Research on Biomedical Engineering
Research on Biomedical Engineering
Original Article

Finite element simulation of fracture in a restored premolar tooth using high aspect ratio elements

Maryam Ramezani; Estevam Barbosa de Las Casas; Cláudia Machado de Almeida Mattos; Osvaldo Luís Manzoli; Eduardo Alexandre Rodrigues


Abstract: Introduction: The term cracked tooth syndrome refers to an incomplete fracture of a vital posterior tooth that involves the dentin and occasionally extends into the pulp. There is a very limited number of publications trying to model dentin crack growth using numerical techniques. Therefore, it is essential to numerically model this phenomenon in order to improve the clinical procedures.

Methods: A 2D finite element model is proposed to simulate crack initiation and propagation in a restored premolar tooth. The geometric model was based on computed tomography data. A special finite element technique, named mesh fragmentation technique, is used to model and analyze the behavior of the tooth. This technique was used to model cracks in quasi-brittle materials based on the use of interface solid finite elements with high aspects ratio. A tension damage constitutive relation between stresses and strains consistent with the continuous strong discontinuity approach is used to describe crack formation and propagation.

Results: The main aspects of modeling technique and procedures are explained in detail as well as the whole results, including both elastic and fracture analyses of the restored tooth.

Conclusion: The results of the current fracture analysis show that, under various loading conditions, there is no crack initiation in the restored tooth under typical loading magnitude. However, in the case of tooth with a pre-existing crack, which can be aroused during the restoration process, a crack propagation was observed, while they did not reach a critical fracture state.


Finite element method, Fracture mechanics, Restored tooth, Biomechanics


3M Company. Filtek™ Z250 Universal Restorative System: technical product profile [Internet]. Saint Paul: 3M; 1998. [cited 2014 January 28]. Available from:

Baker MI, Eberhardt AW, Martin DM, McGwin G, Lemons JE. Bone properties surrounding hydroxyapatite-coated custom osseous integrated dental implants. J Biomed Mater Res B Appl Biomater. 2010; 95(1):218-24. PMid:20725958.

Banerji S, Mehta SB, Millar BJ. Cracked tooth syndrome. Part 2: Restorative options for the management of cracked tooth syndrome. Br Dent J. 2010; 208(11):503-14. PMid:20543791.

Cameron CE. Cracked-tooth syndrome. J Am Dent Assoc. 1964; 68(3):405-11. PMid:14128028.

Chung SM, Yap AU, Koh WK, Tsai KT, Lim CT. Measurement of Poisson’s ratio of dental composite restorative materials. Biomaterials. 2004; 25(13):2455-60. PMid:14751729.

Cornacchia TPM, Las Casas EB, Cimini CA Jr, Peixoto RG. 3D finite element analysis on esthetic indirect dental restorations under thermal and mechanical loading. Med Biol Eng Comput. 2010; 48(11):1107-13. PMid:20635221.

El Mowafy OM, Watts DC. Fracture toughness of human dentin. J Dent Res. 1986; 65(5):677-81. PMid:3457822.

Ellis SG, Macfarlane TV, McCord JF, Ellis SGS, Macfarlane TV, McCord JF. Influence of patient age on the nature of tooth fracture. J Prosthet Dent. 1999; 82(2):226-30. PMid:10424989.

Ellis SG. Incomplete tooth fracture — proposal for a new definition. Br Dent J. 2001; 190(8):424-8. PMid:11352390.

Hamouda IM, Shehata S. Fracture resistance of posterior teeth restored with modern restorative materials. J Biomed Res. 2011; 25(6):418-24. PMid:23554719.

Hiatt WH. Incomplete crown-root fracture in pulpal-periodontal disease. J Periodontol. 1973; 44(6):369-79. PMid:4513616.

Hisam MJ, Lim JY, Kurniawan D, Nor FM. Stress Distribution due to loading on premolar teeth implant: a three dimensional finite element analysis. Procedia Manuf. 2015; 2:218-23.

Jager P, Steinmann P, Kuhl E. Modeling three-dimensional crack propagation - a comparison of crack path tracking strategies. Int J Numer Methods Eng. 2008; 76(9):1328-52.

