This investigation addresses an extended version of the Gurson-Tvergaad-Needleman isotropic hardening model (GTN) which is the first micromechanical model introducing a strong coupling between deformation and damage (par exemple, Benzerga, Leblond, 2010). To put it in a nutshell, the material is assumed to be composed of a dense elastic-plastic matrix sprinkle with evenly distributed spherical microvoids. When the stress triaxiality (the ratio of the first to second stress invariants) is high enough, the voids remain near spherical, and in such cases the ductile fracture process is rather well described by the GTN model. If void nucleation is disregarded, this model cannot describe ductile damage evolution for shear stress close to zero. Indeed, continued softening leading to ductile failure is known to occur at low triaxiality and even in circumstances of pure shear (Cowie et al., 1989, Barsoum, Faleskog, 2007).

An extension of the GTN's plastic potential was proposed by Mc Elwain et al., (Mc Elwain et al., 2006) who focused their study on the determination of yield surfaces for porous materials using a huge number of finite element simulations. Rather the considered RVE was a cube containing a spherical void. The obtained yield points was fitted by a new yield function which turned out to be similar to the Gurson one for porosity ranging between a very small value to the percolation threshold. The proposed yield function was found to explicitly depend upon the third stress invariant. In this investigation, in order to examine the effect of stress triaxiality and shearing upon material failure, a constitutive GTN-like model based on the proposed plastic potential is numerically implemented in a finite element program (Vumat in Abaqus/Explicit). The presence of the third stress invariant in the yield function typically results in a high degree of non-linearity. The constitutive equations and the coalescence criterion based on the effective porosity are integrated using an algorithm based on the return mapping method.

The proposed constitutive model is then used to analyze the behavior of a three-dimensional butterfly specimen subjected to a combination of shear and traction loading conditions. This specimen has been optimized by Dunand and Mohr, (Dunand and Mohr, 2011). Two loading paths have been considered: shear-dominated and tension-dominated deformation resulting in low and high stress triaxialities in the middle section of the specimen, respectively. The calculations have been carried out in Abaqus Explicit and similar values for the damage parameters have been used for both the proposed model and the GTN one in order to compare their ability to predict void growth to coalescence and the corresponding failure mechanism. The main observed results may be summarized as follows: a) at high stress triaxialities, the proposed constitutive model gives similar predictions as the GTN model. Indeed, up to the failure initiation of the specimen, the predictions incorporating the present model are in a close agreement with those provided by the GTN model, confirming the potential of the former constitutive model to fulfill to the requirement of transferability between different loading conditions; b) at and beyond failure points of specimen, noticeable disagreement has been observed between predictions of both models. In particular, for shear-dominated deformation, ductility (strain at failure) predicted by the proposed model is higher than the one associated to the GTN model.