Development of a contact force model with a fluid damping factor for immersed collision events

Impact behavior in a fluidic environment is an inevitable phenomenon in multibody systems. This investigation studies the motion of a contact body in an unbounded and incompressible Newtonian viscous fluid. In allusion to the physical impact in immersed fluid, a dissipated coefficient is introduced to describe the dissipated energy caused by the hydrodynamic forces, including the drag force, added mass force, and history force. To attain the fluid damping factor during impact, the kinetic energy corresponding to the physical impact has four discrepant destinations at the end of the compression phase. According to this principle, a new fluid damping factor is derived based on the energy conservation during impact for simultaneously depicting the coupling between liquid and solid and the coupling between solid and solid. More importantly, to determine the coefficient of restitution (CoR) corresponding to the actual physical impact, a new CoR is proposed according to the definitions of dry and wet CoRs. Subsequently, since both compression and recovery phases happen in the presence of hydrodynamic forces, fluid damping force should be imposed on the Hertz contact model. Consequently, a new contact force model with a fluid damping factor tailored for immersed collision events is proposed. Although the viscosity of the fluid is not explicitly exhibited in the hysteresis damping loop from the new contact force model, the effect of fluid on the immersed collision cannot be neglected, especially for the initial distance of contact bodies. Finally, the rationality and correctness of the proposed model are validated by the reference solution obtained from the solitary wave propagation of a horizontal one-dimension granular chain.