Stress relaxation behavior of tessellated cartilage from the jaws of blue sharks

Abstract

Much of the skeleton of sharks, skate and rays (Elasmobranchii) is characterized by a tessellated structure, composed of a shell of small, mineralized plates (tesserae) joined by intertesseral ligaments overlaying a soft cartilage core. Although tessellated cartilage is a defining feature of this group of fishes, the significance of this skeletal tissue type – particularly from a mechanical perspective – is unknown. The aim of the present work was to perform stress relaxation experiments with tessellated cartilage samples from the jaws of blue sharks to better understand the time dependent behavior of this skeletal type.In order to facilitate this aim, the resulting relaxation behavior for different loading directions were simulated using the transversely isotropic biphasic model and this model combined with generalized Maxwell elements to represent the tessellated layer. Analysis of the ability of the models to simulate the observed experimental behavior indicates that the transversely isotropic biphasic model can provide good predictions of the relaxation behavior of the hyaline cartilage. However, the incorporation of Maxwell elements into this model can achieve a more accurate simulation of the dynamic behavior of calcified cartilage when the loading is parallel to the tessellated layer. Correlation of experimental data with present combined composite models showed that the equilibrium modulus of the tessellated layer for this loading direction is about 45 times greater than that for uncalcified cartilage. Moreover, tessellation has relatively little effect on the viscoelasticity of shark cartilage under loading that is normal to the tessellated layer.