Numerical integration algorithm of a new model for metal plasticity and fracture including pressure and lode angle dependence

This paper describes an efficient numerical integration algorithm of a new model for metal plasticity and fracture [2]. The constitutive equations of the material model critically include both the effect of pressure through the triaxiality ratio and the effect of third deviatoric stress invariant through the lode angle in the description of material. The necessary steps required to implement the model within an implicit quasi-static finite element environment are discussed. In particular, the stress update procedure, which is based on the so-called operator split concept resulting in the standard elastic predictor/return mapping algorithm, and the computation of tangent matrix consistent with the stress update are described. Finally, the convergence for large increments is illustrated and iso-error maps are used to analyse the accuracy and stability of the integration algorithm. The simulation of a cylindrical notched bar specimen subjected to tension [1] is presented to illustrate the robustness of the proposed algorithm.