## 1 Introduction  
Many patients suffering from periodontal disease need orthodontic treatment. Nevertheless, a reduction in periodontal support (i.e., bone and periodontal ligament--PDL) affects the biomechanical behavior of the tooth during various orthodontic movements [1; 2; 3; 4; 5]. The bracket and enamel components of the tooth are the first to suffer from stresses produced by orthodontic force application. The most sensitive area is the internal side of the bracket where the bracket-cement-enamel bond/attachment is found and the failure usually occurs (i.e., 6-28.3% of the failure rate, especially in posterior teeth mandibular [1]) [1; 2; 3; 4; 5]. Among the consequences of the failure of the bracket bond are the complication of the movements and fine adjustments due to difficulty in finding the original position and angulation of the bracket and the increase in treatment time [1; 2]. This type of failure is due to interference with contact loading, incorrect bonding procedures, fatigue of the bonding material, and/or the association of these factors [1; 2]. Moreover, the slot walls are also subjected to various forms of deformation that significantly influence the biomechanical stress distribution in the bracket and enamel depending on the bracket and arch materials, geometry, dimensions, and applied forces [5; 6]. There are studies [1; 2; 3; 4; 5; 6; 7] limited only to the assessment of the stress distribution in the bracket (either in the slot walls or on the attachment/internal side), but no studies describing how the progress of periodontal breakdown influences the stress distribution in the bracket and enamel (or in the tooth and PDL) were found. A clear image of the stress distribution and dissipation that occurs in the bracket and enamel is possible only via in vitro experiments and finite elements analysis (FEA) [1; 2; 3; 4; 5; 6; 7]. In vitro tests allow us to identify the maximum amount of force to be applied and maximum bond strengths (e.g., brackets attached to various types of surfaces subjected to machine testing loads), but do not provide any data regarding the stress distribution and absorption or the areas suffering from higher stresses (since the bonding area is not equally loaded) [1; 2; 3]. There are also reports of variable changes in physical properties of teeth subjected to in vitro experiments [8]. Other reports considered FEA analysis to be superior to in vitro experiments regarding accuracy due to issues in modeling and validation [9]. On the other hand, FEA studies can accurately reconstruct the anatomical tissues and properties compared with in vitro studies where the tooth is integrated with various materials not resembling human tissue [9]. Earlier reports showed that shear, compressive, and tensile stresses are not homogenous, with the weak point being a void, a crack, or the border of the bracket [2; 3]. Nevertheless, the FEA method also has limitations, the most significant being that it cannot accurately reproduce the complexity of clinical situations. Cement is a brittle material that has no elastic deformation, ending rapidly in the fracture and debonding of the bracket [2]. The bracket is made of several types of materials, the most common being stainless steel (a ductile material) and ceramics (a brittle material), which behave completely differently biomechanically when subjected to orthodontic stresses [2; 3]. According to the material's yielding theory, the ductile materials have the ability to undergo various reversible elastic deformations (before the plastic one occurs), while the brittle materials suffer directly from various plastic deformations closely followed by buckling (changes in shape under loads) and fracture. Despite the acknowledged engineering data related to the type of material (brittle, ductile, liquid, and gas) with the specific failure criteria, its use in dental studies is almost nonexistent (except for a few studies [10; 11; 12; 13]).