Achieving realistic simulations of terrain vehicles in their work environment does not only require a careful model of the vehicle itself but the vehicle's interactions with the surroundings are equally important. For off-road ground vehicles the terrain will heavily affect the behaviour of the vehicle and thus puts great demands on the terrain model. The purpose of this project has been to develop and evaluate a deformable terrain model, meant to be used in real-time simulations with multi-body dynamics. The proposed approach is a modification of an existing elastoplastic model based on linear elasticity theory and a capped Drucker-Prager model, using it in an adaptive way. The original model can be seen as a system of rigid bodies connected by elastoplastic constraints, representing the terrain. This project investigates if it is possible to create dynamic bodies just when it is absolutely necessary, and store information about possible deformations in a grid. Two methods used for transferring information between the dynamic bodies and the grid have been evaluated; an interpolating approach and a discrete approach. The test results indicate that the interpolating approach is preferable, with better stability to an equal performance cost. However, stability problems still exist that have to be solved if the model should be useful in a commercial product.

One commonly used representation of complex objects in physics-based simulations are triangle meshes. This representation utilizes a collection of triangles to approximate an object. An alternative representation is a Signed Distance Field (SDF). This thesis aims to evaluate the effectiveness of representing a heavy machine bucket as an SDF, specifically in the application of collision detection with a de-formable terrain. Additionally, this thesis describes the implementation of two collision detection routines which uses SDFs to detect collisions with spheres and heightfields. The SDFs are stored using two alternative spatial data structures, a uniform grid and an octree. The implementations are compared against a triangle mesh representation. While there are limitations to the SDF representation, such as the need for high resolutions to capture fine details or that small features may become heavily distorted, the benefits of using SDFs include the ability to perform point to distance queries and provide a robust description of an object’s interior and exterior. The findings of this study showed that the SDF stored in a uniform grid demonstrated better performance in the benchmarks and was able to reproduce comparable data to the triangle mesh in the digging tests. These results indicate that the SDF representation could be a promising alternative to the triangle mesh representation. However, further development and research are required.