Daniel C. Simkins

Young's modulus and hardness of shark tooth biomaterials

To date, the majority of studies on feeding mechanics in sharks have focused on the movement of cranial components and muscle function, with little attention to tooth properties or function. Attributes related to mechanical properties, such as structural strength, may also be subjected to natural selection. Additionally it is necessary to characterize these properties in order to construct biomechanical models of tooth function. The goal of this study was to determine hardness and elastic modulus for the shark tooth materials enameloid, osteodentine, and orthodentine. Five teeth each from one carcharhiniform species, the bonnethead Sphyrna tiburo, and one lamniform, the sand tiger shark Carcharias taurus, were utilized for nanoindentation testing. Each tooth was sectioned transversely, air-dried, and polished. Both enameloid and dentine were tested on each tooth via a Berkovich diamond tip, with nine 2 microm deep indentations per material. t-Tests were used to determine if there were differences in hardness and Youngs modulus between the tooth materials of the two species. There was no significant difference between the two species for the material properties of enameloid, however both hardness and Youngs modulus were higher for osteodentine than for orthodentine. This may be due to differences in microanatomy and chemical composition, however this needs to be studied in greater detail.

Biology meets engineering: The structural mechanics of fossil and extant shark teeth

The majority of studies on the evolution and function of feeding in sharks have focused primarily on the movement of cranial components and muscle function, with little integration of tooth properties or function. As teeth are subjected to sometimes extreme loads during feeding, they undergo stress, strain, and potential failure. As attributes related to structural strength such as material properties and overall shape may be subjected to natural selection, both prey processing ability and structural parameters must be considered to understand the evolution of shark teeth. In this study, finite element analysis was used to visualize stress distributions of fossil and extant shark teeth during puncture, unidirectional draw (cutting), and holding. Under the loading and boundary conditions here, which are consistent with bite forces of large sharks, shark teeth are structurally strong. Teeth loaded in puncture have localized stress concentrations at the cusp apex that diminish rapidly away from the apex. When loaded in draw and holding, the majority of the teeth show stress concentrations consistent with well designed cantilever beams. Notches result in stress concentration during draw and may serve as a weak point; however they are functionally important for cutting prey during lateral head shaking behavior. As shark teeth are replaced regularly, it is proposed that the frequency of tooth replacement in sharks is driven by tooth wear, not tooth failure. As the tooth tip and cutting edges are worn, the surface areas of these features increase, decreasing the amount of stress produced by the tooth. While this wear will not affect the general structural strength of the tooth, tooth replacement may also serve to keep ahead of damage caused by fatigue that may lead to eventual tooth failure. J. Morphol., 2011.

A Framework For Studying The RKEM Representation of Discrete Point Sets

The application of engineering analysis to new areas, such as nanomechanics and the life sciences, often involves geometric problem domains defined by discrete point sets as measured from diagnostic equipment. The development of a suitable mesh for finite element analysis can be a tedious task. One approach to simplifying the geometric description is to use a parametrized set of basis functions, and fit the parameters to the data set. In this paper, we discuss the problem of determining suitable parameters for the Reproducing Kernel Element Method representation of discrete point sets, and in particular the solution of the inverse problem of determining pre-image evaluation points in the parametric space that correspond to a given input point. We justify our solution by posing a theoretical framework and an error indicator.

Meshfree Modeling in Laminated Composites

A problem of increasing importance in the aerospace industry is in detailed modeling of explicit fracture in laminated composite materials. For design applications, the simulation must be capable of initiation and propagation of changes in the problem domain. Further, these changes must be able to be incorporated within a design-scale simulation. The use of a visibility condition, coupled with the local and dynamic nature of meshfree shape function construction allows one to initiate and explicitly open and propagate holes inside a previously continuous problem domain. The method to be presented naturally couples to a hierarchical multi-scale material model incorporating external knowldege bases to achieve the goal of a practical explicit fracture modeling capability for full-scale problems.