Simulation of Elastic Rods with Applications in Knot Tying and Soft Robotics

Accurate frictional contact is critical for simulating the assembly of rod-like structures in practical applications, such as knots, hairs, and flagella. These systems pose significant challenges due to their high geometric nonlinearity and elasticity, making rod-on-rod contact a persistent issue in computational mechanics and computer graphics. In this talk, we present a fully implicit penalty-based frictional contact method, the Implicit Contact Model (IMC), which efficiently captures frictional contact responses while maintaining computational robustness. Unlike conventional methods that treat frictional contact as independent constraints at each time step—often leading to slower simulations and numerical convergence issues—IMC integrates contact conditions directly within the equations of motion, allowing for larger time-step integration and faster convergence. We demonstrate the capabilities of IMC through simulations of complex scenarios like flagella bundling in a fluid medium, a challenging contact problem that has significant implications for both biological systems and soft robotics. Additionally, we compare IMC's performance with Incremental Potential Contact (IPC), a state-of-the-art contact handling algorithm, showing that IMC achieves comparable accuracy with improved convergence speed.

Our computational framework is implemented in DiSMech, an open-source software platform built on discrete differential geometry (DDG). DiSMech is specifically designed for fast and accurate simulations of flexible structures, making it well-suited for capturing complex interactions in systems like soft robots and other deformable materials.