Multi-scale modeling and mechanical performance characterization of stingray skeleton-inspired tessellations

Abstract

Sharks and rays have distinctive skeletons among vertebrate animals, consisting primarily of unmineralized cartilage wrapped in a surface tessellation of minute polygonal tiles called tesserae, linked by unmineralized collagenous fibers. The discrete combination of hard and soft tissues is hypothesized to enhance the mechanical performance of tessellated cartilage (which performs many of the same functional roles as bone) by providing either rigidity or flexibility, depending on the nature of the applied load. These mechanisms and the effect of tesserae ultrastructure on cartilage mechanics, however, have never been demonstrated in the actual tissue, nor in bio-accurate models. Here, we develop bio-inspired three-dimensional tesserae computer models, incorporating material properties and ultrastructural features from natural tessellated cartilage. The geometries of ultrastructural features were varied parametrically, and the effective modulus of whole tesserae was evaluated using finite element analysis (FEA) to determine the roles of ultrastructural features in mechanics. Whereas altering some structural features had no effect on the macroscopic in-plane modulus of tesserae, a three-fold increase in the contact surface area between two adjacent tesserae increased the effective modulus of tesserae by 6%. Modeled stress distributions suggest that tesseral ‘spokes’ (distinct hypermineralized features in tesserae) bear maximum stresses in the skeleton and serve to funnel stresses to particular populations of cells in tesserae, while spokes’ lamellated structure likely helps dissipate crack energy, making tesserae more damage-tolerant. Simulations of multi-tesseral arrays showed that maximum stresses in tension and compression are borne by different tissues, supporting hypotheses of multi-functional properties of tessellated cartilage. Further, tesseral array models showed that minor alterations to tesserae/joint shape and/or material properties can be used to tune the mechanical behavior of the whole tiled composite. Our models provide the first functional understanding of the distinct morphologies of spokes and of ‘stellate’ tesserae (a tesseral shape observed first over 150 years ago), while also being useful drivers for hypotheses of growth, mechanics, load management, and the prevention and ‘directing’ of cracks in tessellated cartilage, as well as other biological composites. Additionally, these results establish guidelines and design principles for bio-inspired, tunable tiled materials.