  Covering elastic substrates with stiff biomimetic scales significantly alters
the bending behavior via scales engagement. This engagement is the dominant
source of nonlinearity in small deflection regime. As deformation proceeds, an
initially linear bending response gives way to progressive stiffening and
thereafter a geometrically dictated 'locked' configuration. However,
investigation of this system has been carried out until date using assumption
of periodic engagement even after scales contact. This is true only under the
most ideal loading conditions or if the scales are extremely dense akin to a
continuum assumption on the scales. However, this is not true for a practical
system where scales are more discrete and where loading can alter periodicity
of engagement. We address this nonlinear problem for the first time in small
deflection and rotation regime. Our combined modeling and numerical analysis
show that relaxing periodicity better represents the geometry of discrete
scales engagement and mechanics of the beam under general loading conditions
and allows us to revisit the nonlinear behavior. We report significant
differences from predictions of periodic models in terms of predicting the
behavior of scales after engagement. These include the difference in the
angular displacement of scales, normal force magnitudes along the length,
moment curvature relationship as well as a distinct nature of the locking
behavior. Therefore, non-periodicity is an important yet unexplored feature of
this problem, which leads to insights, absent in previous investigations. This
opens way for developing the structure-property-architecture framework for
design and optimization of these topologically leveraged solids.
