## 3 Results  
The results of this analysis (Figures 2-6, Table 2) are based on a total of 405 FEA simulations. No differences related to gender, periodontal status, or age were seen. From a qualitative point of view (i.e., color-coded projections), all five types of failure criteria displayed higher stress areas on and around the bracket area, Figures 2-6. The stress distribution areas remained the same (with some small particularities) independently of levels of bone loss, suggesting that periodontal breakdown does not change the stress distribution pattern from 0 to 8 mm of tissue loss. As expected, the maximum stress areas were displayed on sites/surfaces of applied force, on the internal surface of the brackets, and on the enamel around the bracket area. The Von Mises (maximum overall/equivalent stress) and Tresca (maximum shear stress) criteria displayed similar stresses and visible distribution patterns for all five movements and periodontal breakdown levels (0-8 mm), opposite to the other three failure criteria (Maximum Principal Tensile stress, Minimum Principal Compressive stress, and Hydrostatic Pressure). From a quantitative point of view (i.e., average numerical values in KPa), all five types of failure criteria showed comparable results, Table 2. Hydrostatic pressure criteria displayed the lowest values among all five criteria. The amount of stress displayed on the bracket (internal surface and force appliance site/surface) was higher than that displayed in the enamel component. Based on the quantitative results, rotation and translation movements seem to be the most stressful among all five types. During simulated bone loss, both T and VM showed a small variation (less than 10%) in the amounts of stress: a light increase for intrusion and extrusion, a light decrease for translation and tipping, and consistent results for rotation. The light variations were also seen for the other three criteria: a general slight increase for intrusion and extrusion and a decrease for translation; for rotation, a decrease for S1 and HP and an increase for S3; and for tipping, an increase for S1 and S3 and a decrease for HP. The quantitative results (stress displayed) of the simulations for enamel (in KPa) in this study were lower than those reported for enamel (in MPa) for maximum compressive stress of 62.2 MPa (premolars and canines) [8], maximum tensile strength of 11.5-42.1 MPa (third molar) [15], and maximum shear stress of 53.9-104 MPa (third maxillary molar) [16]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Resorption** & & & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \multirow{4}{*}{Tipping} & \multirow{2}{*}{S3} & E & \(-441.82\) & \(-452.34\) & \(-462.87\) & \(-473.39\) & \(-483.92\) & \(-474.67\) & \(465.42\) & \(-456.17\) & \(-446.92\) \\  & & B & \(-549.31\) & \(-560.34\) & \(-571.38\) & \(-582.42\) & \(-593.45\) & \(-583.00\) & \(-572.59\) & \(-562.16\) & \(-551.74\) \\  & & B ext. & \(-549.31\) & \(-557.14\) & \(-564.97\) & \(-572.80\) & \(-580.63\) & \(-573.40\) & \(-566.18\) & \(-558.95\) & \(-551.74\) \\  & & B int. & \(-441.82\) & \(-452.34\) & \(-462.87\) & \(-473.39\) & \(-483.92\) & \(-474.67\) & \(-465.42\) & \(-456.17\) & \(-446.93\) \\ \hline \multirow{4}{*}{Tipping} & \multirow{2}{*}{**Tresca**} & \multirow{2}{*}{E} & \(254.60\) & \(246.45\) & \(238.30\) & \(230.15\) & \(222.01\) & \(221.81\) & \(221.61\) & \(221.41\) & \(221.21\) \\  & & B & \(102.25\) & \(95.27\) & \(88.30\) & \(81.31\) & \(74.34\) & \(74.27\) & \(74.20\) & \(74.15\) & \(74.11\) \\  & & B ext. & \(81.79\) & \(76.76\) & \(71.74\) & \(66.70\) & \(61.07\) & \(61.60\) & \(61.50\) & \(61.40\) & \(61.42\) \\  & & B int.