An Accurate Incremental Bekker Equation for Computational Tire-Soil Modeling

In this paper, an accurate computational model for analyzing tire-soil interaction is presented. In the traditional approach, Bekker equation is written in a global form and a quasi-static analysis is done to iteratively model the interaction of the tire and soil. This is due to the nonlinear relationship between soil sinkage and pressure and the unknown loading and unloading status of soil as they are dependent on past loading histories. In this work, an incremental form of Bekker model is proposed. The resulting tire-soil interaction problem is described by a set of nonlinear complementarity equations, which are easier to solve compared to the iterative approach required in the traditional Bekker model. Two numerical examples are presented to demonstrate the effectiveness of the algorithm presented in this work.