Modeling dynamic cracks initiation and propagation with the local to global approach

The recently proposed local to global (L2G) method shows an excellent ability of modeling complex arbitrary cracking problem with high efficiency and robustness. Here, we extend the L2G to model dynamic cracks initiation and propagation, in which additional nodes are dynamically introduced to capture displacement discontinuities induced by cracks' propagation, but displacements/accelerations of additional nodes are obtained by solving local nonlinear problems of cracked elements associated with a crack. This unique operation removes the divergence risks caused by adding nodes, and improves the numerical efficiency by decreasing iteration times of the global problem. Crack branching problem is also taken into consideration in current work. Numerical examples for dynamic cracks propagation are provided to demonstrate the effectiveness and robustness of the proposed method.