Finite Element Analysis of Molars Restored with Ceramic Crowns
SORIN POROJAN, FLORIN TOPALĂ, LILIANA SANDU
School of Dentistry
“V. Babeş” University of Medicine and Pharmacy 9 Revolutiei 1989 Blv., 300041 Timişoara
ROMANIA [email protected]
Abstract: With improvement in material properties of ceramic restorative materials, these materials have been
used as the definitive restoration material instead of the dental alloy, even in the posterior region. The incomplete fit of full crown restorations remains a critical problem for dentists, leading many researchers to
study this problem. The distribution and magnitude of stress at any point can be precisely analyzed using finite
element analysis. The geometry of tooth preparation has been the subject of many debates without clear
evidence that one type of tooth preparation or method of fabrication provides consistently superior marginal fit.
Two margin designs may be used for complete ceramic crowns: chamfer, and shoulder. The objective of this
study was to evaluate, by finite element analysis, the influence of different marginal geometries (chamfer,
shoulder) and preparation taper on the stress distribution in teeth prepared for ceramic crowns and in the
restorations. A 3D model of a molar was created: intact teeth, unrestored teeth different marginal geometries:
with chamfer, with shoulder preparations; the same tooth restored full ceramic crowns. These were exported in
Ansys finite element analysis software for structural simulations. Maximal equivalent stresses were recorded in
the tooth structures and in the restoration for all preparation types. In all cases the values were higher in the
crowns. Shoulder preparation is the recommended preparation tooth design for ceramic crowns, from
biomechanical point of view.
Key-Words: molar, complete ceramic crown, marginal geometries, preparation taper, finite element analysis,
stresses.
1 Introduction Owing to improved material properties of ceramics,
jacket crowns have become popular as esthetic
restorations. However, in order to function for a
long term, it is necessary to ensure that they possess
high mechanical strength and that microleakage
should be avoided as much as possible. Therefore,
in choosing a material for the definitive restorations,
it should be one where stress will not concentrate at
the cervical area [1].
With improvement in material properties of ceramic
restorative materials, these materials have been used
as the definitive restoration material instead of the
dental alloy, even in the posterior region [2]. The incomplete fit of full crown restorations
remains a critical problem for dentists, leading many
researchers to study this problem. Marginal and
internal accuracy of fit is valued as one of the most
important criteria for the clinical quality and success
of complete crowns. The geometry of tooth preparation has been the subject of many debates
without clear evidence that one type of tooth
preparation or method of fabrication provides
consistently superior marginal fit [3].
A well-designed preparation has a smooth and even
margin. Rough, irregular margins substantially
reduce the adaptation of the restoration. The cross-
section configuration of the margin has been the
subject of much analysis and debate. The
minimization of crown marginal gaps is an
important goal in prosthodontics [4]. The geometry
of tooth preparation has been the subject of many
debates without clear evidence that one type of tooth
preparation or method of fabrication provides
consistently superior marginal fit [5, 6].
Finite element analyses have been used for many
investigations, because they can reproduce
structures of various shapes of teeth with many
elements defined with specific Young’s modulus
and Poisson’s ratio values. In this manner, the
distribution and magnitude of stress at any point can be precisely analyzed [2].
With finite element analysis, finite element
modeling is a complex and difficult task. However,
this method can analyze the distributions and
magnitudes of internal stress by changing the
Recent Researches in Medicine and Medical Chemistry
ISBN: 978-1-61804-111-1 187
characteristics of materials. This also means that the
results of finite element analysis depend on its
modeling methods and the given values of material
properties [1].
Two margin designs may be used for complete
ceramic crowns: chamfer, and shoulder. A chamfer
margin is particularly suitable for full crowns. It is
distinct and easily identified, provides space for
adequate bulk of material, although care is needed
to avoid leaving a ledge of unsupported enamel.
Shoulder margins always offer space for the crown
material. It should form a 90 degree angle with the
unprepared tooth surface [5].
Traditional tooth preparation margin designs are still
advised by most manufacturers for indirect
restorations [7-11].
2 Purpose The objective of this study was to evaluate, by finite
element analysis, the influence of different marginal
geometries (chamfer, shoulder) and preparation taper on the stress distribution in teeth prepared for
full ceramic crowns and in the restorations.
3 Materials and Method For the experimental analysis, a 3D model of a
molar was created: intact teeth, unrestored teeth
different marginal geometries: with chamfer, with
shoulder preparations; the same tooth restored with
full cast metal crowns. The geometry of the intact
tooth were obtained by 3D scanning using a
manufactured device. The nonparametric modeling
software (Blender 2.57b) was used to obtain the
shape of the teeth structures (Fig. 1).
Fig. 1. 3D model of the molar after NURBS
modeling.
