Application of Iso-Strain Boundary Conditions to Deduce Orthotropic Elastic Constants of Biomineralized Fish Scale

Abstract

The Atractosteus spatulas (Alligator gar) was used as the model structure for computational analysis to estimate elastic properties. The Alligator gar possesses a flexible dermal armor consisting of overlapping ganoid scales. Each scale is a bilayer hydroxyapatite and collagen-based biocomposite and is thought to be used for protection against predators. The exoskeleton fish scale is comprised of a stiff outer ganoine layer, a characteristic “sawtooth” pattern at the interface and a compliant bone inner layer with all materials exhibiting a decreasing elastic modulus from the external to the internal layers. Scanning electron microscopy (SEM) images of the cross section of gar fish scales revealed a two-layered structure. Nanoindentation measured modulus was correlated to structural changes across the scale’s layers. Piecewise linear grading functions were used to vary the properties within and between layers as well as explicit modeling of the sawtooth interface geometry. The fish scale composite was computationally modeled using a representative volume element (RVE). The model used iso-strain boundary conditions to determine the full elastic tensor for the composite system. Using isotropic behavior for individual elements, the results show that the RVE exhibits orthotropic symmetry with slight variations due to the sawtooth interface.