A new stress state-dependent plasticity model for metals

Classical metal plasticity theory neglects the influence of hydrostatic pressure (stress triaxiality) and the third deviatoric stress invariant (Lode angle parameter) on the constitutive response of materials. However, recent studies have demonstrated that the effects of both the stress triaxiality and the Lode angle parameter are non-negligible and should be explicitly incorporated into the constitutive relationship. In this study, linear and cosine functional forms are proposed to represent the effects of the stress triaxiality and the Lode angle parameter, respectively, on the material strain hardening. Simplified numerical implementation and calibration procedures for the associated free model parameters are also developed, avoiding the need to derive and implement complex flow rules and return-mapping formulations specifically associated with stress state-dependent yield criteria. The proposed stress state-dependent functional form (varying linearly with stress triaxiality and cosinusoidally with Lode angle parameter) and the associated simplified numerical implementation and calibration procedures are validated using experimental data from the literature for mild steel, high strength steel, stainless steel across a wide range of stress triaxiality and Lode angle conditions. Finite element simulations demonstrate that the proposed approach improves the prediction of load-displacement responses, achieving an average error of 1.29%, compared with 2.61% for the Bai and Wierzbicki model and 5.66% for the model without stress state correction.