Purpose: The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.Design/methodology/approach: One of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.Findings: Through the analysis of the evolution of internal variables, such as damage and effective plastic strain, obtained by performing a set of numerical tests using a Butterfly specimen, it is possible to conclude that the extended GTN models are in close agreement with experimental evidence.Research limitations/implications: Even though the results obtained with the modified GTN models have shown improvements, it can also be observed that both shear mechanisms have inherent limitations in the prediction of the location of fracture onset for some specific stress states.Originality/value: From the results reported, it is possible to identify some shortcomings in the recently proposed extensions of the GTN model and point out the direction of further improvements.