Well-posedness for the microcurl model in both single and polycrystal gradient plasticity

TL;DR

This paper establishes the well-posedness of the microcurl gradient plasticity model for single and polycrystals, incorporating micromorphic fields and local hardening, using functional analysis.

Contribution

It introduces a rigorous mathematical formulation and proof of well-posedness for the microcurl model in both crystal types, extending previous models with micromorphic fields.

Findings

Model is well-posed with local hardening.

Comparison with relaxed micromorphic and dislocation models.

Framework applicable to rate-independent gradient plasticity.

Abstract

We consider the recently introduced microcurl model which is a variant of strain gradient plasticity in which the curl of the plastic distortion is coupled to an additional micromorphic-type field. For both single crystal and polycrystal cases, we formulate the model and show its well-posedness in the rate-independent case provided some local hardening (isotropic or linear kinematic) is taken into account. To this end, we use the functional analytical framework developed by Han-Reddy. We also compare the model to the relaxed micromorphic model as well as to a dislocation-based gradient plasticity model.