## 2 Materials and Methods  
For this study, Bone-Level (BL \(\mathcal{O}\) 3.3 mm, NC, SLActive(r) 10 mm, Roxolid(r), Guided) and Tissue-Level (SP \(\mathcal{O}\) 3.3 mm, RN, SLActive(r) 10 mm, Roxolid(r), Guided) implants were selected (Straumann Dental Implant System, Waldenburg, Switzerland). Figure 1 shows the selected implants for this study. After the abutment installation (for BL: Straumann(r) NC [Narrow CrossFit(r)] Anatomic Abutment with 2 mm gingiva height (GH), abutment height of 6.0 mm, and abutment diameter of 4.0 mm; for TL: Straumann(r) RN synOcta(r) Cementable Abutment, designed for Regular-Neck (RN) Tissue-Level implants with abutment height of 5.5 mm and abutment diameter of 4.8 mm) following the manufacturer's recommendation, each specimen was embedded in self-curing red methyl-methacrylate (Acryfix, Struers GmbH, Willich, Germany) and cross-sectioned along the longitudinal axis using a precision cutting machine under constant water cooling. The internal configuration was visually inspected and photographed under reflected-light scanning electron microscopy (XL20, Philips, Eindhoven, The Netherlands) at a 10\(\times\) magnification, and each photomicrograph was joined to create the background for the modeling step. Figure 2 shows a microscopical photo of the implant-abutment interface for the respective Bone-Level implant and Tissue-Level implant. To generate the 3D file in Standard for the Exchange of Product Data (STEP), the photomicrography figures were imported to computer-aided design software (Rhinoceros version 5.0 SR8, McNeel North America, Seattle, WA, USA) as background BMP files. Based  
Figure 1: Selected implants and abutments for this study. (**A**) Bone-Level implant. (**B**) Tissue-Level implant. Figure 2: Microscopical photo of implant–abutment interface. (**A**) Bone-Level implant. (**B**) Tissue-Level implant. on the visible connection, the profiles of each implant consisting of a screw, abutment, and implant are connected by lines from the photomicrography. They show the three parts that are touching for the Bone-Level implant and the Tissue-Level implant in three different colors (Figure 3). In the sequence, an axis-symmetric 3D solid structure was creatred according to each model. Figure 4 shows the geometries finished in CAD software (Rhinoceros software) version 5.0 SR14 (McNeel North America, Seattle, WA, USA)) for the Bone-Level implant and the Tissue-Level implant. Figure 3: Profile lines were generated based on photomicroscope background. (**A**) Bone-Level implant. (**B**) Tissue-Level implant. In sequence, the 3D file formatted in Standard for the Exchange of Product Data (STEP) was finished with computer-aided design software (Rhinoceros version 5.0 SR8, McNeel Noth America, Seattle, WA, USA). The model consisted of the following components: an implant fixture (4.1 \(\times\) 11 mm), prosthetic screw, and abutment. The dimensional parameters and geometrical relationships were based on ISO 14801 guidelines [19] for the loading test in endosseous dental implants. Following the completion of the modeling phase, the three-dimensional model was subsequently imported into analysis software (ANSYS 23.0, ANSYS Inc., Houston, TX,  
Figure 4: Geometries finished in CAD software. (**A**) Bone-Level implant. (**B**) Tissue-Level implant. USA). To perform the static analysis, the titanium alloy was designated as homogeneous, linear, and isotropic. The values for Young's modulus and Poisson's ratio were 110 GPa and 0.3, respectively. To replicate the absence of joint defects, all contact interactions were assumed to be rough. Rough contact is typically modeled when two surfaces are in physical contact, and there is friction or resistance to sliding between them. It simulates a condition where the surfaces are not perfectly smooth but instead have microscopic asperities (roughness) that prevent relative motion. The formation of four distinct groups was conditional on the combination of implant design and contacting surfaces at the abutment-implant joint.