Meeting Abstract
Rayed fish use their lightweight pectoral fins, comprised of bony rays and a membranous skin fold, for propulsion, steering, and maneuvering and need sufficient bending stiffness to exert hydrodynamic forces. Previous mathematical work identified the principle of curvature-induced stiffness as a key factor for the bending stiffness of rayed fins. The underlying mechanics, demonstrated by slightly curling a dollar bill to stiffen it, arises from the coupling of longitudinal bending and in-plane stretching due to curvature. By examining the internal morphology of a mackerel pectoral fin, the past work hypothesized that even an externally flat fin may manifest functional curvature and exhibit the same mechanics as a curved structure. Functional curvature couples bending and stretching because the preferred bending directions of adjacent rays are misaligned and bending the fin rays stretches the membrane. Here, we experimentally demonstrate stiffening due to functional curvature through load-displacement tests on intact and membrane-transected pectoral fins of the mackerel (Scomber scombrus). The fin was removed from the body and rays were clamped 1-2 mm distal to the radial joint before mounting on a force sensor. The distal fin was vertically displaced by a knife-edge and the reaction force was recorded. Then, without removing the fin from the clamp, the membrane connecting adjacent fin rays was incised for the proximal-distal extent of each ray and the test was repeated. Upon transecting the membrane, the elastic energy (area under the load-displacement curve) was substantially reduced, by 23% and 57% for two fins that we tested. Importantly, the fins were held externally flat. Therefore, these results support the hypothesis that functional curvature is manifested within the internal structure of the mackerel pectoral fin.
