Stress and Displacement Analysis of First Molar Hollow Tooth during Dental Filling Operation using Three-Dimensional Finite Element Method

Document Type: Original Article


1 Department of Mechanical Engineering, Graduate University of Advanced Technology, Kerman, Iran

2 Department of Mechanical and Aerospace Engineering, Malek Ashtar University of Technology, Isfahan, Iran

3 Zana Energy Rojhelat Co., Kermanshah, Iran


the amount of rotten tooth that is come out of teeth is an important issue in dental filling because of its effects on strength of teeth. The main goal of this study is to determine a criterion for the amount of rotten tooth which can be brought out. To do so, first, a three-dimensional finite element model of the complex shape of Right First Molar Mandibular has been established. Then, cylindrical holes with different values of height and diameter (diameter of holes from 3 mm to 8 mm and height of 3 mm to 5.9 mm) is created on the cusp of the tooth. A uniform pressure (from 10 Pa to 10 kPa) is applied around the tooth resembling the belt which is utilized in reality. According to the obtained displacement and stress contours, the diameter of tooth hole can be increased up to 7 mm for pressures under 10 Pa while for higher pressures, the diameter of tooth hole can just be increased up to 6 mm. In addition, due to sudden increase in stress at a pressure of 10 kPa, increasing the value of pressure to higher values is not recommended.


[1]     Wakabayashi, N., et al., “Nonlinear Finite Element Analyses: Advances and Challenges in Dental Applications”, Journal of dentistry, Vol. 36, No. 7, 2008, pp. 463-471.

[2]     Yettram, A., Wright, K., and Pickard, H., “Finite Element Stress Analysis of the Crowns of Normal and Restored Teeth”, Journal of Dental Research, Vol. 55, No. 6, 1976, pp. 1004-1011.

[3]     Peters, M., et al., “Stress Analysis of a Tooth Restored with a Post and Core”, Journal of Dental Research, Vol. 62, No. 6, 1983, pp. 760-763.

[4]     Khera, S., et al., “A Three-Dimensional Finite Element Model”, Operative dentistry, Vol. 13, No. 3, 1987, pp. 128-137.

[5]     Salis, S. G., et al., “Impact-Fracture Energy of Human Premolar Teeth”, The Journal of prosthetic dentistry, Vol. 58, No. 1, 1987, pp. 43-48.

[6]     Yang, H. S., Chung, H. J., and Park, Y. J., “Stress Analysis of a Cantilevered Fixed Partial Denture with Normal and Reduced Bone Support”, The Journal of prosthetic dentistry, Vol. 76, No. 4, 1996, pp. 424-430.

[7]     Winkler, M., Katona, T., and Paydar, N., “Finite Element Stress Analysis of Three Filling Techniques for Class V Light-Cured Composite Restorations”, Journal of dental research, Vol. 75, No. 7, 1996, pp. 1477-1483.

[8]     Yaman, S. D., Alaçam, T., and Yaman, Y., “Analysis of Stress Distribution in a Maxillary Central Incisor Subjected to Various Post and Core Applications”, Journal of Endodontics, Vol. 24, No. 2, 1998, pp. 107-111.

[9]     Versluis, A., Tantbirojn, D., and Douglas, W., “Do Dental Composites Always Shrink Toward the Light?”, Journal of Dental Research, Vol. 77, No. 6, 1998, pp. 1435-1445.

[10]  Toparli, M., Gökay, N., and Aksoy, T., “An Investigation of Temperature and Stress Distribution on a Restored Maxillary Second Premolar Tooth Using a Three‐Dimensional Finite Element Method”, Journal of oral rehabilitation, Vol. 27, No. 12, 2000, pp. 1077-1081.

[11]  Joshi, S., et al., “Mechanical Performance of Endodontically Treated Teeth”, Finite elements in analysis and design, Vol. 37, No. 8, 2001, pp. 587-601.

