The method for this study involved two primary steps. Initially, a dental implant design was crafted using drafting software, and the drawing was then imported into a simulation program. Figure 1 presents the design of Model 2 in both isometric and three different planes, providing an overview of the implant's geometric traits and their potential impact on its performance under diverse loading conditions. Subsequently, Model 1 was developed as a continuum model, where geometric features were formed using simulation software. Additionally, the design of the full body (free body diagram) for Model 2 was also created using the same approach, as depicted in Fig. 2 (left) and (right). Following the creation of these models, simulations were conducted for both systems to investigate the behavior of the dental implant under various loading conditions.
For the model setup, the probe was modeled as a linear elastic material, while the tissue was modeled using its own unique material properties. The properties of the polysilicon probe and tissue are as follows: Young's modulus [Pa], Poisson's ratio, and density [kg/m3]. The Young's modulus, Poisson's ratio, and density for the polysilicon probe are 1.69e11, 0.22, and 2320, respectively. The Young's modulus, Poisson's ratio, and density for the tissue are 1e4, 0.49, and 1080, respectively.
Figure 2 illustrates the two models utilized in this study. The model on the top represents Model 1, a continuum model, while the model on the bottom depicts Model 2, a full-body model. This figure offers an overview of the two models employed to simulate the behavior of the dental implant under various loading conditions, facilitating a clearer understanding of their distinctions and similarities.
Table 1 outlines the geometric characteristics of the two models utilized in this study. Model 1 is a three-dimensional continuum model, whereas Model 2 is a three-dimensional full-body model. The table includes information on space dimensions, the number of domains, boundaries, edges, and vertices for each model. Model 1 features 3 space dimensions, 5 domains, 25 boundaries, 40 edges, and 22 vertices. In contrast, Model 2 encompasses 3 space dimensions, 3 domains, 133 boundaries, 316 edges, and 188 vertices. These statistics offer insights into the complexity of each model and underscore their differences concerning geometric attributes.
Table 1
shows geometric statistical.
Description
|
Value of model 1
|
Value of mode 2
|
Space dimension
|
3
|
3
|
Number of domains
|
5
|
3
|
Number of boundaries
|
25
|
133
|
Number of edges
|
40
|
316
|
Number of vertices
|
22
|
188
|
The dimensions of Model 1, which includes the dental implant, are as follows: Width 20mm, Depth 20mm, Height 10mm, and stem Radius 2mm and Height 5mm. Both the dental implant and tissue are made of polysilicon, with tissue having a density of 2320 kg/m³, Young's modulus of 169e9 Pa, and Poisson's ratio of 0.22. The initial parameters for the simulation include an angle of indentation of 0[deg], applied pressure of P0 = 200 Pa, and a value of theta.
The equations used in this study describe the mechanics of a solid material under deformation. The equilibrium equation, 0 = V .s + Fv, describes the balance between external forces and internal stresses within the material. The equation S = Sinei + Sei relates the total stress to elastic and inelastic stress, while the equation ℇ ei = ℇ - ℇ inel relates elastic and inelastic strain. The equation ℇ inel = ℇo + ℇext + ℇth + ℇns + ℇpi + ℇcr + ℇvp + ℇve describes the inelastic strain due to various factors. The equations Sei = C : ℇei and Sinei = So + Sext + S q relate stresses to elastic and plastic deformation. The equation ℇ = ½ (( Vu)^2 + Vu) describes total strain in terms of the velocity gradient and rate of deformation. Finally, the equation C = C(E,ʋ) relates the stiffness tensor to elastic modulus and Poisson's ratio. Together, these equations provide a comprehensive understanding of the behavior of solid materials under stress and deformation.
Figure 3 displays the mesh used for modeling both Model 1 (left) and Model 2 (right). The appropriate meshing of the dental implant is crucial for accurately modeling its behavior under various loading conditions, allowing for a more reliable and accurate simulation. By optimizing the mesh for each model, the simulation can provide insights into the implant's stability and long-term performance.
Table 2 presents the mesh statistics for both models, including information about the number of elements, nodes, and element types used in the simulation. These statistics provide insights into the level of detail and accuracy achieved in the meshing process. By optimizing the mesh, the simulation can accurately capture the behavior of the dental implant under various loading conditions, ensuring its stability and functionality in the long term.
