An adaptive multi-grid peridynamic method for dynamic fracture analysis

The standard way of implementing Peridynamics is a meshfree approach which uses a uniform discretization. This is inefficient when a very dense grid spacing for a localized area is required. In this paper, a radically new strategy to couple grids with different spacing is put forward. It is free of ghost forces in static cases and spurious waves in dynamic problems can be controlled and made negligible thanks to proper discretization. There is no loss of volume due to non-uniform discretization at the interface between different grids. An efficient algorithm is developed to apply the refinement adaptively. It permits to increase the resolution of the analysis only in the critical zones. The performance is investigated by solving dynamic problems, including cases of crack propagation in brittle materials. We compare the solutions of the proposed method with those of a standard peridynamic model, which employs uniform discretization, and show that the same accuracy is obtained at a much smaller computational cost.