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 lilianasandu@gmail.com

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

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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

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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.

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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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Recent Researches in Medicine and Medical Chemistry

ISBN: 978-1-61804-111-1 190