The Poisson's ratio of dentin as anisotropic medium with hexagonal symmetry

The Poisson's ratio (coefficient of transverse deformation) plays an important role in the deformation behavior of materials. Along with the Young's module, it constitutes a pair of independent and most informative material constants of solids. For hard tissues of the tooth (enamel and dentin), the Poisson's ratio should correspond to the Poisson's ratio of restorative materials in order to avoid overstresses at the boundary of the sections restorative material-enamel and restoration material-dentin. In addition, the value of the Poisson's ratio affects the deformation strength of enamel and dentin, namely, crack resistance, when they occur in a stress-strain state. In this paper, the orientational dependence of the Poisson's ratio of teeth dentin on the basis of matrices of elastic constants and the compliance coefficients of hexagonal crystals, such as crystals of dentine hydroxyapatite, was obtained for the first time. The results of calculating the Poisson's ratios of dentin as a crystalline system with a hexagonal structure are presented in the form of tables and diagrams in the polar and Cartesian coordinate systems. The minimum and maximum coefficients for the corresponding directions of the longitudinal and transverse deformations in the crystallographic coordinate system are also calculated. It is shown that the maximum value of the Poisson's ratio of dentin (0.53) is greater than the upper limit for the Poisson's ratio of isotropic materials, including known restoration materials, which in some cases may reduce the quality of restorations. It is noted that a similar analysis can be performed for tooth enamel.