On the modeling of friction and rolling in flexible multi-body systems

This paper is concerned with the dynamic analysis of flexible, nonlinear multi-body systems undergoing contact involving friction and rolling. A continuous friction law is used to model the friction forces between contacting bodies. This avoids the numerical problems associated with the discontinuity inherent to Coulomb's friction law and eliminates the need for different sets of equations modeling sliding and rolling as distinct phenomena. On the other hand, continuous friction laws eliminate specific physical phenomena implied by Coulomb's friction law. The condition of vanishing relative velocity between two contacting bodies is not possible: sticking or rolling are replaced by creeping with a small relative velocity. Discrete events such as transition from slipping to rolling or rolling to slipping are eliminated, together with the high frequency phenomena they are likely to cause. The computational issues associated with the continuous friction law and with the enforcement of the non-holonomic rolling constraint are addressed in this paper. This work is developed within the framework of energy preserving and decaying time integration schemes that provide unconditional stability for nonlinear, flexible multi-body systems undergoing contact involving friction and rolling.