Numerical strength analysis of anterior tooth crown reconstruction for
various cases of incisal angle loss
G. Milewski, R. Szczuc
Institute of Applied Mechanics, Cracow University of Technology, ul. Warszawska 24, 31-155 Cracow, Poland
1. Introduction
In clinical practise the way of cavity preparation often becomes a compromise between the rule of maximal
maintenance of dentine, enamel and tooth pulp and proper retentive shape preventing the proper strength of tooth
hard tissues as well as filling itself for extreme occlusal loadings. Badly shaped geometry and settlement of
retentive surfaces as well as the character and properties of bonding and composite materials could influence a
microleakage, pulp reaction, secondary carries and finally could result in local stress concentrations and lower
durability of tooth crown reconstruction. The basic rule for proper retentive cavity surfaceses shape is to eliminate
straight and sharp angles [1], what is not always used in clinical practise when preparing the cavities.
The aim of the paper was to evaluate the influence of the geometry of cavity preparation on the effort of hard
tissues of tooth crown in order to optimize the way of reconstruction. Incisal angle loss was taken for the
numerical simulations as the case of the most often destruction of anterior teeth crowns.
2. Methods
Numerical modelling and calculations were done with the use of CAD CATIA and FEM ANSYS programs.
Figure 1 presents the models of various retentive cavity shapes for different cases of incisal angle loss of anterior
tooth crown.
Fig. 1. CAD anterior tooth crown models of various retentive cavity shapes for different cases of
incisal angle loss.
Two types of occlusions, so called edge-to-edge and end-to-end bites for anterior teeth, were taken into
consideration. All tooth structures, i.e. enamel, dentine and pulp were modeled as elastic, isotropic materials.
Their strength properties, i.e. Young’s modulus and Poisson’s ratio were taken after [2]. Micro hybrid composite
filling material of E=16.6 GPa and ν=0.3 was taken for numerical calculations [3]. No contact and friction
phenomena were taken into consideration when modeling the interaction between composite material and hard
tissues of tooth. The value of occlusal loading 150 N was applied to the crown model on the certain areas with
regards to the type of bitting activity.
3. Results
The results of numerical calculations were analysed with respect to von Mises equivalent stress, strain intensity
and maximal principal strain distributions. A special attention was paid to the area of apical region of prepared and
reconstructed tooth cavity. For comparison, so called ‘healty tooth’ was analysed, too. The example of von Mises
equivalent stress distribution in anterior tooth crown for the case of incisal angle loss for straight angle retentive
cavity shape in normal end-to-end bite for the occlusion 150 N is presented in figure 2.
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Fig. 2. Von Mises equivalent stress distribution [MPa] in anterior tooth crown for the case of incisal
angle loss for various retentive cavity shape in normal occlusion of 150 N.
On the other hand, table 1 gives a set of the maximal values of von Mises equivalent stress, and maximal principal
strain in the the area of apical region of prepared and reconstructed tooth cavity for all considered geometry of
fillings.
Table 1 The maximal values of von Mises equivalent stress, and maximal principal strain in the the
area of apical region of prepared and reconstructed tooth cavity for all considered geometry
of fillings.
Cavity angle
von Mises equivalent stress
[MPa]
maximal principal strain
‘healthy’ tooth
45°
45° rounded
25.0
48.0
46.5
0.33
1.29
1.00
90°
44.0
1.16
90° rounded
36.4
1.19
110°
37.6
1.44
110° rounded
33.3
1.38
1 x 10-3
4. Discussion
The results of the numerical simulations prove that the way of cavity preparation is a compromise between the
rule of maximal maintenance of hard tissues of tooth and proper retentive shape preventing the proper strength of
reconstructed tooth crown. However the tendency is obvious: the higher apical angle of prepared cavity the better,
the less effort of dentine and enamel.
References
[1] Z. Jańczuk Z. (red.), Stomatologia zachowawcza. Zarys kliniczny (PZWL, Warszawa 2007).
[2] R.G. Craig, F.A. Peyton, Elastic and mechanical properties of human dentin (Journal of Dental Research, vol. 37, no. 4,
1958), pp. 661 – 668.
[3] Powers M.J., Sakaguchi R.L. (red.), Robert G. Craig – Materiały stomatologiczne (Elsevier, Urban & Partner, Wrocław
2008).
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