An improved damage evolution law based on continuum damage mechanics and its dependence on both stress triaxiality and the third invariant

•New damage evolution law, regarding CDM.•Two stress states for defining materials parameters.•Introduction of both effects: stress triaxiality and third invariant.

In this contribution, it is suggested a damage evolution law which is based on Continuum Damage Mechanics (CDM) and dependent on the hydrostatic pressure, by the stress triaxiality, and the third invariant of deviatoric stress tensor, by the so-called normalized third invariant. The contribution has been motivated meanly by the reason that the accuracy in describe the mechanical behavior of materials and the predictive fracture onset ability of damage constitutive models are strongly dependent on the loading condition used to procedure the calibration of material parameters. Regarding classical damage models as Lemaitre and Gurson, the level of material degradation can be optimist or conservative for loading conditions far from the calibration point. In the first part of this paper, the suggested damage evolution law is presented and the new state and dissipation potential are determined. The plastic flow rules for associative and non-associative plasticity are derived and an implicit numerical integration algorithm is suggested, based on the operator split methodology. The numerical algorithm is also implemented in an “in house” finite element framework and its robustness is tested for a set of numerical simulations upon wide range of stress triaxiality. Numerical results are compared with experimental data presented in literature and parameters as reaction curve, evolution of the equivalent plastic strain and damage variable at fracture are analyzed. In a critical situation, the numerical results have shown that the original damage models as Lemaitre’s model has a prediction of 68% in disagreement with experimental data and the proposed damage evolution law has around 1%, regarding the determinations of the displacement at fracture initiation.