Finite Elements Analysis of Tooth-A Comparative Analysis of Multiple Failure Criteria

Abstract

Herein Finite elements analysis (FEA) study assesses the adequacy and accuracy of five failure criteria (Von Mises (VM), Tresca, maximum principal (S1), minimum principal (S3), and Hydrostatic pressure) for the study of tooth as a structure (made of enamel, dentin, and cement), along with its stress absorption-dissipation ability. Eighty-one 3D models of the second lower premolar (with intact and 1-8 mm reduced periodontium) were subjected to five orthodontic forces (intrusion, extrusion, tipping, rotation, and translation) of 0.5 N (approx. 50 gf) (in a total of 405 FEA simulations). Only the Tresca and VM criteria showed biomechanically correct stress display during the 0-8 mm periodontal breakdown simulation, while the other three showed various unusual biomechanical stress display. All five failure criteria displayed comparable quantitative stress results (with Tresca and VM producing the highest of all), showing the rotational and translational movements to produce the highest amount of stress, while intrusion and extrusion, the lowest. The tooth structure absorbed and dissipated most of the stress produced by the orthodontic loads (from a total of 0.5 N/50 gf only 0.125 N/12.5 gf reached PDL and 0.01 N/1 gf the pulp and NVB). The Tresca criterion seems to be more accurate than Von Mises for the study of tooth as structure.

Keywords: Finite elements analysis (FEA); dentin; enamel; failure criteria selection; orthodontic movements; periodontal breakdown; stress absorption–dissipation ability; tooth.

Figure 1

Mesh model: (A) 2nd lower right premolar model with 4 mm bone loss and applied vector for extrusion; (B) 2nd lower right premolar model with 4 mm bone loss and applied vector for intrusion; (C) 2nd lower right premolar model with 4 mm bone loss and applied vector for rotation; (D) 2nd lower right premolar model with 4 mm bone loss and applied vector for tipping; (E) 2nd lower right premolar model with 4 mm bone loss and applied vector for translation, (F) tooth model; (G) tooth model with 4 mm reduced PDL; (H) no bone loss 3D model; (I) 2nd lower right premolar model with 8 mm bone loss and applied vector for extrusion.

Figure 2

3D model without the mesh borders: (A) 2nd lower right premolar model with intact periodontium; (B) 2nd lower right premolar model with intact PDL and NVB; (C) 2nd lower right premolar model; (D) 2nd lower right premolar’s intact PDL; (E) 2nd lower right premolar’s dental pulp and NVB; (F–H) 3D model different sections.

Figure 3

Comparative stress display of the five failure criteria in intact, 4 mm and 8 mm periodontal breakdown for the extrusion movement under 0.5 N of load: (A) Tresca; (B) Von Mises; (C) Pressure; (D) S1; (E) S3.

Figure 4

Comparative stress display of the five failure criteria in intact, 4 mm and 8 mm periodontal breakdown for the intrusion movement under 0.5 N of load: (A) Tresca; (B) Von Mises; (C) Pressure; (D) S1; (E) S3.

Figure 5

Comparative stress display of the five failure criteria in intact, 4 mm and 8 mm periodontal breakdown for the rotation movement under 0.5 N of load: (A) Tresca; (B) Von Mises; (C) Pressure; (D) S1; (E) S3.

Figure 6

Comparative stress display of the five failure criteria in intact, 4 mm and 8 mm periodontal breakdown for the tipping movement under 0.5 N of load: (A) Tresca; (B) Von Mises; (C) Pressure; (D) S1; (E) S3.

Figure 7

Comparative stress display of the five failure criteria in intact, 4 mm and 8 mm periodontal breakdown for the translation movement under 0.5 N of load: (A) Tresca; (B) Von Mises; (C) Pressure; (D) S1; (E) S3.