Advanced modelling of soft soil-tyre contact for off-road vehicle dynamics simulations

The locomotion of wheeled and tracked vehicles on soft soil has long been investigated due to its relevance in planetary exploration, agricultural machinery, and military applications. In this context, accurate tyre modelling is crucial for off-road vehicle dynamics, as traction and handling strongly depend on soil properties. This paper presents an advanced contact model developed in Matlab/Simulink for automotive tyres interacting with fine-grained soil. The formulation combines experimentally validated principles from Terramechanics, including pressure-sinkage relationship, shear stress distribution, and lateral bulldozing effects. Innovative features improve the operating capabilities of existing models. An adaptive, deformable contact patch is introduced to represent standstill and low-velocity wheel conditions. A versatile shear-stress formulation ensures robust performance across a wide range of operating scenarios. The moments acting on the wheel, arising from both the contact patch and the sidewalls, are reformulated. The contact model is first tested as standalone routine by evaluating force and moment characteristics under pure longitudinal, lateral, and combined slip conditions. It is then integrated into a simplified single-wheel virtual test rig for time-domain analysis, demonstrating its effectiveness in driving, braking, coasting, and drifting scenarios. The model has proven to be numerically robust and well-suited for integration into full-vehicle dynamics simulations.