Coupled peridynamics and scaled boundary finite element method for the dynamic fracture problem on polygonal meshes
Abstract
To address two critical bottlenecks in peridynamics (PD), namely its strong dependence on uniform discretization and the difficulty in boundary condition implementation, this study proposes a novel Peri-PolySBFEM framework. The framework achieves its advances through three key innovations. First, polygonal meshes are adopted to replace conventional quadrilateral and triangular discretization, thereby effectively improving geometric adaptability for complex configurations. Second, scaled boundary shape functions derived from the Laplace's equation in the scaled boundary finite element method (SBFEM) are embedded into the discontinuous Galerkin weak form of the peridynamic momentum equation. This coupling converts the nonlocal double integrals of PD into a matrix operation form similar to standard finite element methods. Third, an effective boundary correction scheme is developed, which calibrates the micromodulus function by maintaining strain energy density consistency between PD and classical continuum mechanics. Systematic validation through elastic wave propagation, dynamic crack branching, and Kalthoff–Winkler impact tests demonstrates that the framework offers superior excellent control, δ -convergence, and m-convergence, collectively confirming its accuracy, convergence, and reliability in dynamic fracture simulation. The current framework is established and validated for two-dimensional problems. Future work will focus on extending this method to three-dimensional cases and multiphysics coupling analyses.