3.2. Computed Elastic Constants The effective mechanical properties determined from the six loading cases for various ET / EL ratios are determined. The effective stress contours of the local property ratio of ET / EL = 0.2 shown in Fig. 6 indicate large stresses along the boundaries of enamel rods. This may imply an enamel rod boundary is the most likely location where micro-crack would occur under critical or repeated loading due to locally high strains which will disrupt the HAp crystal-protein composite. Computed elastic constants (1) for five different ratios of ET / EL are shown in Fig. 7. Here EL is fixed at 100GPa. As ET changes, large variations on normal stress-strain constants C11, C22 and C33 are observed. In fact, in-plane components C11 and C22 drop to very small values as ET decreases to zero. These behaviors are expected since the HAp fibers are oriented more along the z-axis and the stiffest direction is always along the prism rod axis. This has implications to understanding the structure of the enamel rods in the tooth crown, where the rod heads point in the direction of the tooth cusp around the entire circumference of the tooth. The data indicates that the higher stiffness in the direction of the head-tail may allow enamel to absorb compressive stresses that are generated due to occlusal contact conditions (such as mastication with the primary molars). Other components also change as the ratio of ET / EL changes. In order to verify the accuracy of the present procedure, a homogenized model with these monoclinic constants is separately analyzed. Using the same finite element mesh, the model was then reloaded in similar ways and then the resulting displacements are compared with the original model with inhomogeneous model (i.e., elements with transversely isotropic properties with variable fiber orientations). The differences among them are less than 0.01% for all of the components in averaged strain and stress fields for every ET / EL ratio. 4. Instrumented Indentation One possible method to determine accurate values for the local transversely isotropic model (e.g., ET and EL) is to utilize Fig. 7. Effects local modulus ratio (ET/EL) assigned for local transversely isotropic model on the 13 elastic constants of effective monoclinic model. Isotropic limit 0.0 0.2 0.4 0.6 0.8 1.0 ET / EL Stiffness Constants (GPa) C33 C22 C11 C44, C55, C66 C12, C13, C23 C14, C24, C34, C56 -20 0 20 40 60 80 100 120 176
RkJQdWJsaXNoZXIy MTMzNzEzMQ==