1 the gradient term of the plastic variable survives on the microscopic cell poblem, while for ? ? [0,1) the limit model is defined in terms of a plastic variable without microscopic fluctuation. The latter model can be simplified to a purely macroscopic elastoplasticity model by homogenisation of the elastic part