Bending mechanics of biomimetic scale plates

Abstract

Dermal scale-inspired structures are a unique class of multi-material systems that can exhibit significant nonlinearity and evolving anisotropy, even in small strains. In this work, architecture–property relationships are derived for both synclastic and anticlastic curvatures of the plate using analytical modeling, finite elements, and experiments. The developed model outlines analytical relationships between geometry, deformation, and bending response of the system. 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 curvatures are affected by both the direction and magnitude of bending, as well as scale geometry parameters, and their distribution on the substrate. Similar to 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.