  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.
