Velocity crisis of a bio-inspired self-propelled hyperelastic foil in pitching motion

Interactions between hyperelastic bio-membranes and fluid play a crucial role in the flight (or swimming) motion of many creatures, such as bats, flying squirrels and lemurs. Bio-membranes are characterised by high stretchability and micro-bending stiffness, leading to unique fluid–solid coupling properties (Mathai et al. , 2023, Phys. Rev. Lett. , vol. 131, 114003). This study presents a high-fidelity numerical exploration of the hyperelastic characteristics of a pitching foil inspired by bio-membranes in fluid within a low Reynolds number regime. The focus is on the effect of foil compliance on its self-propulsion performance, mimicking natural propulsion mechanisms, with the foil free to move in the horizontal direction. We find that with certain compliance, the foil may experience a velocity crisis, meaning that its propulsive capability is completely lost. This phenomenon is caused by the loss of beat speed when the foil’s passive deformation is out of phase with the pitching motion. By contrast, the two motions can be in phase at proper compliance, leading to an increased beat speed. This will significantly enhance propulsive velocity up to $33\,\%$ compared with the rigid case. The results demonstrate the feasibility of compliance tuning to circumvent the velocity crisis and improve the propulsive speed, which are helpful in the design of micro aerial robots using biomimetic membranes.