Kahler B, Swain MV, Moule A. Fracture-toughening mechanisms responsible for differences in work to fracture of hydrated and dehydrated dentine. J Biomech. 2003; 36(2):229-37. PMid:12547360.

Kinney JH, Balooch M, Marshall GV, Marshall SJ. A micromechanics model of the elastic properties of human dentine. Arch Oral Biol. 1999; 44(10):813-22. PMid:10530914.

Komatsu K. Mechanical strength and viscoelastic response of the periodontal ligament in relation to structure. J Dent Biomech. 2010; 2010:1-18. PMid:20948569.

Las Casas EB, Manzoli OL, Mattos CMA. Crack propagation in post-core rehabilitation of a maxillary central incisor after root reconstruction. Bluc Mech Eng Proc. 2014; 1(1):1-11.

Lin CL, Chang HY, Hsieh SK, Chang WJ. Estimation of the failure risk of a maxillary premolar with different crack depths with endodontic treatment by computer-aided design/computer-aided manufacturing ceramic restorations. J Endod. 2013; 39(3):375-9. PMid:23402510.

Lin CP, Cheng JH, Versluis A, Douglas WH. Failure criteria of dentin-resin adhesion - a mixed mode fracture mechanics approach. Scr Mater. 2000; 42(4):327-33.

Litonjua LA, Andreana S, Patra AK, Cohen RE. An assessment of stress analyses in the theory of abfraction. Biomed Mater Eng. 2004; 14(3):311-21. PMid:15299243.

Lubisich EB, Hilton TJ, Ferracane J. Cracked teeth: a review of the literature. J Esthet Restor Dent. 2010; 22(3):158-67. PMid:20590967.

Lynch CD, McConnell RJ. The cracked tooth syndrome. J Can Dent Assoc. 2002; 68(8):470-5. PMid:12323102.

Lyons MF, Cadden SW, Baxendale RH, Yemm R. Twitch interpolation in the assessment of the maximum force-generating capacity of the jaw-closing muscles in man. Arch Oral Biol. 1996; 41(12):1161-8. PMid:9134105.

Magni E, Ferrari M, Hickel R, Ilie N. Evaluation of the mechanical properties of dental adhesives and glass-ionomer cements. Clin Oral Investig. 2010; 14(1):79-87. PMid:19241096.

Manzoli OL, Gamino AL, Rodrigues EA, Claro G. Modeling of interfaces in two-dimensional problems using solid finite elements with high aspect ratio. Comput Struc. 2012; 94-95:70-82.

Manzoli OL, Maedo MA, Bitencourt LAG Jr, Rodrigues EA. On the use of finite elements with a high aspect ratio for modeling cracks in quasi- brittle materials. Eng Fract Mech. 2016; 153:151-70.

Manzoli OL, Maedo MA, Rodrigues EA, Bittencourt TN. Modeling of multiple cracks in reinforced concrete members using solid finite elements with high aspect ratio. In: Bićanić N, Mang H, Meschke G, Borst R, editors. Computational modelling of concrete structures. Vol. 1. Balkema: CRC Press; 2014. p. 383-92.

Mattos CM, Las Casas EB, Dutra IG, Sousa HA, Guerra SM. Numerical analysis of the biomechanical behaviour of a weakened root after adhesive reconstruction and post-core rehabilitation. J Dent. 2012; 40(5):423-32. PMid:22343185.

Miguez PA, Pereira PN, Atsawasuwan P, Yamauchi M. Collagen cross-linking and ultimate tensile strength in dentin. J Dent Res. 2004; 83(10):807-10. PMid:15381724.

Misch CE, Qu Z, Bidez MW. Mechanical properties of trabecular bone in the human mandible Implications for dental implant treatment planning and surgical placement. J Oral Maxillofac Surg. 1999; 57(6):700-6, discussion 706-8. PMid:10368096.

Misch CE. Dental implant prosthetics. 2nd ed. Netherlands: Elsevier; 2015.

Munari LS, Cornacchia TMP, Moreira AN, Gonçalves JB, Las Casas EB, Magalhães CS. Stress distribution in a premolar 3D model with anisotropic and isotropic enamel. Med Biol Eng Comput. 2015; 53(8):751-8. PMid:25850984.

