An anisotropic ductile damage model based on irreversible thermodynamics

The paper deals with fundamental constitutive issues in the elastic–plastic-damage rate theory and the numerical modelling of the large strain elastic–plastic deformation behavior of anisotropically damaged ductile metals. The proposed model is based on a generalized macroscopic theory within the framework 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 lead to the definition of damage strain tensors. The modular structure of the continuum theory is accomplished by the kinematic decomposition of strain rates into elastic, plastic and damage parts. To be able to address both the plastic flow and the anisotropic damage process, respective Helmholtz free energy functions of the fictitious undamaged configuration and of the current damaged configuration are introduced separately. A generalized yield condition based on invariants of the effective stress tensor is used to adequately describe the plastic flow properties of ductile metals and the plastic strain rate tensor is determined by a non-associated flow rule. Considering the damaged configurations a damage criterion is formulated using stress components referred to the elastically unloaded damage configuration. The damage strain rate tensor takes into account isotropic as well as anisotropic effects providing a realistic physical representation of ductile material degradation. Identification of material parameters is discussed in some detail. The applicability of the proposed continuum damage theory is demonstrated by numerical simulation of the inelastic deformation process of tension specimens.