## 3 Results
The quantitative wall deformations for stainless-steel were 0.3 \(\upmu\)m top, 0.1 \(\upmu\)m middle, and 0 \(\upmu\)m bottom (for 4 N) and up to 44.8 \(\upmu\)m top, 36.8 \(\upmu\)m middle, and 9.28 \(\upmu\)m bottom (for 28.5 N), while titanium deformed two to four times more. In both models of bracket (stainless steel and titanium), deformations were exclusively found at the slot walls, while the base of the bracket and the internal side/attachment suffered no deformation (which is biomechanically unusual, suggesting no bond failure risks and contradicting clinical-data-related knowledge). Biomechanically, the slot walls, through deformations, absorb and dissipate the applied force (e.g., an applied torque of 7.14 N generating a torque of 4 N), but there should be stress areas in the attachment side of the bracket since it transmits the movement to the tooth, while the average reported risks of bond failure are up to 28.3% [1]. Moreover, in our study, the applied force was 0.5 N (eight times lower than [PERSON] et al. [5]) and generated stress areas in the attachment side and entire base of the bracket, confirming stress distribution areas and risks of bond failure [1]. [PERSON] et al. [3] investigated bond strength (intrusion/extrusion, translation, and tipping) of three type of brackets (stainless steel, 68,192 elements/99,487 nodes; ceramic, 73,922 elements/108,071 nodes; and titanium, 60,599 elements/80,019 nodes) on upper central incisors by qualitatively and quantitatively assessing shear stress and maximum principal stress, with (200 \(\upmu\)m height) and without adhesive/cement. They reported that shear loading at the short side (e.g., intrusion/extrusion) of the bracket resulted in the highest bond strengths and the lowest maximum principal stress on both the cement and enamel compared with other loading modes. They also concluded that the manner of loading and choice of bracket materials influence the bond strength and stress distribution. Our results agreed with some of these reports (i.e., intrusion/extrusion movements are less harmful than rotation and translation, while the loading conditions are extremely important for stress distribution). However, their study unusually displayed stress areas located only at the edges of the bracket's internal surface, suggesting that the entire base of the bracket suffers no stress (biomechanically debatable if the yielding and failure behaviors of materials are acknowledged), which opposes our simulation results, where, with no exception, the entire surface of the bracket had various color-coded stress areas. [PERSON] et al. [2] (in vitro and FEA experiments) studied the shear and tensile bond strengths of metal brackets in an FEA analysis limited only to the bracket and a small enamel wall (100 N of intrusion, translation, and tipping on a stainless-steel bracket with 23,392 elements in isotropic, homogenous, and linear elasticity conditions) and reported that the stress distribution in the bracket-cement-enamel system is not homogeneous, in agreement with our results. They [2] also reported that bracket design and loading method is more important (i.e., direct correlation between loading and stress distribution) for the bond strength than the size of the bonding area, which is also in line with our research. In the color-coded stress distribution [2], the stress areas in the internal surface of bracket had various displays: For 100 N of translation, a maximum shear stress of 20.6 MPa appeared at the edge of loading side (similarly for 100 N of intrusion and 15.9 MPa), with a progressive decrease toward force-free side, which is comparable with our qualitative and quantitative results (0.384-0.5 MPa for 0.5 N of translation and 0.15 MPa for 0.5 N of intrusion).