A variational mechanics perspective on dual-horizon bond-based peridynamics
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When the classical peridynamic equations are applied to regions with different horizon sizes, the forces between interacting points are no longer equal and opposite. This imbalance appears as artificial external forces, sometimes called ghost forces, which disturb wave propagation and produce spurious reflections in simulations. We analyze this effect by deriving the equations of motion from Hamilton’s principle and examining how varying horizons affect the internal force exchange. No surprise, the study shows that the lack of interaction symmetry is the main reason for the ghost forces. When the horizons of both interacting points are taken into account in a consistent way, the variational formulation naturally leads to a dual-horizon bond-based peridynamics model, which restores momentum balance and eliminates spurious force effects. Moreover, we capitalize on Hamilton’s principle and derive different explicit and implicit variational integrators for dual-horizon peridynamics, which are then analyzed in terms of convergence and energy behavior for different benchmark problems. The chosen examples highlight the elimination of nonphysical forces and reflections at horizon transition regions. This work provides a robust foundation for peridynamic simulations with spatially varying horizons and motivates extensions toward spatially adaptive formulations for fracture dynamics.
