Resolving Force Indeterminacy in Contact Dynamics Using Compatibility Conditions

TL;DR

This paper introduces a compatibility-based post-processing method for contact dynamics that ensures unique contact force solutions aligning with soft particle models, improving the accuracy of rigid body simulations.

Contribution

It proposes a novel compatibility condition approach to resolve force indeterminacy in contact dynamics, aligning rigid body results with soft particle methods.

Findings

Effectively filters out non-physical force distributions.

Applicable to complex contact scenarios with multiple materials.

Integrates easily into existing contact dynamics codes.

Abstract

Contact dynamics (CD) is a powerful method to solve the dynamics of large systems of colliding rigid bodies. CD can be computationally more efficient than classical penalty-based discrete element methods (DEM) for simulating contact between stiff materials such as rock, glass, or engineering metals. However, by idealizing bodies as perfectly rigid, contact forces computed by CD can be non-unique due to indeterminacy in the contact network, which is a common occurence in dense granular flows. We propose a CD method that is designed to identify only the unique set of contact forces that would be predicted by a soft particle method, such as DEM, in the limit of large stiffness. The method involves applying an elastic compatibility condition to the contact forces, which maintains no-penetration constraints but filters out force distributions that could not have arisen from stiff elastic contacts. The method can be used as a post-processing step that could be integrated into existing CD codes with minimal effort. We demonstrate its efficacy in a variety of indeterminate problems, including some involving multiple materials, non-spherical shapes, and nonlinear contact constitutive laws.