Anisotropic Elasticity of Dentin: Micromechanical Considerations

Objectives: (1) To develop a micromechanical model that relates the anisotropic elastic properties to the microstructure of dentin using a virtual bond idealization. (2) To study the average force constants and anisotropy parameters utilizing the developed model in order to understand how the dentin elasticity is affected by the presence of water. Methods: The underlying material microstructure is conceptualized as a collection of interacting grains modeled by virtual bonds. With the view of bridging behavior at nano and micro-scales, the virtual bond force-displacement relationships are formulated taking inspiration from atomic-bond interactions. The force-displacement relationships are formulated for both central and non-central interactions, denoted by the force constants Kn and Kw, respectively. The dentin microstructure is characterized by a virtual bond directional distribution function modeled by first-term of the spherical harmonic expansion denoted by anisotropy parameter a20. Results: Closed form expressions of the transverse isotropic stiffness tensor are obtained for the case of linear inter-granular interactions. These expressions are utilized to compute the force constants and anisotropy parameters for dentin. The force constants Kn and Kw, respectively are as follows (in GPa): 183.2, 0.0 (dry dentin), 199.7, 0.0 (wet dentin) based upon kinematic approach, and 196.5, 45.7 (dry dentin), 243.2, 38.3 (wet dentin) based upon static approach. The anisotropy parameter a20 are as follows 0.0 (dry dentin), -0.234 (wet dentin) based upon kinematic approach, and 0.0 (dry dentin), -0.218 (wet dentin) based upon static approach. Conclusions: The force constant for wet dentin is higher than that of dry dentin indicating that the presence of water results in the stiffening of bonds that contribute to the mechanical stiffness at the sample scale. Moreover, the anisotropy parameter of wet dentin indicates that the bond density becomes higher in the isotropy plane in the presence of water. Supported in part: NIH/NIDCR DE014392