Energy Dissipation Analysis for Elastoplastic Contact and Dynamic Dashpot Models

This investigation aims to analyze the underlying relationship between the dynamic dashpot and the static force-displacement models used in multibody systems. By ignoring the plastic flow of the contact body made of elastoplastic material, the coefficient of restitution of the dynamic dashpot model can be calculated by using the static force-displacement model proposed by Ma and Liu (Ma-Liu model). Simulation results show the consistency of energy dissipation between the Ma-Liu model and Flores et al. model, but there are still slight differences. This is because the Hertz contact stiffness of the dynamic dashpot model overestimates the actual contact stiffness in the elastoplastic phase. Therefore, in order to eliminate this discrepancy when depicting energy dissipation during impact, the Hertz contact stiffness can be replaced by the linearized elastoplastic contact one from the Ma-Liu model; subsequently, a new hysteresis damping factor is derived based on the linearized elastoplastic contact stiffness and energy conservation during impact. Finally, a new elastoplastic dashpot model can be obtained by the elastoplastic contact stiffness combined with a new hysteresis damping factor. To verify the practicability and effectiveness of the new model, a granular chain and a slider-crank mechanism with a clearance joint are employed as numerical examples.