Homogenization for dislocation based gradient visco-plasticit

TL;DR

This paper develops a homogenization framework for a complex gradient viscoplasticity model involving dislocation mechanics, linear kinematic hardening, and non-associative plastic flows, providing a rigorous mathematical foundation.

Contribution

It introduces a homogenization approach for dislocation-based gradient viscoplasticity models with general monotone plastic flows, extending previous theories to more complex constitutive relations.

Findings

Derived uniform estimates for solutions of the quasistatic problems.

Established the homogenized system of equations using unfolding and monotone operator techniques.

Extended Korn's inequality to incompatible tensor fields in this context.

Abstract

In this work we study the homogenization for infinitesimal dislocation based gradient viscoplasticity with linear kinematic hardening and general non-associative monotone plastic flows. The constitutive equations in the models we study are assumed to be only of monotone type. Based on the generalized version of Korn's inequality for incompatible tensor fields (the non-symmetric plastic distortion) due to Neff/Pauly/Witsch, we derive uniform estimates for the solutions of quasistatic initial-boundary value problems under consideration and then using an unfolding operator technique and a monotone operator method we obtain the homogenized system of equations.