Nonlinear complementarity equations for modeling tire–soil interaction—An incremental Bekker approach

In this work, an accurate computational model for analyzing tire–soil interaction problems is described. In the traditional approach, Bekker equation is written in a global form and a quasi-static analysis is then carried out to iteratively capture the interaction of the tire, which is modeled as a rigid wheel and the soil. The iteration is tedious but required in order to model the nonlinear relationship between soil sinkage and pressure, and the unknown loading/unloading/reloading status of the soil that is dependent on past histories. An incremental form of Bekker model is proposed to overcome some of the difficulties in the traditional approach. The method involves formulating the contact dynamics with a set of complementarity equations. This approach allows the contact forces to be evaluated as part of the solution of the unknown kinematics, and thereby, stay current during an iteration. In contrast, the contact forces in the traditional Bekker method are always be one time-step back. The net result is enhanced computational accuracy and convergency for the proposed incremental Bekker approach. Two examples are solved to demonstrate the effectiveness of the proposed algorithm. Solutions for soil sinkage, drawbar pull, normal pressure, and shear stress for a tire interacting with three types of soil; loose sand, soft soil, and LETE sand are provided and compared with published results. The comparison shows good agreement.