Dynamics of soft filaments that can stretch, shear, bend and twist

Soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. We present a general numerical approach to simulate the dynamics of filaments that, at every cross-section, can undergo all six possible modes of deformation, allowing the filament to bend, twist, shear and stretch, consistent with dynamics on the full Euclidean group SE(3). Additionally, we also account for the interaction of an active filament with itself and the environment via self-contact, surface friction and hydrodynamics. We examine the accuracy of our energy preserving and second order spatio-temporal method by means of a number of benchmark problems with known analytic solutions. Finally, we demonstrate the capabilities of our approach both on passive physical problems related to solenoid and plectoneme formation in twisted, stretched filaments, and active biophysical problems in the context of limbless locomotion on solid surfaces and in bulk liquids. All together, our approach allows for a broad computational generalization of available methods to study the dynamics of soft filaments.