HOMOGENIZATION IN GRADIENT PLASTICITY
Hauke Hanke · Mathematical Models and Methods in Applied Sciences · 2011
This paper yields a two-scale homogenization result for a rate-independent elasto-plastic system. The presented model is a generalization of the classical model of linearized elasto-plasticity 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 ε > 0. The additional gradient term of the plastic variables z is contained in the elastic energy with a prefactor εγ(γ ≥ 0). We derive different limiting models for ε → 0 in dependence of γ. For γ > 1, the limiting model is the two-scale model derived in Ref. 17, where no gradient term was present. For γ = 1, the gradient term of the plastic variable survives on the microscopic cell problem, while for γ ∈ [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 elasto-plasticity model by homogenization of the elastic part.