## 3 Results
The application of compressive stress to materials leads to their shortening, such that when the maximum compressive strength is reached, buckling (sudden change in form/shape under deformation) and then structural failure occurs. The yielding point is the limit moment of elastic behavior and the beginning of the plastic one. Below the yielding point, the material will suffer from elastic deformation (returning to original form if stress is removed), while if this yielding point is passed, the deformation will be permanent and non-reversible, ending with the fracture of material. Polymers are also considered as ductile materials suffering from plastic deformation. Brittle materials (e.g., glass, stone, clay, concrete, cast iron) suffer from extremely small deformations (usually non-recoverable) before fracture/destruction occurs. There are also materials that have a more ductile behavior depending upon the temperature (i.e., higher or lower) called thermoplastic materials (soft and hard). Soft thermoplastic materials suffer from a wide range of plastic deformation (i.e., copper, gold, steel, rubber). Hard thermoplastics suffer a minimal plastic deformation (e.g., plastic, rubber, crystal). For liquids/gas, pressure criteria were specially designed since there are no shear stresses in their biomechanical behavior. The internal structure of materials (i.e., homogenous, non-homogenous) is important in accurately describing their behavior [7; 10; 11; 13]. For ductile materials, Tresca is designed for non-homogenous materials, while Von Mises for homogenous ones [7; 10; 11; 13]. For brittle materials, Maximum Principal Tensile S1 and Compressive S3 stresses accurately describe their behavior. For liquids and gases, pressure criteria are suitable [7; 10; 11; 13]. In our analysis all five of the above failure criteria were assessed. The analyzed bracket was made of stainless steel and considered a ductile material. The enamel component is a brittle material due to its micro-architecture and physical properties [8; 12; 15; 16; 18]. Nevertheless, the enamel component accounts for only an extremely small percentage of the total volume of the tooth, while all other tooth components (dentine, cement, dental pulp, and neuro-vascular bundle) are considered of ductile resemblance. Thus, from the biomechanical point of view, the tooth structure behaves as a ductile non-homogenous material with a certain brittle mode flow, being accurately described by VM and T failure criteria [8; 11; 13; 14; 15]. Moreover, biomechanically speaking, a small orthodontic force of 0.5 N produces extremely small movements able to display an almost linear-elastic behavior [10; 11; 13; 24; 25]. If brittle materials or liquid/gas criteria are used in these conditions, the biomechanical description of stress distribution and dissipation might not be entirely correct [10; 11; 12; 24; 25]. Previous studies [10; 11; 13; 24; 25] analyzing the description of the biomechanical behavior of the tooth and surrounding periodontitis under small orthodontic forces (0.5 N) during periodontal breakdown have been reported for PDL, dental pulp, NVB, and tooth structure ductile resemblance, where only T and VM criteria are suitable (with T providing the better accuracy), while S1, S3, and HP provided inaccurate results [10; 11; 13]. Here, the results agree with these findings, proving that Tresca and Von Mises criteria are better suited for the analysis of stainless-steel brackets and enamel. A stress increase was also reported in the apical, middle, and cervical third of the PDL, and radicular dentine correlated with the progression of periodontal breakdown, with visible increase in color-coded stress display areas and quantitative results (all lower than MHP of 16 KPa) [10; 11; 13].