Mechanics and properties of fish fin rays in nonlinear regimes of large deformations.

Fins from ray-finned fishes do not contain muscles, yet fish can change the shape of their fins with high precision and speed, while producing large hydrodynamic forces without collapsing. This remarkable performance has been intriguing researchers for decades, but experiments have so far focused on homogenized properties, and models were developed only for small deformations and small rotations. Here we present fully instrumented micromechanical tests on individual rays from Rainbow trout in both morphing and flexural deflection mode and at large deflections. We then present a nonlinear mechanical model of the ray that captures the key structural elements controlling the mechanical behavior of rays under large deformations, which we successfully fit onto the experiments for property identification. We found that the flexural stiffness of the mineralized layers in the rays (hemitrichs) is 5-6 times lower than their axial stiffness, an advantageous combination to produce stiff morphing. In addition, the collagenous core region can be modeled with spring elements which are 3-4 orders of magnitude more compliant than the hemitrichs. This fibrillar structure provides negligible resistance to shearing from the initial position, but it prevents buckling and collapse of the structure at large deformations. These insights from the experiments and nonlinear models can serve as new guidelines for the design of efficient bioinspired stiff morphing materials and structures at large deformations. STATEMENT OF SIGNIFICANCE: Fins from ray-finned fishes do not contain muscles, yet fish can change the shape of their fins with high precision and speed, while producing large hydrodynamic forces without collapsing. Experiments have so far focused on homogenized properties, and models were developed only for small deformations and small rotations providing limited insight into the rich nonlinear mechanics of natural rays. We present micromechanical tests in both morphing and flexural deflection mode on individual rays, a nonlinear model of the ray that captures the mechanical behavior of rays under large deformations and combine microCT measurements to generate new insights into the nonlinear mechanics of rays. These insights can serve as new guidelines for the design of efficient bioinspired stiff morphing materials and structures at large deformations.