An implicit simulation framework to handle frictional contact in elastic rods

Frictional contact is essential for understanding the assembly of rod-like structures in the practical world, for example, knots, hairs, furs, bacteria, etc. Simulating those structures with accurate frictional contact responses is challenging because of their high geometric nonlinearity.

Mathematically, frictional contact is usually regarded as constraints for a physical system's equations of motion (EOM). Researchers in mechanics and computer graphics implemented different ways to incorporate such constraints in EOMs to achieve better performance in computation speed and physical accuracy. Commonly, the constraints of frictional contact are usually treated as additional variables and computed independently at every time step in a dynamics system. Although physical accuracy is guaranteed, such methods decrease the computation speed of the simulation a lot. We propose a fully implicit penalty-based frictional contact framework, Implicit Contact Model (IMC), which combines the constraints with the degrees of freedom (DOF)s directly. IMC can capture the frictional contact responses in rod-rod contact scenarios with good efficiency and accuracy. We showcase IMC’s performance in achieving physically accurate results for knot-tying cases and visually realistic results for a challenging and novel contact scenario of flagella bundling in fluid medium. In addition, we offer a side-by-side comparison with Incremental Potential Contact (IPC), a state-of-the-art contact handling algorithm, which has excellent performance in computation efficiency and visual realism. The comparison shows that IMC has comparable performance to IPC while faster converging speed.