An Alternative Finite Element Formulation to Predict Ductile Fracture in Highly Deformable Materials

Abstract

An alternative finite element formulation to predict ductile damage and fracture in highly deformable materials is presented. For this purpose, a finite-strain elastoplastic model based on the Gurson–Tvergaard–Needleman (GTN) formulation is employed, in which the level of damage is described by the void volume fraction (or porosity). The model accounts for large strains, associative plasticity, and isotropic hardening, as well as void nucleation, coalescence, and material failure. To avoid severe damage localization, a nonlocal enrichment is adopted, resulting in a mixed finite element whose degrees-of-freedom are the current positions and nonlocal porosity at the nodes. In this work, 2D triangular elements of linear-order and plane-stress conditions are used. Two systems of equations have to be solved: the global variables system, involving the degrees-of-freedom; and the internal variables system, including the damage and plastic variables. To this end, a new numerical strategy has been developed, in which the change in material stiffness due to the evolution of internal variables is embedded in the consistent tangent operator regarding the global system. The performance of the proposed formulation is assessed by three numerical examples involving large elastoplastic strains and ductile fracture. Results confirm that the present formulation is capable of reproducing fracture initiation and evolution, as well as necking instability. Convergence analysis is also performed to evaluate the effect of mesh refinement on the mechanical response. In addition, it is demonstrated that the nonlocal parameter alleviates damage localization, providing smoother porosity fields.