[12]  Ausiello, P., et al., “3D-Finite Element Analyses of Cusp Movements in a Human Upper Premolar, Restored with Adhesive Resin-Based Composites”, Journal of biomechanics, Vol. 34, No. 10, 2001, pp. 1269-1277.

[13]  Ausiello, P., Apicella, A., and Davidson, C. L., “Effect of Adhesive Layer Properties on Stress Distribution in Composite Restorations a 3D Finite Element Analysis”, Dental Materials, Vol. 18, No. 4, 2002, pp. 295-303.

[14]  Toparli, M., “Stress Analysis in a Post‐Restored Tooth Utilizing the Finite Element Methodˮ, Journal of oral rehabilitation, Vol. 30, No. 5, 2003, pp. 470-476.

[15]  de Castro Albuquerque, R., et al., “Stress Analysis of an Upper Central Incisor Restored with Different Posts”, Journal of Oral Rehabilitation, Vol. 30, No. 9, 2003, pp. 936-943.

[16]  Nakamura, T., et al., “Stress Analysis of Endodontically Treated Anterior Teeth Restored with Different Types of Post Material”, Dental materials journal, Vol. 25, No. 1, 2006, pp. 145-150.

[17]  Sorrentino, R., et al., “Three-Dimensional Finite Element Analysis of Strain and Stress Distributions in Endodontically Treated Maxillary Central Incisors Restored with Different Post, Core and Crown Materials”, dental materials, Vol. 23, No. 8, 2007, pp. 983-993.

[18]  Yamanel, K., et al., “Effects of Different Ceramic and Composite Materials on Stress Distribution in Inlay and Onlay Cavities: 3-D Finite Element Analysis”, Dental materials journal, Vol. 28, No. 6, 2009, pp. 661-670.

[19]  de Miranda Coelho, C. S., et al., “Finite Element Analysis of Weakened Roots Restored with Composite Resin and Posts”, Dental materials journal, Vol. 28, No. 6, 2009, pp. 671-678.

[20]  Jiang, W., et al., “Stress Distribution in Molars Restored with Inlays or Onlays with or Without Endodontic Treatment: A Three-Dimensional Finite Element Analysis”, The Journal of prosthetic dentistry, Vol. 103, No. 1, 2010, pp. 6-12.

[21]  Al-Omiri, M. K., Rayyan, M. R., and Abu-Hammad, O., “Stress Analysis of Endodontically Treated Teeth Restored with Post-Retained Crowns: A Finite Element Analysis Study”, The Journal of the American Dental Association, Vol. 142, No. 3, 2011, pp. 289-300.

[22]  Kumar, G. A., Kovoor, L. C., and Oommen, V. M., “Three-Dimensional Finite Element Analysis of the Stress Distribution Around the Implant and Tooth in Tooth Implant-Supported Fixed Prosthesis Designs”, Journal of Dental Implants, Vol. 1, No. 2, 2011, pp. 75.

[23]  Pałka, K., et al., “Finite Element Analysis of Thermo-Mechanical Loaded Teeth. Computational Materials Science”, Vol. 64, No. 2, 2012, pp. 289-294.

[24]  Kazemi, A., Khamesi, V., and Hajimahamadi, S., “Finite Element Study of the Effect of Canal Diameter on the Stress Distributions in Post-Core Restored Endodontically Treated Maxillary Incisor”, Applied Mechanics and Materials, Vol. 19, No. 11, 2012, pp 34-41.

[25]  Benazzi, S., et al., “Comparison of Occlusal Loading Conditions in a Lower Second Premolar Using Three-Dimensional Finite Element Analysis”, Clinical oral investigations, Vol. 18, No. 2, 2014, pp. 369-375.

[26]  Rubin, C., et al., “Clinical Science Stress Analysis of the Human Tooth Using a Three-dimensional Finite Element Model”, Journal of Dental Research, Vol. 62, No. 2, 1983, pp. 82-86.