## 2 Materials and Methods
In this context, to ensure a relevant and reproducible comparison of the analyzed scenarios, a standardized loading model was adopted, allowing for linear parametric analysis. This model incorporates both vertical (axial) and horizontal (lateral) components, applied at the occlusal contact point, in accordance with data from the scientific literature [26]. To accurately replicate the biomechanical behavior of the dento-periodontal system, the constraints applied in the simulation were designed to mimic the anchorage (fixation) of the premolar within the dental alveolus. The external surface of the periodontal ligament was restricted in translation but allowed minor physiological rotations (<0.1\({}^{\circ}\)), reflecting its damping capacity. Additionally, the root apex was rigidly connected to a global reference point, simulating dental stabilization within the alveolar bone. This configuration enabled the identification of compression zones in the regions where the force was applied, as well as in the support area, through the analysis of the resulting images. Complemented by the adoption of a homogeneous loading model, this approach facilitated a linear parametric analysis of masticatory force distribution [26]. Additionally, both tensile and compressive zones were observed in the studied region. These findings support clinical observations indicating that improperly fabricated or applied materials may lead to the formation of cracks and, consequently, to erosion. After the introduction of all necessary data, the next step involved solving the systems of differential equations that described the studied process. The results obtained could be visualized using a color-coded scale or presented in alphanumeric format. The correct interpretation of these data requires a thorough understanding of the mathematical principles underlying the analysis, as well as the theories of material strength, such as the von Mises and Mohr-Coulomb criteria or thermal analysis. These areas of knowledge are essential to ensure accurate and meaningful results [31]. The [PERSON] stress criterion is based on the Mises-Hencky theory, also known as the maximum distortion energy theory or the shear energy theory. By defining the principal stresses as \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\), the von Mises stress is expressed as follows [32]:  
\[\sigma_{\text{von Mises}}=\left[\frac{\left(\sigma_{1}-\sigma_{2}\right)^{2}+ \left(\sigma_{2}-\sigma_{3}\right)^{2}+\left(\sigma_{1}-\sigma_{3}\right)^{2 }}{2}\right]^{\frac{1}{2}} \tag{3}\]  
This theory states that a ductile material begins to deform at the point where the von Mises stress exceeds the yield stress (\(\sigma_{\text{limit}}\)). In most cases, the ultimate tensile strength is used as the limit stress. However, using specialized software allows for the input of a custom yield stress based on the following condition: (\(\sigma_{\text{von Mises}}\geq\sigma_{\text{limit}}\)) [26]. Additionally, the shear stress (\(\tau\)) is also a defining characteristic for \(\sigma_{\text{von Mises}}\), expressed as follows:  
\[\sigma_{\text{von Mises}}=(3)^{\frac{1}{2}}\cdot\tau \tag{4}\]  
For \(\tau_{\text{max}}=0.577\)\(\sigma\), the failure phenomenon occurs. \begin{table}
\begin{tabular}{c c c} \hline
**Applied Forces (N)** & **Amalgam** & **Composite** \\ \hline
200 & Stable, no risk of fracture, good tolerance & Stable, no risk of cracking, effective bonding \\ \hline
400 & Stable, microcracks possible near margins & Possible microcracks if bonding is suboptimal \\ \hline
600 & Risk of marginal fracture, especially in large cavities & Potential debonding or marginal microcracking, bonding under stress \\ \hline
800 & Increased risk of coronal and marginal fracture, brittle behavior & Bonding fails, risk of internal cracks, less brittle than amalgam \\ \hline \end{tabular}
\end{table} 
Table 2: Material behavior as a function of applied forces [29; 30].