New Insight into 3D Explicit Discontinuous Deformation Analysis: Consistency-Based Mass Lumping, Finite Deformation Correction, and Robust Contact Algorithms
摘要
Discontinuous deformation analysis (DDA) is a numerical method for modeling the mechanical behavior of discrete rock block systems. However, extending DDA to three dimensions remains challenging due to the complexity of contact detection, contact iteration, and their coupling. This study addresses these challenges by presenting systematic algorithmic advancements toward a robust and practical 3D explicit DDA. The central contribution is consistency-based mass lumping via optimal placement of mathematical nodes. This approach preserves the correct mass, mass center, moment of inertia tensor, and kinetic energy under the mass lumping condition, thereby enabling explicit computation not only computationally feasible but also physically consistent. A finite deformation correction based on hyperelasticity is then introduced to prevent spurious expansion under large rotations, and a second-order dissipative time integration scheme is employed to enhance the accuracy and stability of long-term simulations. Finally, the contact algorithm is reformulated based on the Gilbert–Johnson–Keerthi (GJK) algorithm and the expanding polytope algorithm (EPA). Two major modifications are introduced: one for handling parallel contacts, and another for mitigating numerical creep in locked contacts. The effectiveness of the proposed framework is validated through several tests, including large rotation, planar sliding, wedge sliding, toppling, and rockfall simulations.
Highlights There is a unique set of mathematical nodes preserving correct mass, mass center, moment of inertia, and kinetic energy on mass lumping condition. Rotational expansion errors are eliminated by finite deformation correction. Robust 3D contact detection is enabled by GJK–EPA with parallel-contact correction. Numerical creep in sliding contact is effectively suppressed by an initial tangential force.