A representative volume element based micromechanical analysis of a Bi-layered Ganoid Fish scale

Abstract

The Mississippi Alligator gar (Atractosteus spatula) possesses a flexible exoskeleton armor consisting of overlapping ganoid scales used for predatory protection. Each scale is a two-phase biomineralized composite containing bio-modified hydroxyapatite (hard) minerals and collagen (soft) fibers. The protective layer consists of a stiff outer ganoine layer, a characteristic “sawtooth” pattern at the interface with the compliant bone inner layer. The garfish scale exhibits a decreasing elastic modulus from the external to the internal layers. Scanning electron microscopy (SEM) images of the cross-section revealed a two-layered structure. Elastic moduli, measured from nanoindentation experiments, were correlated to structural changes across each layer. The “material” symmetry of this materially and geometrically nonlinear biomineralized composite is unknown. Therefore, to be able to determine the stiffness tensor requires the use of finite element analysis (FEA). The gar fish scale was computationally modeled using the representative volume element (RVE) based approach. As a result, the unknown symmetry induced by the architecture and material layering require the use of complex FEA boundary conditions. The simulation was conducted in the pure uniaxial strain regimes of tension and shear, which necessitated the mathematical determination so appropriate surface loading conditions could be applied. This paper provides the results from a highly-resolved mesoscale RVE model based on iso-strain boundary conditions (ISBC) to determine the elastic stiffness tensor for the composite system. By assuming isotropic behavior in individual elements, the results for the RVE reveal the fish scale has an “orthotropic symmetry” with slight local strain variations occurring at the sawtooth interface.