Anisotropic and Dissipative Elasto-Plastic Materials with Damaged Structure

The proposed framework for anisotropic damage coupled to finite elasto-plasticity is based on the multiplicative decomposition of the deformation gradient into its elastic (reversible) and plastic components, which involves the existence of a tensorial damage variable, Fd, i.e. F = FeFdFp. Fd appears like a kinematic variable, whose rate in time produces the variation in internal power dissipated during the irreversible process. The material is characterized by an elastic type constitutive equations, which is dependent on Fd, with respect to the stress free and damaged configuration. Fp and Fd are described by the evolution equations written with respect to the stress free and undamaged configuration. The dissipative nature for the irreversible behavior is modeled by the requirement to be satisfied the principle of the free energy imbalance, on the isothermal processes. The constitutive and evolution equations are derived to be compatible with the free energy imbalance.