Multi-Phase-Field Method for Dynamic Fracture in Composite Materials Based on Reduced-Order-Homogenization

In this manuscript, we extend the quasi-static multi-phase-field method for composite materials to the dynamic case. In the dynamic multi-phase-field method, each phase of the composites has its individual phase field, and the degradation of each phase is governed by its respective phase field. The macroscopic response is then obtained by averaging and homogenization approaches through the reduced-order-homogenization (ROH) framework. Through the ROH and the Francfort-Marigo variational principle, we can obtain the equations that govern the motion of the composites and the evolution of each phase field. This method is capable of capturing the characteristics of dynamic fracture, such as crack branching, without the need for any additional bifurcation criterion. Moreover, it can capture dynamic fracture patterns in composite materials, including matrix cracking, fiber breakage, and delamination. The corresponding numerical algorithm that includes spatial and temporal discretization is developed. An implicit, staggered Newton-Raphson iterative scheme is implemented to solve the nonlinear coupled equations. Finally, this method is tested with several sets of dynamic fracture benchmarks, which demonstrates good agreement with the experiments and other numerical methods.