An Explicit Phase-Field Material Point Method for Dynamic Brittle Fracture Problem

  • Zeng, Zhixin (Tsinghua University)
  • Zhang, Xiong (Tsinghua University)

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The phase field method is an effective method to simulate arbitrary crack propagation, branching and convergence. Material Point Method (MPM) combines Eulerian method and Lagrangian method, which has advantages in simulation for large deformation problem. The implicit Phase-Field MPM has been studied by many researchers for quasi-static fracture problem. However, few work has been presented to study the application of the explicit Phase field on MPM. Due to the iteration in updating phase field of particles, the implicit Phase-Field MPM has poor simulation efficiency and is inappropriate for dynamic fracture problem. On the contrary, explicit phase field is established by importing the viscous dissipation of phase field evolution. And the phase field can be updated with forward difference scheme which avoids the iteration. In this work, A novel explicit Phase-Field Material Point Method (exPFMPM) is introduced for simulation of dynamic fracture problem in elastic media. Many studies have been done in explicit Phase Field Finite Element Method (FEM), but few works study the stability of the time integration of explicit phase field. In this work, the effect of particle position and neighbouring cell interaction on stability of exPFMPM is studied. An explicit critical time step formula is obtained based on the system eigenvalues in one dimension, and is then extended to two and three dimensions. And the critical time step formula can also be used in explicit Phase Field FEM. Several tests are performed to verify the critical time step formula. The effectiveness and validity of the exPFMPM method is assessed through several numerical examples (Three-point bending, Dynamic crack branching, ie) for dynamic fracture in brittle materials.