Symmetric Boundary‐Represented Contact Model for the Combined Finite–Discrete Element Method

Large‐scale three‐dimensional (3D) finite‐discrete element method (FDEM) simulations impose high demands on contact models. Existing contact formulations typically evaluate these contacts by explicitly reconstructing overlap volumes or contact surface patches, which requires expensive geometric clipping and can become the dominant computational bottleneck. In this work, we develop a symmetric boundary‐representation contact model for 3D tetrahedral FDEM (SBC‐FDEM). Based on Stokes' theorem, this approach recasts the contact vector area as a boundary integral evaluated exclusively from oriented boundary segments. For each tetrahedron pair, these segments are identified via a fixed 4 4 sweep of lightweight triangle‐triangle intersection tests. By bypassing computationally expensive overlap volume or surface patch reconstructions, this boundary‐only formulation is considerably simpler and maps naturally onto modern GPU architectures. The same boundary representation also yields a boundary depth factor that removes the flat‐facet force jump, so the contact force grows continuously from zero. Moreover, strict swap invariance is achieved by evaluating both the boundary segments and the depth factor symmetrically. The method is verified using pair‐level swap tests, elastic rebound tests, closed‐loop energy tests, and laboratory‐scale UCS and BTS simulations. SBC‐FDEM is swap‐invariant to machine precision and keeps the shallow‐contact spurious energy small. Large‐scale impact fragmentation and slope collapse simulations further demonstrate its robustness in handling rapidly evolving contact interactions. On NVIDIA V100 and A100 GPUs, SBC‐FDEM accelerates the contact force computation by 1.9–2.9× compared with the state‐of‐the‐art contact algorithm (ENIC‐FDEM) and by 7.6–17.0× compared with the widely used classical potential‐based contact model (CPC‐FDEM). The proposed method can be generalized to FDEM formulations based on polygonal and polyhedral discretizations.