Bending of Biomimetic Scale Covered Beams Under Discrete Non-periodic Engagement

Abstract

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.