The Eshelby stress tensor, angular momentum tensor and scaling flux in micropolar elasticity

TL;DR

This paper derives fundamental tensors and fluxes in micropolar elasticity using Noether's theorem, revealing broken symmetries and non-conserved integrals, with explicit formulas for configurational forces and moments.

Contribution

It introduces explicit formulas for the Eshelby stress tensor, angular momentum tensor, and scaling flux in micropolar elasticity, accounting for inhomogeneities and defects.

Findings

Derived non-conserved J-, L-, and M-integrals for micropolar elasticity.

Identified balance laws including effects of inhomogeneities and defects.

Provided explicit formulas for configurational forces and moments.

Abstract

The (static) energy momentum tensor, angular momentum tensor and scaling flux vector of micropolar elasticity are derived within the framework of Noether's theorem on variational principles. Certain balance (or broken conservation) laws of broken translational, rotational and dilatational symmetries are found including inhomogeneities, elastic anisotropy, body forces, body couples and dislocations and disclinations present. The non-conserved J-, L- and M-integrals of micropolar elasticity are derived and discussed. We give explicit formulae for the configurational forces, moments and work terms.