X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model

Abstract

In this paper, the dynamic large deformation X-FEM method is presented for modeling the full process of dynamic ductile fracture based on a nonlocal damage visco-plasticity model. The effect of inertia is modeled using an explicit central difference scheme which is enhanced through the use of mass lumping, reduced integration with hourglass control, and numerical damping. The material nonlinearity and the flow stress dependency on strain rate, hardening and temperature are modeled with the Johnson–Cook visco-plastic model. The micro-void nucleation, growth and coalescence are modeled macroscopically with an isotropic damage model. The localization phenomenon due to the damage and thermal softening is suppressed by using the visco-plastic regularization in combination with the nonlocal visco-plastic model. The large deformation and large strain formulations are implemented within the X-FEM framework to model the macro crack discontinuities using an updated Lagrangian approach. Crack propagation and crack direction criteria are presented and the issues relating to the combination of X-FEM with the damage visco-plasticity model are addressed. Finally, the robustness and accuracy of the proposed method are verified through several numerical examples.