Understanding slipping of wheels in granular media locomotion

Slipping of circular wheels at high rotation rates on granular media like sand is a commonly experienced phenomenon. At the same time, granular materials themselves are known to be rate-insensitive for a fairly large range of strain rates. In order to identify the fundamental phenomena responsible for the sudden increase in the slipping of wheels above a certain rotational velocity, a plasticity-based continuum modelling study is performed. Lugged wheel locomotion simulations, validated against experimental findings, are performed for a wide range of rotation rates. A momentum conservation-based argument is proposed to explain and predict the onset of increased slipping. An empirical form of optimal rotation rates for wheel locomotion in terms of various associated system parameters is also suggested.