Implicit Bonded Discrete Element Method with Manifold Optimization

TL;DR

This paper introduces a new implicit bonded discrete element method that combines variational integration and manifold optimization to significantly improve the speed and accuracy of fracture simulations.

Contribution

It presents a novel variational integrator and manifold optimization technique for BDEM, enhancing computational efficiency and modeling precision in fracture analysis.

Findings

Achieves 2.8 to 12 times faster simulation speeds

Introduces a manifold optimization approach with nullspace operator

Develops specialized element packing and surface reconstruction methods

Abstract

This paper proposes a novel approach that combines variational integration with the bonded discrete element method (BDEM) to achieve faster and more accurate fracture simulations. The approach leverages the efficiency of implicit integration and the accuracy of BDEM in modeling fracture phenomena. We introduce a variational integrator and a manifold optimization approach utilizing a nullspace operator to speed up the solving of quaternion-constrained systems. Additionally, the paper presents an element packing and surface reconstruction method specifically designed for bonded discrete element methods. Results from the experiments prove that the proposed method offers 2.8 to 12 times faster state-of-the-art methods.