# A complementarity-based rolling friction model for rigid contacts

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## Abstract

In this work (also, preprint ANL/MCS-P3020-0812, Argonne National Laboratory) we introduce a complementarity-based rolling friction model to characterize dissipative phenomena at the interface between moving parts. Since the formulation is based on differential inclusions, the model fits well in the context of nonsmooth dynamics, and it does not require short integration timesteps. The method encompasses a rolling resistance limit for static cases, similar to what happens for sliding friction; this is a simple yet efficient approach to problems involving transitions from rolling to resting, and vice-versa. We propose a convex relaxation of the formulation in order to achieve algorithmic robustness and stability; moreover, we show the side effects of the convexification. A natural application of the model is the dynamics of granular materials, because of the high computational efficiency and the need for only a small set of parameters. In particular, when used as a micromechanical model for rolling resistance between granular particles, the model can provide an alternative way to capture the effect of irregular shapes. Other applications can be related to real-time simulations of rolling parts in bearing and guideways, as shown in examples.

## Keywords

Variational inequalities Contacts Rolling friction Multibody Complementarity## Notes

### Acknowledgements

A. Tasora thanks Ferrari Automotive and TP Engineering for financial support. Mihai Anitescu was supported by the U.S. Department of Energy, under Contract No. DE-AC02-06CH11357.

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