Dual-horizon peridynamics-based variational damage modeling for complex dynamic fractures

Fracture simulation by cutting bonds in non-ordinary state-based peridynamics may suffer from numerical instability. To solve this problem, we develop a dual-horizon peridynamics equipped with variational damage for the dynamic brittle fracture modeling in elastic solid. Without using damage variables explicitly, the damage field is a natural outcome or a post-processing of the strain energy field. Since the bond-cutting process is removed, the numerical stability of fracture propagation is greatly enhanced. Unlike peridynamics, which tracks the damage state of each bond throughout the simulation, the variational damage model employs a scalar damage variable to represent the state of each material point. This model expresses damage as a function of the “positive” strain energy density, utilizing the spectral decomposition of the strain tensor. Such a decomposition scheme effectively prevents crack surface interpenetration when the crack closes, ensuring physically consistent fracture behavior. A flowchart outlining the numerical implementation of this approach is presented. We demonstrate the capabilities of the current method by simulating a notched plate subjected to tensile/shear boundary conditions, the Kalthoff & Winkler experiment and fragmentation simulation in two and three dimensions.