On the Constitutive Relations for Damaged Elastoplastic Materials Coupling Anisotropic Damage and Plasticity

The objective of this paper is to propose the constitutive relations for damaged elastoplastic materials, which are capable of coupling anisotropic damage, damage hardening, plastic anisotropy, and isotropic/kinematic hardening. Some fundamentals of continuum damage mechanics and thermodynamics are briefed, and the conventional damage tensors are modified to be of more concise forms and clearer physical meanings. The constitutive relations in the undamaged configuration, the damage evolution law, and the constitutive relations in the damaged configuration are subsequently derived. The applicability and power of the proposed constitutive relations are validated using examples such as predicting the stress-strain and damage factor-strain curves of damaged elastoplastic materials of various material properties. More sophisticated material properties can be incorporated.