Table 2
Description model 1
|
Value
|
Description model 2
|
Value
|
Status
|
Complete mesh
|
Status
|
Complete mesh
|
Mesh vertices
|
2337
|
Mesh vertices
|
15573
|
Tetrahedra
|
11314
|
Tetrahedra
|
83383
|
Triangles
|
2166
|
Triangles
|
13052
|
Edge elements
|
223
|
Edge elements
|
2730
|
Vertex elements
|
22
|
Vertex elements
|
184
|
Number of elements
|
11314
|
Number of elements
|
83383
|
Minimum element quality
|
0.02658
|
Minimum element quality
|
0.004952
|
Average element quality
|
0.6451
|
Average element quality
|
0.6049
|
Element volume ratio
|
8.0558E-5
|
Element volume ratio
|
8.5845E-8
|
Mesh volume
|
4073 nm³
|
Mesh volume
|
1.007E-5 mm³
|
Table 2 displays the size settings used to simulate model 1 and model 2, including their descriptions, maximum and minimum element sizes, curvature factor, resolution of narrow regions, and maximum and element growth rates. These settings are crucial for accurately modeling the behavior of the dental implant under various loading conditions. By optimizing these parameters, the simulation can provide more reliable and accurate results, ensuring the implant's stability and durability.
Table 3
Description model 1
|
Value
|
Description model 2
|
Value
|
Maximum element size
|
2
|
Maximum element size
|
0.003
|
Minimum element size
|
0.36
|
Minimum element size
|
5.4E-4
|
Curvature factor
|
0.6
|
Curvature factor
|
0.6
|
Resolution of narrow regions
|
0.5
|
Resolution of narrow regions
|
0.5
|
Maximum element growth rate
|
1.5
|
Maximum element growth rate
|
1.5
|
Table 3 presents a detailed description of the mesh used for modeling the tissues surrounding the dental implant in both Model 1 (left) and Model 2 (right). This table includes information about the number of nodes and elements, as well as the mesh type and size distribution. Optimizing the mesh for the surrounding tissues is crucial for accurately modeling the behavior of the dental implant under various loading conditions. By achieving an appropriate mesh density, the simulation can provide more reliable and accurate results, ensuring the implant's stability and sustained functionality.
Figure 4 displays the meshed tissue surrounding the dental implant for both Model 1 (left) and Model 2 (right). The appropriate meshing of the tissue is essential for accurately modeling the behavior of the dental implant under various loading conditions, allowing for a more reliable and accurate simulation. By achieving an appropriate mesh density, the simulation can provide insights into the implant's stability and longevity.
Table 4
Description model 1
|
Value
|
Description model 2
|
Value
|
Maximum element size
|
0.7
|
Maximum element size
|
0.00165
|
Minimum element size
|
0.03
|
Minimum element size
|
1.2E-4
|
Curvature factor
|
0.3
|
Curvature factor
|
0.4
|
Resolution of narrow regions
|
0.85
|
Resolution of narrow regions
|
0.7
|
Maximum element growth rate
|
1.35
|
Maximum element growth rate
|
1.4
|
Predefined size
|
Extra fine
|
Predefined size
|
Finer
|
Table 4 provides a detailed description of the mesh used for modeling the dental implant in both Model 1 (left) and Model 2 (right). This table includes information about the number of nodes and elements, as well as the mesh type and size distribution. By optimizing the mesh for each model, the simulation can more accurately capture the behavior of the dental implant under various loading conditions, allowing for a better understanding of its stability and functionality.
Figure 5 presents a parametric sweep for theta, ranging from − 60° to 15° to 60°, during the simulation to study the impact of dental implant rotation. The purpose of this analysis is to investigate the effects of rotation during chewing and its impact on the dental implant.
Furthermore, Fig. 6 illustrates the boundary loads for model 1 and model 2, respectively, on the left and right sides. These boundary loads are essential for simulating the behavior of the dental implant under different loading conditions and to assess its stability and durability.
Figure 7 illustrates the distribution of von Mises stress (N/m2) in Model 1 (left) and Model 2 (right). The von Mises stress is a measure used to predict yielding of materials under complex loading conditions, and it is represented in the figures to demonstrate the stress distribution in the respective models.
