ESHELBY STRESS IN ELASTOPLASTICITY AND DUCTILE FRACTURE

The local balance of pseudomomentum (canonical momentum in analytical continuum mechanics) is a fully material balance law in which the flux is the Eshelby energy-momentum tensor referred to the reference configuration, and the source term is the material force of inhomogeneity. Basing on first principles of thermomechanics, we deduce the expressions of these in the elastoplasticity with hardening of so-called generalized standard materials in finite strains. The elastoplastic Eshelby stress involves an effective ''Lagrangian'' density in which the time integral of dissipation is present. It is shown in finite strains that the Eshelby stress referred to the intermediate configuration allows one to formulate plastic-like evolution equations in which the question of the plastic spin is irrelevant. Furthermore, in the presence of a crack in an otherwise homogeneous body and for small strains, there follows a proof of the expression of the (not path-independent) J-integral in dynamic ductile fracture.