An Elementary Extension of Korn's First Inequality to H(Curl) motivated by Gradient Plasticity with Plastic Spin

TL;DR

This paper extends Korn's first inequality to tensor fields without gradient structure, providing a fundamental mathematical tool relevant for gradient plasticity theories involving plastic spin.

Contribution

It introduces a novel Korn-type inequality applicable to tensor fields lacking gradient structure, broadening the mathematical framework for gradient plasticity models.

Findings

Established a Korn-type inequality for tensor fields without gradient structure

Generalized Korn's first inequality to a broader class of tensor fields

Provides a mathematical foundation for gradient plasticity with plastic spin

Abstract

We prove a Korn-type inequality for tensor fields without gradient structure, which generalizes Korn's first inequality.