The Biomechanical Analysis of Tibial Implants Using Meshless Methods: Stress and Bone Tissue Remodeling Analysis
Abstract
:1. Introduction
2. Numerical Formulation
2.1. Meshless Methods Formulation
2.1.1. Influence Domains
2.1.2. Shape Functions
2.2. Weak Form and Discrete System of Equations
2.3. Bone Tissue Remodeling Algorithm
3. Tibia and Implant Numerical Models
4. Results and Discussion
4.1. Structural Analysis of the Proximal Tibia
4.2. Structural Analysis of the Implant and Influence of Implant Length
4.3. Bone Remodeling Analysis
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Implant Length | Element Type | Nodes | Elements |
---|---|---|---|
0 | 4-node tetrahedral | 2083 | 9522 |
12 mm | 4-node tetrahedral | 5273 | 1171 |
30 mm | 4-node tetrahedral | 6908 | 1487 |
40 mm | 3-node plane stress | 1901 | 3630 |
40 mm | 4-node tetrahedral | 6299 | 1360 |
Young’s Modulus [GPa] | Poisson’s Ratio | |
---|---|---|
Implant—Ti-6Al-4V | 110 | 0.34 |
Low-stiffness bone | 5 | 0.33 |
Healthy cortical bone | 17 | 0.33 |
High-stiffness bone | 25 | 0.33 |
Method | Young’s Modulus | Point | ux [mm] | uy [mm] | uz [mm] | |u| [mm] |
---|---|---|---|---|---|---|
FEM | 5 GPa | A | −0.0281 | −0.0158 | −0.0451 | 0.0555 |
B | −0.0241 | −0.0193 | −0.0035 | 0.031 | ||
17 GPa | A | −0.0082 | −0.0046 | −0.0132 | 0.0163 | |
B | −0.007 | −0.0056 | −0.001 | 0.0091 | ||
25 GPa | A | −0.0056 | −0.0031 | −0.009 | 0.0111 | |
B | −0.0048 | −0.0038 | −0.0007 | 0.0062 | ||
RPIM | 5 GPa | A | −0.0286 | −0.0161 | −0.0471 | 0.0575 |
B | −0.0246 | −0.0203 | −0.004 | 0.0322 | ||
17 GPa | A | −0.0084 | −0.0047 | −0.0138 | 0.0169 | |
B | −0.0072 | −0.0059 | −0.0011 | 0.0094 | ||
25 GPa | A | −0.0057 | −0.0032 | −0.0094 | 0.0115 | |
B | −0.0049 | −0.004 | −0.0008 | 0.0064 |
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Pais, A.; Moreira, C.; Belinha, J. The Biomechanical Analysis of Tibial Implants Using Meshless Methods: Stress and Bone Tissue Remodeling Analysis. Designs 2024, 8, 28. https://doi.org/10.3390/designs8020028
Pais A, Moreira C, Belinha J. The Biomechanical Analysis of Tibial Implants Using Meshless Methods: Stress and Bone Tissue Remodeling Analysis. Designs. 2024; 8(2):28. https://doi.org/10.3390/designs8020028
Chicago/Turabian StylePais, Ana, Catarina Moreira, and Jorge Belinha. 2024. "The Biomechanical Analysis of Tibial Implants Using Meshless Methods: Stress and Bone Tissue Remodeling Analysis" Designs 8, no. 2: 28. https://doi.org/10.3390/designs8020028