Eshelby stress tensor in large strain anisotropic damage mechanics

Abstract

The paper deals with a framework for anisotropically damaged elastic–plastic solids and the definition of the Eshelby stress tensor in anisotropic continuum damage mechanics. The proposed anisotropic elastic–plastic-damage model is based on a generalized macroscopic theory within the context of nonlinear continuum damage mechanics taking into account kinematic description of damage. It employs the consideration of damaged as well as fictitious undamaged configurations related via metric transformations which allow for the interpretation of damage tensors. A macroscopic yield condition is used to adequately describe the plastic flow properties of ductile metals and a damage criterion takes into account isotropic as well as anisotropic effects providing a realistic physical representation of material degradation. Furthermore, the unbalance of pseudo-momentum is established based on the second law of thermodynamics formulated with respect to the damaged configurations. Evaluation of a strain energy function and assuming the existence of pseudo-potentials of plastic as well as of damage dissipation leads to the definition of the Eshelby stress tensor, inhomogeneity force and material dissipation force.