Cosserat micropolar elasticity: classical Eringen vs. dislocation form

TL;DR

This paper compares two formulations of the linear isotropic Cosserat elastic model, highlighting differences between the classical microrotation vector approach and a new dislocation-based skew-symmetric matrix formulation.

Contribution

It introduces an alternative energy representation for the Cosserat model, facilitating comparison with other generalized continuum theories.

Findings

Provides a detailed comparison of classical and dislocation form formulations.

Offers an alternative energy expression to connect with relaxed micromorphic models.

Enhances understanding of Cosserat elasticity frameworks.

Abstract

In this paper we do a comparative presentation of the linear isotropic Cosserat elastic model from two perspectives: the classical Mindlin-Eringen-Nowacki description in terms of a microrotation vector and a new formulation in terms of a skew-symmetric matrix and a curvature energy in dislocation form. We provide the reader with an alternative representation of the energy for the isotropic Cosserat model to ease the comparison with the relaxed micromorphic model and the geometrically nonlinear Cosserat elastic model.