Coupled bend-twist mechanics of biomimetic scale substrate

We develop the mechanics of combined bending and twisting deformation of a one-dimensional filamentous structure with protruding stiff fish-scale-like plates embedded at an angle on the surface. We develop a Cosserat kinematic formulation along with scale contact constraints. This geometrically exact model allows us to bypass the limitations of small deflection finite element computations, thereby preserving the accuracy of scale kinematics. The derived structure–property relationships reveal, for the first time, the combined effect of bending and twisting on a slender fish-scale inspired substrate. The model subsumes previous models on pure bending and pure twisting, but also shows previously unobserved phenomena that arise due to the coupled effects of these loads. These include a new interpretation of kinematic locking behavior, multiple contact regimes, asymmetric sensitivities of one curvature over the other, and discontinuous transitions in the nonlinear moment–curvature and torque–twist behaviors, reflecting the complex scale engagement patterns.