Numerical implementation of a new coupled cyclic plasticity and continum damage model

If effective stress is replaced by true stress for calculation of damage, the problems which arise due to strain softening are eliminated. This consideration leads to the coupling between damage and plasticity models. Despite beneficial features of this consideration, different orders of complexity will appear in the numerical solution of the resulting constitutive equations. In this work, the fundamental equations for coupling damage with nonlinear cyclic plasticity model based on small deformation assumption are derived and the continuum relations for plastic multiplier and tangent matrix are obtained. For implementing the proposed model in finite element code, an implicit method with explicit updating is used for solving the system of nonlinear equations instead of matrix inversion. Corrector relations for stress, back stress and plastic strain tensors as well as damage are introduced. Although, generality has been observed in the damage formulation, the proposed integration scheme is modified to accommodate the Bonora damage model which is implemented in the commercial finite element code MSC.MARC. The numerical implementation is validated by comparing the numerical results with analytical solutions for the damage evolution law under different stress triaxiality levels and damage exponents. Also, two different models are considered for FE simulations and a comparison is made between the uncoupled and the proposed models.