Discrete element models of fracture in tooth enamel: Failure mode competition and statistical effects

Abstract

Capturing how cracks initiate and propagate in tooth enamel is difficult because of the complex three-dimensional microstructure of this material. In this work we use the discrete element method (DEM) to model fracture in idealized enamel structures where the enamel rod microstructure is explicitly represented with DEM elements. The model captures the interactions of a propagating crack with the mineral rods and their interfaces, including crack deflection and penetration into the rods. We used this model to assess the effect of relative strength and stiffness between the rods and the interfaces, of the decussation angle, and of statistical distributions of defects in the mineral rods. We show that higher strength rods (smaller flaws) promote interface crack deflection and branching which increases toughness through spreading of an inelastic region. Stiffer rods increase the load carried by the rod, which ultimately decreases crack resistance. Statistical variations in rod strength were shown to have an overall negative impact on the average crack resistance. In particular, for high coefficients of variation we observed substantial nucleation of ‘daughter’ cracks far from the main crack, which steer the main crack along the weakest trajectories and decrease overall toughness. This model and results provide insights to better interpret fracture experiments in human or bovine enamel, as well as better guidelines for the design of synthetic dental and bioinspired materials.