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

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.