The collected data were used to construct three
dimensional models using Rhinoceros (McNeel
North America) NURBS (Nonuniform Rational B-Splines) modeling program (Fig. 3).
The tooth preparations: chamfer, shoulder and
degree of taper (between 0 and 10 degree) were
designed (Fig. 2).
a
b
Fig. 2. Tooth preparations: a. chamfer, b. shoulder.
Complete ceramic crowns were designed for all
preparation types.
Models were exported in Ansys finite element
analysis software for structural simulations. An
occlusal load of 200 N was applied in 10 points,
according to the contact points with the antagonists
(Fig. 3).
Fig. 3. Points selected for loading on the restored
molar.
The forces were applied perpendicular to the tooth
surface in each point. The mesh structure of the
solid 3D model was created using the computational
Recent Researches in Medicine and Medical Chemistry
ISBN: 978-1-61804-111-1 188
simulation of Ansys finite element analysis software
(Fig. 4).
Von Mises equivalent stresses were calculated and
their distribution was plotted graphically.
Fig. 4. Mesh structure of the restored molar.
3 Results and Discussions Maximal equivalent stresses were recorded in the
tooth structures and in the restoration for all
preparation types. In all cases the values were
higher in the crowns. The stresses were distributed
around the contact areas with the antagonists (Fig.
5). The distribution areas were larger for chamfer
preparation, and the values were higher for the
shoulder preparations. The values of the maximal
equivalent stress in the tooth structures were also
higher for the shoulder preparations, but distributed
occlusal (Table 1, 2, Fig. 6).
Table 1. Maximal Von Mises equivalent stress
values in the crowns for chamfer prepared teeth and
in the restored molars.
Preparation
taper
Maximal Von Mises equivalent
stress [Pa]
total crown prepared
tooth
0 1.17E+08 1.17E+08 9.22E+06
1 1.31E+08 1.31E+08 9.27E+06
2 1.32E+08 1.32E+08 8.76E+06
3 1.27E+08 1.27E+08 9.12E+06
4 1.33E+08 1.33E+08 8.35E+06
5 1.21E+08 1.21E+08 7.50E+06
6 1.17E+08 1.17E+08 8.09E+06
7 1.20E+08 1.20E+08 8.52E+06
8 1.18E+08 1.18E+08 9.47E+06
9 1.21E+08 1.21E+08 9.73E+06
10 1.17E+08 1.17E+08 1.01E+07
Regarding the stress distribution for the chamfer
preparation design, the areas were larger and higher
near the marginal line. For all the biggest
disadvantage is that high stresses are present around
the marginal areas.
Table 2. Maximal Von Mises equivalent stress
values in the crowns for shoulder prepared teeth and
in the restored molars.
Preparation
taper
Maximal Von Mises equivalent
stress [Pa]
total crown prepared
tooth
0 1.27E+08 1.27E+08 9.89E+06
1 1.33E+08 1.33E+08 9.53E+06
2 1.41E+08 1.41E+08 9.05E+06
3 1.30E+08 1.30E+08 7.80E+06
4 1.26E+08 1.26E+08 8.65E+06
5 1.15E+08 1.15E+08 9.64E+06
6 1.20E+08 1.20E+08 8.60E+06
7 1.07E+08 1.07E+08 9.63E+06
8 1.15E+08 1.15E+08 8.79E+06
9 1.18E+08 1.18E+08 9.65E+06
10 1.20E+08 1.20E+08 1.16E+07
a
b
Fig. 5. Von Mises equivalent stress in the complete
ceramic crown for different marginal designs:
a. chamfer, b. shoulder.
Recent Researches in Medicine and Medical Chemistry
ISBN: 978-1-61804-111-1 189
a
b
Fig. 6. Von Mises equivalent stress in the restored
teeth with different marginal designs:
a. chamfer, b. shoulder.
It was also found that margin design is a
determining factor in establishing the extent of the
minimal preparation for a cast metal crown [11].
The shoulder preparation emerged as the
recommended preparation design from both
mechanical and periodontal points of view. As for a
less invasive preparation design, the slight chamfer
preparation would be the recommended option [7].
4 Conclusion Within the limitations of the present study, the
following conclusions can be drawn:
1. Numerical simulations provide a biomechanical
explanation for stress distribution in prepared
teeth and overlying crowns.
2. The maximal equivalent stress values were
higher in the crowns. Stresses are distributed
around the contact areas with the antagonists.
3. Shoulder preparation is the recommended
preparation tooth design for ceramic crowns,
from biomechanical point of view.
5 Acknowledgements This work was supported by CNCSIS-UEFISCSU,
project number PN II-RU TE_217/2010.
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ISBN: 978-1-61804-111-1 190
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