A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis

Peridynamics is a new nonlocal theory that provides the ability to represent displacement discontinuities in a continuum body without explicitly modeling the crack surface. In this paper, an explicit dynamics implementation of the bond-based peridynamics formulation is presented to simulate the dynamic fracture process in 3D elastic solid. Based on the variational theory, the Discontinuous Galerkin (DG) approach is utilized to formulate the classic peridynamics governing equation. As a result, the spatial integration can be carried out through finite element approach to enforce the boundary conditions, constraints, contacts as well as to handle the non-uniform mesh in the engineering practices. The classic material parameters, such as the elastic modulus and fracture energy release rate are employed for the determination of material response and failure in brittle material. Several numerical benchmarks are conducted to invest the convergence and mesh sensitivity of simulations of dynamic crack propagation process with different refinements. The results demonstrate that the proposed peridynamics formulation can capture the 3D dynamic crack process in brittle material effectively and accurately including multi-crack nucleation, propagation and branching.