Numerical implementation of a non-local GTN model for explicit FE simulation of ductile damage and fracture

Abstract

In this study, we follow the work of Tvergaard and Needleman (1995, 1997) and Needleman and Tvergaard (1998) and present the numerical implementation and initial applications of a non-local Gurson-Tvergaard-Needleman (GTN) model for explicit finite element (FE) analysis. The delocalization relates to the damage mechanism and is incorporated in terms of an integral condition on the rate of change of the porosity. To demonstrate the mesh independence during all stages of ductile damage and fracture, several material test specimens were simulated using different mesh sizes until full fracture occurred. For comparison purposes, the results are also obtained for the corresponding local GTN model in all cases. The effect of the material characteristic length on the ductile damage and fracture behavior and on the mesh sensitivity of the results is discussed. The numerical study shows that simulation results obtained in all stages of the ductile fracture process, including void growth, fracture initiation by coalescence and crack propagation all the way to a fully fractured specimen, are mesh independent for a certain mesh size ratio related to the material characteristic length, provided the non-local integral is evaluated on the current configuration. This ratio is unique for each individually simulated specimen as it depends on the spatial gradients of the porosity and the material parameters adopted for the problem at hand. It is shown that excessive averaging occurs at large deformations if the non-local integral is evaluated on the reference configuration, i.e., without updating the element interaction matrix resulting from the discretization of the non-local integral.