Asymptotics in soil-wheel interaction

Three-dimensional numerical simulations were performed to investigate the asymptotic behavior associated with wide and narrow wheels indenting cohesive and frictional materials. The wheel is taken to be rigid, and the material is elastic-perfectly plastic. Simulations reveal that deformation induced by both wide and narrow wheels can be approximated by plain strain, with the wheel indentation process resembling indentation of a flat punch in both cases. Numerical results are supplemented with a simple, albeit approximate analytic approach that captures essential features of the wheel indentation process and derives from fundamental solutions to the punch problem. Localization present for wide and narrow wheels on frictional soil is attributed to the planar modes of deformation present, as localized deformation was not observed for wheels of intermediate width. Previous studies on soil-wheel interaction assume that deformation occurs only within the plane of the wheel diameter, and the results obtained in this paper point to basic discrepancies arising with this assumption for a narrow wheel, both in terms of the dimensionless force-penetration relationship and soil kinematics.