An elastoplastic damage-induced anisotropic constitutive model at finite strains

In this paper, a hyperelastic plastic damage-induced anisotropic constitutive model is proposed based on the logarithmic strain in finite deformations. The evolution equations are written in terms of the material time derivative of the stress tensor conjugate to the logarithmic strain. The dissipation inequality is considered in the intermediate configuration with some appropriate internal variables. The Helmholtz free energy is considered as combination of three parts including elastic, plastic and damage. The exponential isotropic plasticity hardening and linear isotropic damage hardening are considered. For taking into account the unilateral effect in the damage growing, a modified stress tensor is considered. A return mapping two-step operator split algorithm, elastic predictor and plastic-damage corrector, is adopted for the integration of the evolution equations. To present some numerical results, the proposed constitutive model has been implemented into a finite element implicit code. For validating the model and also showing its capabilities, several benchmark examples are solved. In these examples, the deterioration in the material properties due to the propagation of the damage is well simulated.