Hydrodynamics of hyperelastic membranes

Oscillating pitching and heaving motions are commonly seen in swimming organisms such as fish, flying insects, and birds. Previous studies of these fluid-structure interactions have primarily been focused on inextensible structures – rigid plates or flexible filaments, such as sheets or low stretchability materials. Here, we numerically and theoretically investigate the dynamic behavior of an ultra-elastic membrane undergoing finite strains due to hydrodynamic interactions while oscillating in a free-stream flow. We quantify the transition from drag to thrust as a function of the membrane’s oscillation amplitude, frequency, and phase, as well as the membrane's (nonlinear) elastic and inertial properties. We compare our results with propulsion and energy extraction measurements performed in the lab.