  A new continuous contact force model for contacting problems with regular or
irregular contacting surfaces and energy dissipations in multibody systems is
presented and discussed in this work. The model is developed according to Hertz
law and a hysteresis damping force is introduced for modeling the energy
dissipation during the contact process. As it is almost impossible to obtain an
analytical solution based on the system dynamic equation, an approximate
dynamic equation for the collision system is proposed, achieving a good
approximation of the system dynamic equation. An approximate function between
deformation velocity and deformation is founded on the approximate dynamic
equation, then it is utilized to calculate the energy loss due to the damping
force. The model is established through modifying the original formula of the
hysteresis damping parameter derived by combining the energy balance and the
law of conservation of linear momentum. Numerical results of five different
continuous contact models reveal the capability of our new model as well as the
effect of the geometry of the contacting surfaces on the dynamic system
response.
