A detailed description of the Gurson-Tvergaard-Needleman model within a mixed velocity-pressure finite element formulation

In an effort to implement Gurson-type models into a mixed velocity-pressure finite element formulation with the MINI-element P1(+)/P1, the algorithm proposed by Aravas (IJNME, 1987) to integrate the pressure dependent plasticity as well as the formulations of consistent tangent moduli have been analyzed. This work firstly reviews and clarifies the mathematical basis of the formulations used by Aravas (IJNME, 1987) and demonstrates the equality of the tangent moduli formulations proposed by Govindarajan and Aravas (CNME, 1995) and Zhang (CMAME, 1995), which are widely used in the literature. A unified formulation to calculate the tangent moduli is proven, and its accuracy is also investigated by the finite difference method. The implementation of the Gurson-Tvergaard-Needleman model is then detailed for the mixed velocity-pressure finite element formulation, which employs the MINI-element P1(+)/P1. Due to the particularity of this element, one needs to calculate two tangent moduli instead of one. The formulas for calculating the linear tangent modulus' and the bubble tangent modulus' are then detailed. Finally, comparison tests are carried out with ABAQUS (Dassault System, Simulia Corp., Providence, RI, USA) in order to validate the present implementation for both homogeneous and heterogeneous deformations. Copyright (c) 2013 John Wiley & Sons, Ltd.