Jun Liu

Coupled peridynamics and scaled boundary finite element method for the dynamic fracture problem on polygonal meshes

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.

Crack propagation in porous materials with an adaptive ordinary state-based peridynamics and quadtree-based scaled boundary finite element method coupling

Erosion-driven earth dam failure: A two-phase multi-state smoothed particle hydrodynamics model

Earth dam failures are typically triggered by overtopping, involving complex soil–water interactions and progressive structural collapse. Empirical and semi-empirical models provide efficient estimates of breach parameters and outflow hydrographs, but they usually offer limited resolution of the local stress state, rheological transition, and morphology evolution during overtopping-induced erosion. In this study, a graphics processing unit-accelerated two-dimensional, two-phase dam failure numerical model has been developed based on the Drucker–Prager yield criterion and weakly compressible smooth particle hydrodynamics. Combined with the Herschel–Bulkley–Papanastasiou (HBP) rheological model, the two-dimensional framework represents the yield-stress and strain-rate-dependent behavior of yielded soil during overtopping erosion. Stable inflow boundary conditions are established to simulate overtopping-induced erosion, entrainment, and subsequent transport of yielded soil particles by the water flow. Different failure modes of earth dams with different power law indexes are simulated. By comparing with experimental data, it can be observed that the model captures the key physical phenomena of scour thickening and “headcut” on the downstream slope. A transition in the modeled mechanical response of the eroded soil at the soil–water interface is identified, where the material changes from an unyielded state governed by the Drucker–Prager criterion to a yielded flow state described by the HBP model. Furthermore, the study findings indicate that the migration of fine particles and the rheological evolution of yielding soil during the erosion process lead to a reduction in the strength of earthen dams, which in turn accelerates the expansion of breaches.