Fatigue Life of the Human Teeth: A Continuum Damage Approach

Abstract:

Normal oral food ingestion processes such as mastication would not have been possible without the teeth. The human teeth are subjected to many cyclic loadings per day. This, in turn, exerts forces on the teeth just like an engineering material undergoing the same cyclic loading. Over a period, there will be the creation of microcracks on the teeth that might not be visible ab initio. The constant formation of these microcracks weakens the teeth structure and foundation that result in its fracture. Therefore, the need to predict the fatigue life for human teeth is essential. In this paper, a continuum damage mechanics (CDM) based model is employed to evaluate the fatigue life of the human teeth. The material characteristic of the teeth is captured within the framework of the elastoplastic model. By applying the damage evolution equivalence, a mathematical formula is developed that describes the fatigue life in terms of the stress amplitude. Existing experimental data served as a guide as to the completeness of the proposed model. Results as a function of age and tubule orientation are presented. The outcomes produced by the current study have substantial agreement with the experimental results when plotted on the same axes. There is a notable difference in the number of cycles to failure as the tubule orientation increases. It is also revealed that the developed model could forecast for any tubule orientation and be adopted for both young and old teeth.

• Periodical: Journal of Biomimetics, Biomaterials and Biomedical Engineering (Volume 43)
• Pages: 1-19
• DOI: https://doi.org/10.4028/www.scientific.net/JBBBE.43.1
• Online since: November 2019
• Authors: Theddeus Akano*
• Keywords: Continuum Damage Mechanics, Dentin, Fatigue Life, Teeth

References

[1] H. Chai, J. J.-W. Lee, P. J. Constantino, P. W. Lucas, and B. R. Lawn, Remarkable resilience of teeth,, Proc. Natl. Acad. Sci., vol. 106, no. 18, p.7289–7293, (2009).

DOI: 10.1073/pnas.0902466106

[2] Pulp (tooth) - Wikipedia,, Wikipedia. [Online]. Available: https://en.wikipedia.org/wiki/Pulp_(tooth). [Accessed: 05-Dec-2017].

[3] Y.-R. Zhang, W. Du, X.-D. Zhou, and H.-Y. Yu, Review of research on the mechanical properties of the human tooth,, Int. J. Oral Sci., vol. 6, no. 2, p.61–69, (2014).

[4] R. K. Nalla, V. Imbeni, J. H. Kinney, S. J. Marshall, and R. O. Ritchie, On the development of life prediction methodologies for the failure of human teeth,, Lawrence Berkeley Natl. Lab., (2002).

DOI: 10.1002/9781118788035.ch13

[5] L. L. Howell, Compliant mechanisms. Wiley, (2001).

[6] T. T. Akano and O. A. Fakinlede, Fatigue Failure Model for Polymeric Compliant Systems,, ISRN Polym. Sci., vol. 2013, (2013).

DOI: 10.1155/2013/321489

[7] J. C. S. J. W. Ju and J. C. Simo, Strain and Stress Based Continuum Damage Models,, Int. J. Solids Struct., vol. 23, no. 7, p.821–869, (1987).

DOI: 10.1016/0020-7683(87)90083-7

[8] J. Lemaitre, Formulation and identification of damage kinetic constitutive equations,, in Continuum Damage Mechanics Theory and Application, Springer, 1987, p.37–89.

DOI: 10.1007/978-3-7091-2806-0_2

[9] J. D. Gyllenskog, Fatigue life analysis of T-38 aileron lever using a continuum damage approach. Utah State University, (2010).

[10] D. Kondo, H. Welemane, and F. Cormery, Basic concepts and models in continuum damage mechanics,, Rev. Eur. génie Civ., vol. 11, no. 7–8, p.927–943, (2007).

DOI: 10.1080/17747120.2007.9692970

[11] Y. Xiao, A multi-mechanism damage coupling model,, Int. J. Fatigue, vol. 26, no. 11, p.1241–1250, (2004).

[12] H. Li, J. Li, Z. Zou, and A. S.-L. Fok, Fracture simulation of restored teeth using a continuum damage mechanics failure model,, Dent. Mater., vol. 27, no. 7, pp. e125–e133, (2011).

DOI: 10.1016/j.dental.2011.03.006

[13] K. Tonami and H. Takahashi, Effects of aging on tensile fatigue strength of bovine dentin,, Dent. Mater. J., vol. 16, no. 2, p.156–169, (1997).

DOI: 10.4012/dmj.16.156

[14] J. H. Kinney, R. K. Nalla, J. A. Pople, T. M. Breunig, and R. O. Ritchie, Age-related transparent root dentin: mineral concentration, crystallite size, and mechanical properties,, Biomaterials, vol. 26, no. 16, p.3363–3376, (2005).

DOI: 10.1016/j.biomaterials.2004.09.004

[15] D. D. Arola and R. K. Reprogel, Tubule orientation and the fatigue strength of human dentin,, Biomaterials, vol. 27, no. 9, p.2131–2140, (2006).

DOI: 10.1016/j.biomaterials.2005.10.005

[16] S. Orrego, M. A. Melo, S. Lee, H. H. K. Xu, and D. D. Arola, Fatigue of human dentin by cyclic loading and during oral biofilm challenge,, J. Biomed. Mater. Res. Part B Appl. Biomater., vol. 105, no. 7, p.1978–1985, (2017).

DOI: 10.1002/jbm.b.33729

[17] B. Majd, H. Majd, J. A. Porter, E. Romberg, and D. Arola, Degradation in the fatigue strength of dentin by diamond bur preparations: Importance of cutting direction.,, J. Biomed. Mater. Res. B. Appl. Biomater., vol. 104, no. 1, p.39–49, Jan. (2016).

DOI: 10.1002/jbm.b.33348

[18] R. K. Nalla, J. H. Kinney, S. J. Marshall, and R. O. Ritchie, On the in vitro fatigue behavior of human dentin: effect of mean stress,, J. Dent. Res., vol. 83, no. 3, p.211–215, (2004).

DOI: 10.1177/154405910408300305

[19] R. K. Nalla, V. Imbeni, J. H. Kinney, M. Staninec, S. J. Marshall, and R. O. Ritchie, In vitro fatigue behavior of human dentin with implications for life prediction,, J. Biomed. Mater. Res. Part A, vol. 66, no. 1, p.10–20, (2003).

DOI: 10.1002/jbm.a.10553

[20] M. Mahadevaswamy, Finite element analysis and fatigue test on the bicuspids to support theory of abfraction,, (2010).

[21] J. Lemaitre, A continuous damage mechanics model for ductile fracture,, J. Eng. Mater. Technol., vol. 107, no. 1, p.83–89, (1985).

[22] J.-L. Chaboche, Continuum damage mechanics: Part II—Damage growth, crack initiation, and crack growth,, J. Appl. Mech., vol. 55, no. 1, p.65–72, (1988).

DOI: 10.1115/1.3173662

[23] G. B. Stephenson, Evaluation of the Strain Energy Density Method of Notch Stress Concentration Calculations in the Plastic Range.,, Naval Postgraduate School Monterey CA, (1996).

[24] Mechanical Properties of Dental Materials | Pocket Dentistry., [Online]. Available: https://pocketdentistry.com/mechanical-properties-of-dental-materials-2/. [Accessed: 01-Apr-2019].

[25] ElectroForce Mechanical Test Instruments – TA Instruments., [Online]. Available: https://www.tainstruments.com/products/electroforce-mechanical-testers/. [Accessed: 13-Jul-2019].