A reference contact framework of signed distance fields for efficient frictional dynamic modeling and computation
Year: 2026
Type: article
Abstract: The signed distance field (SDF) method provides an implicit functional representation to simplify contact detection for complex geometries. However, for deformable bodies, utilizing a static SDF defined in the reference configuration often relies on heuristic geometric approximations, leading to kinematic inconsistencies. To address such a problem, this paper presents a reference contact framework (RCF) of SDFs. It defines the frictional contact model in the reference configuration of a deformable body that ensures physical rigor within the static SDF. Firstly, a pulling-back procedure is established to correlate the spatial positions of contact points in the current configuration with their material positions in the reference configuration. Then, the work done by contact forces is formulated directly in the reference configuration, and the generalized contact forces are derived through the variation with respect to generalized coordinates. The resulting formulation of contact forces intrinsically accounts for surface distortions, maintaining variational consistency with the total Lagrangian framework. Additionally, the framework is extended to a frictional contact by incorporating the Coulomb friction model, which is reformulated through a novel definition of relative tangential displacement defined within the reference configuration, i.e. the reference tangential slip. To facilitate efficient implementation, a robust contact detection algorithm, comprising a hierarchical global search and a detailed local search, is integrated into the framework. Finally, several numerical examples of contact dynamics involving finite deformations and intricate surface geometries are presented. Their results demonstrate the efficacy of the proposed method for capturing complex contact physics with superior robustness and precision over the conventional contact algorithms.
Authors: Tiantian Tang, Kai Luo, Qiang Tian, Haiyan Hu
Institution: Beijing Institute of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,830
OpenAlex ID: W7215104769