Coupled Bend-Twist Mechanics of Biomimetic Scale Substrate

Abstract

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 Cosserat kinematic formulation along with scale contact constraints. This geometrically exact model allows us to bypass the limitations of typical finite element computations inherent in these systems when deflections are large. 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 twisting but also shows previously unobserved phenomena that arise due to the coupled effects of these loads. This includes a new interpretation of kinematic locking behavior, multiple contact regimes, asymmetric sensitivities of one curvature over the other, and sharp transitions in the nonlinear moment-curvature and torque-twist behaviors reflecting the complex scale engagement patterns.