Refining Contact Force Models for Energy Dissipation Modelling in Multibody Dynamics

Accurate modelling of energy dissipation during body collisions is essential for improving the reliability of multibody dynamics simulations.Most published contact force models represent energy loss through a damping force, which introduces hysteresis in the contact response.The dissipated energy is governed by a hysteresis damping factor, typically calculated using a constant coefficient of restitution and the initial collision velocity.Although different models propose various formulations for this factor, they all assume the coefficient of restitution to be constant—despite experimental evidence showing its dependence on impact velocity.To address this limitation, an improved contact force model is proposed.It replaces the constant coefficient of restitution with a velocity-dependent function, allowing the model to capture variations in energy dissipation across different impact velocities.The formulation is compatible with both simple two-body collisions and more complex cases involving zero initial relative velocity.The proposed model was implemented in Python and evaluated against models chosen from the literature in simulations involving three to six beads arranged in collinear chains.Initial impact velocities of 0.1, 1, and 3 m/s were considered.Equivalent scenarios were also simulated using Finite Element Method (FEM) models, serving as a reference.Normalised root mean square deviation (RMSD) was used to quantify velocity prediction accuracy.The analysis shows that the proposed model yields substantial improvements, with error reductions up to 33% for six-bead systems at 3 m/s.This approach may benefit not only multibody dynamics, but also granular media simulation, wear prediction, and robotics involving repeated contacts.