## 1 Introduction
It would therefore be of clinical importance to have a simulation of stress distribution in bracket and enamel components during the periodontal breakdown process to find the areas with highest stresses for a better understanding of bracket bond failures and their prevention. FEA allows the individual assessment of stress distribution in the bracket and enamel, but for correct results, the type of analyzed material (ductile of brittle) needs to be considered, since each failure criterion is designed to accurately describe a certain biomechanical behavior. In dental studies the most used failure criteria are the Von Mises (VM) [9; 12; 19; 20; 21; 22; 23] and Tresca (T) [10; 11; 13; 24; 25] criteria designed for ductile materials, the Maximum Principal S1 tensile [12; 20; 26; 27; 28; 29] and Minimum Principal S3 compressive [12; 26; 27; 29; 30; 31; 32] stresses designed for brittle materials, and Hydrostatic pressure (HP) [33; 34; 35; 36; 37] designed for liquids and gases. Additionally, variables such as force levels [38] and mechanical characteristics of orthodontic wires [39] should also be taken into consideration. Nevertheless, there are no studies besides our earlier ones [7; 10; 11; 13; 24; 25] which address this essential issue for the accuracy of the FEA method. Current FEA studies of stress distributions in brackets are concentrated on identifying the bond strength of several types of brackets and stresses in bracket-cement-enamel structures [1; 2; 3]. FEA analysis is usually used to assess the shear bond strength (i.e., 4-10 MPa of Reynolds) and tensile bond strength (i.e., 6-8 MPa of Reynolds) [1; 2; 3], correctly applicable if the analyzed materials are either entirely brittle or ductile. The slot size of the bracket (e.g., reports of 0.018-inch brackets supplying a better torque control than 0.022-inch brackets) and arch diameter, material, and form had equally considerable influence over FEA stress distributions [4]. The bracket slot walls, depending on their design and materials, suffer from several types of deformations [5; 6] that could alter FEA results if the entire tooth's biomechanical behavior is not assessed. However, since previous reports [1; 2; 3; 4; 5; 6] have only concentrated on assessing a small region of the tooth (i.e., artificially designed and 3D modeled [1; 2; 3]) without taking into consideration the analysis of a larger structure, such as the bracket or entire enamel component (i.e., the crown) or tooth and its surrounding supporting structures (improving thus the knowledge), they do not address the problem of selecting the adequate failure criteria in their FEA analyses. Moreover, if analyzed structures are made of different types of materials (i.e., enamel, cement, and ceramic brackets are brittle, while stainless-steel brackets are ductile) in relatively equal percent proportions, the failure criteria must be carefully selected due to their specific mathematical design to better describe the ductile or brittle materials' behaviors [10; 11; 13; 24; 25]. However, if the brittle/ductile material represents only an extremely small percentage of the entire volume of an analyzed structure, the failure criteria that best describe the predominant material's type of structure should be employed [7; 10; 11; 13; 24; 25]. These FEA studies [1; 2; 3] reported that shear loading at the short side of the bracket produced the highest bond strength and lower tensile stress, with ceramic having a higher strength than stainless steel. Moreover, due to the different behavioral mechanical meanings, the tensile bond strength should not be compared with the shear bond strength (Reynolds interval used as reference) [1]. Nevertheless, to find the actual shear bond strength, only pure shear force should be applied directly to bracket-adhesive interface, which is extremely difficult, even in an FEA [1].