26-4 Thursday, Jan. 5 14:15 - 14:30 Curvature-induced stiffening of rayed fins NGUYEN, KD*; YU, N; BANDI, MM; VENKADESAN, M; MANDRE, S; Yale University; Tsinghua University; Okinawa Institute of Science and Technology; Yale University; Brown University email@example.com http://mvlab.yale.edu/
Fishes switch between locomotive modes as ecological needs vary, and this requires rapid and substantial modulation of fin stiffness. Motivated by the commonplace observation that a thin sheet of paper stiffens upon slightly curling it, we analyze the mechanics underlying the stiffness of thin structures like fins. For a thin sheet of paper, transverse curvature couples out-of-plane bending with in-plane stretching, and thereby stiffens it. Although rayed fins are a composite of rays and membranes and not homogeneous like a sheet of paper, we show that a similar mechanical principle carries over, with variation of the intrinsic ray geometry between adjacent rays playing the role of transverse curvature. The ray has a preferred bending direction if the two principal area moments of the ray's cross section are dissimilar, such as for a non-circular cross-section. Now, a systematic variation in the principal bending axes between adjacent rays will couple ray bending with membrane stretching, the same principle as a curled sheet. Using µCT imaging, we find that the rays in the mackerel's pectoral fin have a non-circular cross-section, and the preferred bending axis varies systematically across adjacent rays. Our mathematical analyses identify key material and morphological parameters that affect the fin's stiffness, and its maximal range of variation. As a result of its morphology, we predict that the mackerel's pectoral fin can vary its stiffness over 5-fold by controlling the transverse curvature. We also show that even when the fin appears flat, the ray geometry leads to a "functional curvature", i.e. morphological elements that couple ray bending and membrane stretching.