A Physics-Based Vehicle/Terrain Interaction Model for Soft Soil Off-Road Vehicle Simulations

In the context of off-road vehicle simulations, deformable terrain models mostly fall into three categories: simple visualization of an assumed terrain deformation, use of empirical relationships for the deformation, or finite/discrete element approaches for the terrain. A real-time vehicle dynamics simulation with a physics-based tire model (brush, beam-based or Finite Element models) requires a terrain model that accurately reflects the deformation and response of the soil to all possible inputs of the tire in order to correctly simulate the response of the vehicle. The real-time requirement makes complex finite/discrete element approaches unfeasible, and the use of a ring or beam -based tire model excludes purely empirical terrain models. We present the development of a three-dimensional vehicle/terrain interaction model which is comprised of a tire and deformable terrain model to be used with a real-time vehicle dynamics simulator. The governing equations of both models are physics-based, rather than utilizing popular terramechanics models that are empirical. The tire draws on a lumped-mass model based on a radial spring-damper-mass distribution. The terrain model utilizes Boussinesq and Cerruti soil mechanics equations to determine the pressure distribution and deformation of a volume of soil as a function of normal and tangent forces applied at the soil surface by the tire. The soil volume that describes the terrain is discretized as a set of vertical columns of soil, and the deformation of each is modeled using visco-elasto-plastic compressibility relationships that relate subsoil pressures to a change in bulk density of the soil, which in turn produces soil displacements. Different loading combinations applied by a tire passing over a column of soil will be reflected in the state of each volume of soil contained in the column, rather than treating the column of soil as homogeneous in the vertical direction and only associating one set of parameters with the entire column, e.g. a Bekker type model. Furthermore, the time-dependent elastic and plastic response of the soil to repetitive compression/rebound tire loads is also taken into account. Horizontal soil force/displacement produced by tractive and turning forces will also be incorporated into the model. Both the vertical and horizontal force/displacement relationships allow the calculation of total energy and power required to deform the terrain. These physics-based models will be integrated into a real-time vehicle dynamics simulator and is anticipated to lead to a realistic vehicle dynamic response when driving on off-road, deformable terrain conditions, especially when repeated loading occurs or non-homogeneous soil conditions are present. Additionally, the changes in soil states can be used to directly compute the energy and power required to deform the terrain. In order to retain the ability to run real-time simulations, a GPU-accelerated approach is considered to leverage the inherently parallel nature of performing multiple independent terrain geometry queries and soil-mechanics calculations. Numerical experiments include a single soil volume node under a known load and a simplified tire model applying normal forces on the surface of the terrain. Results are given for the vertical plastic soil deformation, and for the power and energy required to perform the deformations.