Semi-Implicit Pairwise Descent for Nonlocal Continuum Mechanics

2026-09-09

AI Summary

提出Semi-Implicit Pairwise Descent方法，通过非局部视角的成对力表示来模拟大规模超弹性材料，避免了Hessian计算，降低了计算开销，并统一处理接触和摩擦问题。

Abstract

We propose Semi-Implicit Pairwise Descent (SIPD), a unified nonlocal pairwise framework for simulating large-scale hyperelastic materials involving complex contact and friction. By reformulating the Finite Element Method (FEM) equations of motion into a pairwise force representation from a nonlocal perspective, our approach avoids costly Hessian computations, leading to a reduction in per-iteration computational overhead. Furthermore, we propose an analytical projection strategy for projecting our Hessian-free coefficient matrices to positive semi-definiteness. And we treat contact and friction as a unified anisotropic elastic energy, allowing for a seamless integration into the elastic solver framework. We mathematically prove that our method is unconditionally stable and numerically convergent.Experimental results demonstrate that SIPD achieves real-time performance for million-scale simulations even under intricate contact and friction conditions.

Problem

• nonlocal continuum mechanics
• hyperelastic materials
• complex contact and friction
• computational overhead

Innovation

• Semi-Implicit Pairwise Descent
• nonlocal continuum mechanics
• Hessian-free computation
• unified anisotropic elastic energy
• real-time performance