Data from: Curvature-induced stiffening of a fish fin

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 three-dimensional reconstruction of a mackerel (Scomber japonicus) pectoral fin for illustration, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The three-dimensional 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. As 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.鱼类在运动机动过程中如何调节鱼鳍刚度的机制仍未明确。本研究证实，改变鱼鳍的弯曲度可调节其刚度。我们将鱼鳍建模为被鳍膜连接的可弯曲骨鳍条，由此推导得出：鱼鳍的弯曲度表现为相邻鳍条间主弯曲轴的错位。外力作用下，相邻鳍条会发生弯曲并向外展开，进而拉伸鳍膜。鳍条弯曲与鳍膜拉伸之间的耦合效应，正是刚度提升的内在机制。我们以日本鲭（Scomber japonicus）胸鳍的三维重建模型为例，计算了该鱼鳍通过改变弯曲度所能覆盖的刚度范围。三维重建结果显示，即便在几何上呈平整状态，由于单根鳍条的形态特征，鱼鳍微观结构中已蕴含功能性弯曲度。由于推进表面向周围流体传递力的能力受其刚度限制，鱼鳍弯曲度可调控鱼类与周围流体之间的耦合作用。据此，本研究结果为“鱼鳍刚度覆盖范围与鱼类行为及生态位相关”这一假说提供了力学依据与形态学预测支持。