A Splitting Architecture for Exact Reduced Coulomb Friction

2026-07-21

AI Summary

This work addresses the longstanding trade-off in frictional contact dynamics between numerical stability and fidelity to Coulomb’s friction law, which often leads to either inaccurate approximations or monolithic solvers that lack scalability. The authors reformulate exact Coulomb friction—under a simplified setting—as a cone complementarity problem augmented with enhanced velocities, revealing for the first time its inherent structural separability. Leveraging this insight, they propose a hierarchical solution framework: an outer loop explicitly updates non-associated coupling terms, while an inner module solves a strongly convex conic-constrained quadratic program in a modular fashion. Crucially, the method preserves the nonsmooth nature of Coulomb friction without smoothing or relaxation, accurately reproducing canonical stick-slip transitions and stacking behaviors in benchmark tests, thereby achieving high accuracy, robustness, and scalability.

Abstract

Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

Problem

• Coulomb friction
• cone complementarity
• non-associated coupling
• frictional contact dynamics
• reduced formulation

Innovation

• Coulomb friction
• cone complementarity
• splitting architecture
• non-associated coupling
• modular solver