A contact formulation using local frame of SE(3) group for corotational beam against rigid solid via moving signed distance field

Abstract

In this paper, we present a contact formulation for corotational beam and rigid body based on body-attached signed distance field (SDF). All formulations are based on the unified SE(3) framework, whose prominent advantage lies in its frame invariance property. For solid body, the geometry surface can be implicitly described by a moving SDF. Consequently, the interaction between beams and rigid solids can be viewed as immersion in a field-described force. The contact force is formulated using SDF interpolation, and exact tangent matrices are provided to facilitate implicit iteration. Notably, this approach eliminates the need for contact detection during simulation, because the SDF database is constructed before the simulation. To enhance the spatial adaptivity of the SDF algorithm, we introduce an octree refinement strategy. Besides, we incorporate the concept of contact potential volume into the subdivided stopping criterion. Compared to the uniform SDF, this approach demonstrates higher generation speed and smaller errors. Several examples are used to verify the accuracy, convergence and efficiency of the proposed formulation. It is observed that the invariance property of SE(3) description leads to enhanced computational performance. Both frame invariance and SDF-based approach are expected to improve efficiency for large-scale problems. The presented method is easily applicable to other types of flexible bodies.