On the dislocation density tensor in the Cosserat theory of elastic shells

TL;DR

This paper explores the dislocation density tensor within the Cosserat theory of elastic shells, establishing a direct link to bending-curvature measures in 6-parameter shell models, offering a new perspective on curvature strain measures.

Contribution

It introduces a novel dislocation density tensor for Cosserat shells and demonstrates its equivalence to the bending-curvature tensor, enhancing the understanding of curvature measures in shell models.

Findings

Established a one-to-one correspondence between the dislocation density tensor and bending-curvature tensor.

Proposed the dislocation density tensor as an alternative curvature measure in Cosserat models.

Linked three-dimensional Cosserat continuum concepts to shell theory through tensor relationships.

Abstract

We consider the Cosserat continuum in its finite strain setting and discuss the dislocation density tensor as a possible alternative curvature strain measure in three-dimensional Cosserat models and in Cosserat shell models. We establish a close relationship (one-to-one correspondence) between the new shell dislocation density tensor and the bending-curvature tensor of 6-parameter shells.