  We develop the fundamentals of nonlinear and anisotropic bending behavior of
biomimetic scale plates using a combination of analytical modeling, finite
element (FE) computations, and motivational experiments. The analytical
architecture-property relationships are derived for both synclastic and
anticlastic curvatures. The results show that, as the scales engage, both
synclastic and anticlastic deformations show non-linear scale contact
kinematics and cross-curvature sensitivity of moments resulting in strong
curvature-dependent elastic nonlinearity and emergent anisotropy. The
anisotropy of bending rigidities and their evolution with curvature are
affected by both the direction and magnitude of bending as well as scale
geometry parameters, and their distribution on the substrate. Like earlier
beam-like substrates, kinematic locked states were found to occur; however,
their existence and evolution are also strongly determined by scale geometry
and imposed cross-curvatures. This validated model helps us to quantify bending
response, locking behavior, and their geometric dependence, paving the way for
a deeper understanding of the nature of nonlinearity and anisotropy of these
systems.
