Implicit Bonded Discrete Element Method with Manifold Optimization

This article proposes a novel simulation approach that combines implicit integration with the Bonded Discrete Element Method (BDEM) to achieve faster, more stable, and more accurate fracture simulation. The new method leverages the efficiency of implicit schemes in dynamic simulation and the versatility of BDEM in fracture modeling. Specifically, an optimization-based integrator for BDEM is introduced and combined with a manifold optimization approach to accelerate the solution process of the quaternion-constrained system. Our comparative experiments indicate that our method offers better scale consistency and more realistic collision effects than finite element method and material point method fragmentation approaches. Additionally, our method achieves a computational speedup of 2.1 to 9.8 times over explicit BDEM methods.