Oliver J, Cervera M, Manzoli OL. Strong discontinuities and continuum plasticity models: The strong discontinuity approach. Int J Plast. 1999; 15(3):319-51.

Oliver J, Huespe A, Blanco S, Linero D. Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach. Comput Methods Appl Mech Eng. 2006; 195(52):7093-114.

Oliver J, Huespe A, Cante J. An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems. Comput Methods Appl Mech Eng. 2008; 197(21-24):1865-89.

Oliver J, Huespe AE. Continuum approach to material failure in strong discontinuity settings. Comput Methods Appl Mech Eng. 2004; 193(30-32):3195-220.

Palamara JEA, Palamara D, Messer HH. Strains in the marginal ridge during occlusal loading. Aust Dent J. 2002; 47(3):218-22. PMid:12405461.

Phrukkanon S, Burrow MF, Tyas MJ. The effect of dentine location and tubule orientation on the bond strengths between resin and dentine. J Dent. 1999; 27(4):265-74. PMid:10193103.

Pietrzak G, Curnier A, Botsis J, Scherrer S, Wiskott A, Belser U. A nonlinear elastic model of the periodontal ligament and its numerical calibration for the study of tooth mobility. Comput Methods Biomech Biomed Engin. 2002; 5(2):91-100. PMid:12186719.

Proeschel PA, Morneburg T. Task-dependence of activity/bite force relations and its impact on estimation of chewing force from EMG. J Dent Res. 2002; 81(7):464-8. PMid:12161457.

Reilly DT, Burstein AH. Review article. The mechanical properties of cortical bone. J Bone Joint Surg Am. 1974; 56(5):1001-22. PMid:4603167.

Rodrigues EA, Manzoli OL, Bitencourt LAG Jr, Bittencourt TN. 2D mesoscale model for concrete based on the use of interface element with a high aspect ratio. Int J Solids Struct. 2016; 94–95:112-24.

Rosen H. Cracked tooth syndrome. J Prosthet Dent. 1982; 47(1):36-43. PMid:7033512.

Silva GR, Silva NR, Soares PV, Costa AR, Fernandes-Neto AJ, Soares CJ. Influence of different load application devices on fracture resistance of restored premolars. Braz Dent J. 2012; 23(5):484-9. PMid:23306222.

Siso SH, Hurmuzlu F, Turgut M, Altundasar E, Serper A, Er K. Fracture resistance of the buccal cusps of root filled maxillary premolar teeth restored with various techniques. Int Endod J. 2007; 40(3):161-8. PMid:17305692.

Slutzky-Goldberg I, Slutzky H, Gorfil C, Smidt A. Restoration of endodontically treated teeth review and treatment recommendations. Int J Dent. 2009; 2009:1-9. PMid:20309408.

Snyder DE. The cracked-tooth syndrome and fractured posterior cusp. Oral Surg Oral Med Oral Pathol. 1976; 41(6):698-704. PMid:1063974.

Thomaidis S, Kakaboura A, Mueller WD, Zinelis S. Mechanical properties of contemporary composite resins and their interrelations. Dent Mater. 2013; 29(8):e132-41. PMid:23790281.

Van Staden RC, Guan H, Loo YC. Application of the finite element method in dental implant research. Comput Methods Biomech Biomed Engin. 2006; 9(4):257-70. PMid:17132532.

Yahyazadehfar M, Bajaj D, Arola DD. Hidden contributions of the enamel rods on the fracture resistance of human teeth. Acta Biomater. 2013; 9(1):4806-14. PMid:23022547.

Yahyazadehfar M, Ivancik J, Majd H, An B, Zhang D, Arola D. On the mechanics of fatigue and fracture in teeth. Appl Mech Rev. 2014; 66(3):0308031-3080319. PMid:25516632.

Zhang Z, Guazzato M, Sornsuwan T, Scherrer SS, Rungsiyakull C, Li W, Swain MV, Li Q. Thermally induced fracture for core-veneered dental ceramic structures. Acta Biomater. 2013; 9(9):8394-402. PMid:23684764.

5ad4e07b0e88251d6d489554 rbejournal Articles
Links & Downloads

Res. Biomed. Eng.

Share this page
Page Sections