On microcontinuum field theories: the Eshelby stress tensor and incompatibility conditions

Abstract

We investigate linear theories of incompatible micromorphic elasticity, incompatible microstretch elasticity, incompatible micropolar elasticity and the incompatible dilatation theory of elasticity (elasticity with voids). The incompatibility conditions and Bianchi identities are derived and discussed. The Eshelby stress tensor (static energy momentum) is calculated for such inhomogeneous media with microstructure. Its divergence gives the driving forces for dislocations, disclinations, point defects and inhomogeneities which are called configurational forces.

References in corpus (1)

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

Cited by in corpus (2)

• Micromechanics of dislocations in solids: $J$-, $M$-, and $L$-integrals and their fundamental relations
• A geometric formulation of Schaefer's theory of Cosserat solids