An adaptive edge-based smoothed finite element method (ES-FEM) for phase-field modeling of fractures at large deformations.

This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted widespread interest by virtue of its outstanding performance in dealing with complex cracks. The ES-FEM is an excellent member of the S-FEM family developed in combination with meshless ideas and finite element method (FEM), which is characterized by higher accuracy, softer stiffness, and insensitive to mesh distortion. Given that, the advantages of the phase-field method (PFM) and ES-FEM are fully combined by the approach proposed in this paper. With the costly computational overhead of PFM and ES-FEM in mind, a well-designed multi-level adaptive mesh strategy was developed, which considerably improved the computational efficiency. Furthermore, the detailed numerical implementation for the coupling of PFM and ES-FEM is outlined. Several representative numerical examples were recalculated based on the proposed method, and its effectiveness is verified by comparison with the results in experiments and literature. In particular, an experiment in which cracks deflected in rubber due to impinging on a weak interface was firstly reproduced.