On some topics for the numerical simulation of ductile fracture

In this work, we analyze some aspects of the macroscopic Gurson–Tvergaard–Needleman (GTN) constitutive model when it is addressed to solve ductile fracture problems by means of numerical simulations: (i) The analytical solutions of the material discontinuous bifurcation problem is performed. Closed and exact formulas are obtained. The so determined critical conditions and the developed strain localization mode are afterward studied and compared in crack growth problems. Even when this methodology of analysis is rather standard at the present, the conclusions drawn from this study differ significantly from that obtained with a similar analysis in quasi-brittle fracture problems. (ii) A new very robust numerical integration method for the GTN model, namely the Impl–Ex Method, is proposed. It is a low computational cost algorithm, equivalent to a linear problem per each integration step, with a reasonable precision for engineering purposes. Its accuracy and convergence rate is assessed by means of an error study applied to a ductile fracture test simulation. (iii) A detailed analysis of a plane strain ductile crack growth problem is performed in a material containing two size-scale of voids. In the analysis, particular attention is given to the mesh size dependence and to the coalescence of the larger void.