Modeling Contact in Elastic Rods: Addressing Jittering and Discontinuities

Simulating contact and friction in one-dimensional structures like rods poses significant challenges, especially when balancing speed and accuracy. We present an advanced contact model specifically designed for Kirchhoff rod models, addressing these challenges by focusing on reducing jittering caused by geometrical discontinuities at segment junctions. We employ the widely used "Discrete Elastic Rods" algorithm that represents the rod as a series of line segments. While effective, this discrete representation introduces discontinuities during contact simulation. As a result, scenarios like simulating the tightening of a knot can exhibit spurious jittering in the force-time curves. This issue persists even with advanced models like the "Implicit Contact Model," which employs smoothing techniques to manage contact energetics. Our model overcomes these shortcomings by transforming the local contact problem into a continuous representation, allowing us to compute the total energy within the contact zone. This energy is then redistributed across discrete points, seamlessly returning to a discrete framework. We compared our model to existing segment-based methods and newer higher-order contact models, with results demonstrating its effectiveness and highlighting the advantages of continuous contact handling.