Dual Eshelby stress tensors and related integrals in micropolar elasticity with body forces and couples

The Eshelby stress tensor of micropolar elasticity with body forces and body couples, and the corresponding Jk, Lk and M integrals are derived. These are used to determine the energy release rates and configurational forces associated with particular modes of defect motion. The dual Eshelby stress tensor and dual Ĵk , L̂k and M̂ integrals are then introduced. The duality properties Jk þ Ĵk 1⁄4 0, Lk þ L̂k 1⁄4 0 and M þ M̂ 1⁄4 0 are established and used to construct alternative expressions for the configurational forces on moving defects. The three-dimensional results are specialized to the plain strain case and compared with earlier results obtained in the absence of body forces and body couples, which are of interest for two-dimensional dislocation and fracture mechanics problems. 2012 Elsevier Masson SAS. All rights reserved.