Effect of property gradients on enamel fracture in human molar teeth

A model for the fracture of tooth enamel with graded elastic modulus and toughness is constructed using an extended finite element modeling (XFEM) package. The property gradients are taken from literature data on human molars, with maximum in modulus at the outer enamel surface and in toughness at the inner surface. The tooth is modeled as a brittle shell (enamel) and a compliant interior (dentin), with occlusal loading from a hard, flat contact at the cusp. Longitudinal radial (R) and margin (M) cracks are allowed to extend piecewise along the enamel walls under the action of an incrementally increasing applied load. A simple stratagem is deployed in which fictitious temperature profiles generate the requisite property gradients. The resulting XFEM simulations demonstrate that the crack fronts become more segmented as the property gradients become more pronounced, with enhanced propagation at the outer surface and inhibited propagation at the inner. Whereas the growth history of the cracks is profoundly influenced by the gradients, the ultimate critical loads required to attain full fractures are relatively unaffected. Some implications concerning dentistry are considered.