A micromechanics model of the elastic properties of human dentine.

A generalized, self-consistent model of cylindrical inclusions in a homogeneous and isotropic matrix phase was used to study the effects of tubule orientation on the elastic properties of dentine. Closed-form expressions for the five independent elastic constants of dentine were derived in terms of tubule concentration, and the Young's moduli and Poisson ratios of peri- and intertubular dentine. An atomic-force microscope indentation technique determined the Young's moduli of the peri- and intertubular dentine as approx. 30 and 15 GPa, respectively. Over the natural variation in tubule density found in dentine, there was only a slight variation in the axial and transverse shear moduli with position in the tooth, and there was no measurable effect of tubule orientation. It was concluded that tubule orientation has no appreciable effect on the elastic behaviour of normal dentine, and that the elastic properties of healthy dentine can be modelled as an isotropic continuum with a Young's modulus of approx. 16 GPa and a shear modulus of 6.2 GPa.