Quasi-static and dynamic fracture modeling by the nonlocal operator method

In this paper, a phase field model is developed and applied to the simulation of quasi-static and dynamic fracture using the nonlocal operator method (NOM). The phase field's nonlocal weak and associated strong forms are derived by a variational principle. The NOM requires only the definition of the energy. Its differential operators replace the shape functions in methods such as FEM which drastically simplifies the implementation. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.