ADAPTIVE MULTISCALE FINITE ELEMENT METHOD BASED ON ANISOTROPIC FRACTURE PHASE FIELD MODEL

The fiber reinforced composites have complex fracture modes. The anisotropic fracture phase field model can automatically capture the initiation and evolution of cracks, which is suitable for simulating the failure behavior of fiber reinforced composite materials. However, it is computationally expensive. In order to improve the computational efficiency of the anisotropic fracture phase field model, an adaptive multiscale finite element method for the anisotropic fracture phase field model is proposed in this paper. The adaptive mesh algorithm and the extended multiscale finite element method are adopted in the proposed model. Based on the calculational results at the end of each iteration step, the adaptive mesh algorithm determines the crack paths according to the phase field variables and their increments at the mesh nodes. Meanwhile, the algorithm can automatically refine the mesh near the crack path. The fracture phase field model is solved by a staggered iteration algorithm. When updating the displacement field, the refined meshes use the traditional finite element method, while the non-refined meshes use a multiscale finite element method by considering the oscillating boundary conditions. When updating the phase field, all meshes use the traditional finite element method. At the interface between the coarse and fine elements, the numerical basis functions obtained from the multiscale finite element method are employed to constrain the nodes at the interface. The proposed model is applied to analyze the fracture failure behavior of fiber reinforced composite plates with different lay-up angles and variable stiffness under tensile loading. Numerical results demonstrate that the proposed model can accurately capture the crack paths. In addition, the numerical results obtained by the proposed model are in good agreement with the existing models and experimental results. Compared to the traditional finite element phase field model, the computational time of this model is reduced obviously with the same computational accuracy.