instrumented indentation. In the present analysis, simulated indentation results are compared with experimental record. 4.1. Experimental Indentation Measurements Experimental measurement of a spherical-head micro-indentation on the occlusal and transverse surfaces of an enamel sample with a radius of 200ȝm was conducted. The modulus of occlusal surface was measured as Enorm=56.5 ± 2.3GPa and the modulus of the transverse surface was measured as Etran=34.5 ± 3.8GPa using Oliver and Pharr method. The ratio of Etran / Enorm = 0.61 is close to Etran / Enorm = 0.57 reported by He’s group [14] where for shallower indentations (contact radius of ~3ȝm) was used. Measurements on the local elastic moduli of an enamel sample using atomic force acoustic microscopy exhibited 40~50% difference between the moduli of local properties which approximately correspond to the local property ET and EL in the model [15]. 4.2. Finite Element Model Using the unit cell in as the primary geometry, large meshes are constructed for the indentation simulations. Since the model possesses only single symmetry, half geometry must be modeled. After testing several model sizes (must be large enough to avoid boundary effects), we have chosen a model contains 6u12u22 = 866 unit cells with 42u84u168ȝm. Note that the length along the out-of-plane or the prism rod axis is adjusted for each element layers while the in-plane dimensions are kept the same. The total number of elements is 207,360. Due to the monoclinic nature of material properties, the large depth was needed to exclude the bottom boundary effects. 4.3. Indentation Results Displacement controlled indentation was simulated for different local property ratios (ET / EL = 0.1, 0.2, 0.5) up to the maximum depth of 1ȝm The effective stress contours are shown in Fig. 8 for three different load levels. Unlike homogenous materials, they clearly show discontinuous stress fields as the material properties are heterogeneous. The large stress shown in red indicates stiffer response of head region of key-hole shaped prism rods. Note also that the large stresses appear to propagate to the bottom instead of remain near the indentation. Again these are the results of unique tooth enamel microstructure. The indented load-displacement curves are shown in Fig. 9 for three different ratios of ET / EL. As the ratio decreases, the response becomes more compliant. For a comparison, the experimentally obtained data is also shown in the figure. Here the loading portion appears to agree with the ET / EL = 0.2 simulation results. However the unloading curve (also shown at a Fig. 8. Effective stress contours during the indentation for the heterogeneous model for ET / EL = 0.2. >300MPa 0.45PmSpherical head Indenter (R=200Pm) ' = ' = 1.0Pm ' = 0.77Pm 177
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