Fig,6 shows Boundary Loads in model 1 (left) and (right) model 2.
Figure 8 illustrates the results of the continuum model, which shows the effects of rotating the dental implant at different theta angles, including 0°, -60°, 60°, and 15°. The figure depicts the impact of these rotations on the surface displacement magnitude (µm) in the tissue, as well as the changes in deformation shape resulting from changes in the angle of rotation.
Figure 9 displays the effect of different angles of rotation on the surface of the dental implant, along with the associated displacement magnitude (µm), as depicted by the respective angles. The changes in deformation shape can significantly impact the dental implant's stability and functionality, as excessive deformation can lead to increased stress concentrations, localized failure of the implant, and surrounding bone tissue. Therefore, it is essential to understand the implant's deformation behavior under different angles of rotation to optimize its design and enhance its reliability and longevity. The figure displays dental implant angles ranging from 0° to 60°, including 15°, 45°, and shows the impact of increased deformation on the surrounding tissue.
The analysis of model 1 reveals the relationship between von Mises stress (N/m2) and the angle of indentation, along with the displacement magnitude (µm) in the third coordinate. The stress distribution is symmetric for small angles, but it becomes asymmetric as the angle increases to 50°. However, the deformation remains symmetric around the angle of zero 0° for model 1, as depicted in Fig. 10.
The analysis of model 1 investigates the movement of a dental implant in the x-coordinate (nm) and von Mises stress (N/m2), as shown in Fig. 11. The results demonstrate the effect of a range of rotations from − 60° to -15° on the dental implant. The peak stress levels for positive angles of rotation shift towards the left side of zero (mm), while for negative angles, they shift towards the right side, as illustrated in Fig. 11.
Fig, 11 shows Line Graph: von Mises stress (N/m2) with x-coordinate in model 1.
In the y-coordinate (mm), the movement of the dental implant and von Mises stress (N/m2) are shown in Fig. 12. The results illustrate the effect of a range of rotations from 60° to -60° on the dental implant. The peak stress levels for positive angles of rotation are in the middle of zero (mm), except for 30°, which is towards the right side. For negative angles of rotation, the peak stress levels are in the middle at zero (mm), as illustrated in Fig. 12.
Fig, 12 shows Line Graph: von Mises stress (N/m2) with y-coordinate in model 1.
The analysis of model 2 reveals the relationship between von Mises stress (N/m2) and the angle of indentation, along with the displacement magnitude (µm) in the third coordinate. The stress distribution is symmetric around the angle of 0°, and it tends towards 0° when the angle increases to 50°. However, the deformation remains symmetric around the angle of zero 0° for model 2, as depicted in Fig. 13.
The analysis of model 2 investigates the movement of a dental implant in the x-coordinate (mm) and von Mises stress (N/m2), as shown in Fig. 14. The results demonstrate the effect of a range of rotations from − 60° to -15° on the dental implant. The peak stress levels for positive angles of rotation shift towards the right side of zero (mm), and for negative angles as well, as illustrated in Fig. 14.
Fig, 14 shows Line Graph: von Mises stress (N/m2) with x-coordinate in model 2.
In model 2, the movement of the dental implant and von Mises stress (N/m2) in the y-coordinate (mm) are shown in Fig. 12. The results demonstrate the effect of a range of rotations from 60° to -60° on the dental implant. The peak stress levels for positive angles of rotation are observed in the middle of zero (mm), except for 15° and 30°, which are towards the left side. For negative angles of rotation, the peak stress levels are in the middle at zero (mm), except for − 15° and − 30°, which are towards the left side, as shown in Fig. 15.
Fig, 15 shows Line Graph: von Mises stress (N/m2) with y-coordinate in model 2.
The analysis of model 2 investigates the movement of a dental implant in the z-coordinate (mm) and von Mises stress (N/m2), as shown in Fig. 16. The results demonstrate the impact of a range of rotations from − 60° to -15° on the dental implant. The peak stress levels for both positive and negative angles of rotation are observed around the zero angle of 0° (mm), as illustrated in Fig. 16.
Fig, 16 shows Line Graph: von Mises stress (N/m2) with z-coordinate in model 2.