Fast But Accurate: A Real-Time Hyperelastic Simulator with Robust Frictional Contact

2025-03-19

AI Summary

This work addresses the computational challenges in real-time implicit hyperelastic solid simulation arising from strong nonlinearity (hyperelasticity) and nonsmoothness (non-penetration contact and Coulomb friction). Methodologically, it introduces a GPU-accelerated local–global splitting framework: (i) contact and friction are unified under a nonlinear complementarity problem (NCP) formulation; (ii) an efficient solver is designed using explicit sparse matrix inverse representations; and (iii) the NCP preconditioner is enhanced to improve convergence rate and friction accuracy. Contributions include: the first real-time, tightly coupled solver achieving high-fidelity friction modeling and mathematically rigorous non-penetration constraints within a unified NCP framework; stable performance exceeding 60 FPS on large-scale systems, under extreme deformations, and across multi-stiffness material configurations; and broad constitutive model compatibility—including Neo-Hookean and St. Venant–Kirchhoff models—ensuring both physical fidelity and engineering practicality.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

We present a GPU-friendly framework for real-time implicit simulation of elastic material in the presence of frictional contacts. The integration of hyperelasticity, non-interpenetration contact, and friction in real-time simulations presents formidable nonlinear and non-smooth problems, which are highly challenging to solve. By incorporating nonlinear complementarity conditions within the local-global framework, we achieve rapid convergence in addressing these challenges. While the structure of local-global methods is not fully GPU-friendly, our proposal of a simple yet efficient solver with sparse presentation of the system inverse enables highly parallel computing while maintaining a fast convergence rate. Moreover, our novel splitting strategy for non-smooth indicators not only amplifies overall performance but also refines the complementarity preconditioner, enhancing the accuracy of frictional behavior modeling. Through extensive experimentation, the robustness of our framework in managing real-time contact scenarios, ranging from large-scale systems and extreme deformations to non-smooth contacts and precise friction interactions, has been validated. Compatible with a wide range of hyperelastic models, our approach maintains efficiency across both low and high stiffness materials. Despite its remarkable efficiency, robustness, and generality, our method is elegantly simple, with its core contributions grounded solely on standard matrix operations.

Problem

• Real-time simulation of hyperelastic materials with friction.
• Solving nonlinear, non-smooth problems in contact scenarios.
• Enhancing GPU-friendly, efficient, and accurate frictional behavior modeling.

Innovation

• GPU-friendly framework for real-time hyperelastic simulation
• Nonlinear complementarity conditions for rapid convergence
• Sparse system inverse for highly parallel computing