A Three-dimensional Finite Element Model of Prismatic Enamel: A Re-appraisal of the Data on the Young's Modulus of Enamel

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Abstract
The inconsistencies of published data on the Young's modulus of dental enamel, the parameter used to quantify stiffness, have, for a long time, restricted our understanding of the biomechanical behavior of teeth. With the use of modeling techniques, the aim of this paper is to investigate which of the data may be more reliable. In this way, the possible causes of the discrepancies in data will be addressed. Two different structural levels are considered within the model. At an ultrastructural (i.e., crystalline) level, the model considers enamel to behave as a simple composite, being made up of long, parallel crystals held together by an organic matrix. At this level, the stiffness of enamel is predicted by simple composite theory, and the model indicates that stiffness is dependent on chemical composition and crystal orientation. At a microstructural (i.e., prismatic) level, the model considers enamel to behave as a hierarchical composite, being made up of prisms, in which the crystal orientation is heterogeneous. At this level, the stiffness of enamel is predicted by finite element stress analysis, and values of predicted stiffness are found to be dependent on both chemical composition and prism orientation. Within a realistic compositional range, predicted values of Young's modulus along the direction of prisms are comparable with the corresponding experimental values of 77.9 ± 4.8 GPa obtained by Craig et al. (1961) and 73 GPa obtained by Gilmore et al. (1970), but not with those low values of 9.65 ± 3.45 obtained by Stanford et al. (1960). Predictions of Young's modulus values across the direction of prisms are also made, and the model is less stiff in this direction. These findings indicate that human prismatic enamel is almost certainly anisotropic with respect to stiffness.