Curvature-induced stiffening of a fish fin

TL;DR

This study reveals that fish fin stiffness can be modulated by curvature, which affects the interaction with surrounding fluid, with implications for understanding fish locomotion and ecological adaptation.

Contribution

We introduce a mechanical model linking fin curvature to stiffness modulation and analyze a 3D fin reconstruction to predict stiffness ranges.

Findings

Fin curvature causes misalignment of bending axes in rays.

Bending rays stretch the membrane, increasing stiffness.

The fin's microstructure embeds functional curvature.

Abstract

How fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin's curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness. Using analysis of a 3D reconstruction of a Mackerel (Scomber japonicus) pectoral fin, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The 3D reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. Since the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish.