The external force term ${\boldsymbol{f}}^{(p)}_{ext}(\boldsymbol{X}, t)$ includes body forces, wall-particle interactions, and contact forces from other particles. Contact is modeled using a spring-dashpot-slider formulation applied locally when particles come within a critical distance; see \autoref{fig:peridemContact}. This approach introduces nonlinear normal forces, damping, and friction without relying on particle convexity or geometric simplifications. The full formulation of contact detection, force assembly, and implementation is detailed in [[@jha2021peridynamics], Section 2.2].
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