Oshima et al.

Asian Pac J Dent 2016; 16: 1-7

A finite element analysis of stress distribution in roots withdifferent types of post systems
Fujino Oshima, DDS, Daizo Okada, DDS, PhD, Reiko Ogura, DDS, PhD, Chiharu Shin,
DDS, PhD, Yoji Ueda, DDS, PhD, Tasuku Inagaki, DDS, PhD, Rie Fujita, DDS, PhD,
and Hiroyuki Miura, DDS, PhD
Fixed Prosthodontics, Oral Health Sciences, Graduate School of Medical and Dental Sciences, Tokyo
Medical and Dental University, Tokyo, Japan
Purpose: The purpose of this study was to evaluate the stress distributions of various post and core systems anddetermine which post and core system contributes to preventing stress concentration and root fracture.
Materials and Methods: Following seven models were fabricated; a natural tooth model (NT), a vital toothwith preparation for a crown model (VT), a cast metal post and core model (CP), and composite resin core withfour types of prefabricated post models. These prefabricated post materials were stainless steel post (SP) andthree types of glass fiber posts (FP3, FP29, FP45) with different Young’s modulus. In all models, stress
distribution during function was calculated.
Results: Around base of the post and end of the post, SP and CP gave rise to higher stress concentration and FP3,
its Young’s modulus was the lowest among all types of posts, is the exhibited the lowest stress concentration.
Conclusion: Within the limitation of this study, FP3 was found to be the most suitable candidate.
(Asian Pac J Dent 2016; 16: 1-7.)
Key Words: nonlinear finite element analysis, post and core, root fracture, von Mises stress, Young’s modulus

Introduction
Cast metal post and cores have traditionally been used to restore endodontic treated teeth, because they aresuperior in mechanical strength compared to other post and core systems [1-3]. However, a large difference inYoung’s modulus between metal and dentin may cause stress concentration around the end of the post,
sometimes resulting in vertical root fracture [2,4,5] which leads to the extraction of teeth [6]. Recently,
composite resin cores have been used instead of cast post and cores. The reason for the replacement is that asimilarity in Young’s modulus between composite resin and dentin [4,5] may lead to reduce the stressconcentration within the root and prevent serious vertical root fractures. Other advantages using composite resin
cores include the prevention of the elution of metal ions that can cause metal allergy [7] and the satisfaction ofaesthetic demand, for example, shade and translucency when all ceramic crowns or polymer-based restorative
material crowns are chosen as the final restoration [8,9]. On the other hand, there has been reported that thestress is concentrated around the cervical area [10-12]. Therefore composite resin cores will sometimes lead to
repairable horizontal root fracture [4]. The composite resin core is usually built up in conjunction with a post.
There are various kind of post materials such glass fiber [4,9,13], carbon fiber [14], stainless steel [4], quarts
fiber [4,15] and titanium [15]. The large difference in Young’s modulus among these materials may influence
the magnitude and distribution of stress within the root. Above all, glass fiber posts with Young’s modulus
similar to dentin have been more commonly used with composite resin cores. Furthermore, there are many kindsof glass fiber posts with various Young’s modulus [4,5,16-18]. However, no consensus of opinion exists on
which post system is most suitable for composite resin cores.
The purpose of this study was to evaluate the stress distributions of various kinds of post and core systems
during function and determine which post and core system contributes to preventing stress concentration androot fracture.

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Materials and Methods
In this study, three-dimensional nonlinear finite element simulation model of a premolar was fabricated andanalyzed using finite element analysis software (MSC Marc Mentat 2003, MSC Software Corp., Santa Ana, CA,
USA) in accordance with previous reports [10,11]. The simulation tooth model was 18 mm long with a diameterof 6 mm at the crown margin level. The apical 12 mm of the root was modeled as invested in a socket of lamina
dura 0.3 mm thick and had a uniform periodontal ligament thickness of 0.2 mm. The remaining bone wasmodeled as cancellous bone and cortical bone (Fig. 1).

Fig. 1The dimensions and elements ofthe complete model (mm)Fig. 2 Finite element analysis models
NT, a natural tooth model;
VT, a vital tooth with preparation for a crown model;
CP, a cast metal post and core model;
SP, a composite resin core with stainless steel post;
FP, a composite resin core with glass fiber post

Following the criteria of the simulation tooth model, seven models were fabricated; a natural tooth model(NT), a vital tooth with preparation for a crown model (VT), a cast post and core model (CP), and composite
resin core with four types of prefabricated post models. These prefabricated post materials were stainless steel
post (SP) and three types of glass fiber posts with different Young's modulus (FP3, 3,000 MPa; FP29, 29,200
MPa; and FP45, 45,000 MPa) (Fig. 2).
The CP, SP, FP3, FP29, and FP45 models, it was assumed that they were endodontically treated. Therefore,
these models consisted of a crown, luting agent, post and core, dentin, gutta-percha, periodontal ligament, lamina
dura, cancellous bone, and cortical bone (Fig. 2). On the other hand, in NT and VT, it was assumed that they
were vital teeth. Therefore, only the dental pulp was included in the composition materials (Fig. 2).
Each element was assigned unique elastic properties to represent the modeled materials (Table 1)[8,13,19-26]. Homogeneity, isotropy, and linear elasticity were assumed for all materials except for theperiodontal ligament, including continuous interfaces between materials. A nonlinear elastic property wasapplied to the periodontal ligament because it has viscoelastic properties (Fig. 3) [23,27]. The approximate
function for periodontal ligament used in this study was adapted from a previous research [23].

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Table 1 Mechanical properties of materials	 EnamelDentinDental pulp
Periodontal ligament
Lamina dura
Cancellous bone
Cortical bone
Gutta-percha
Gold-silver-palladium alloy
Composite resin core
Glass fiber post (FP3)Glass fiber post (FP29)
Glass fiber post (FP45)
Luting agent
Abbreviations as in Fig. 2

Young's modulus (MPa)80,00015,0002
Nonlinear elastic
13,700345
13,7000.69
86,00012,0003,000
29,20045,0004,500

Fig. 3
Material property of periodontal ligament [28]Poisson's ratio
0.3
0.31
0.45
Nonlinear elastic
0.3
0.31
0.3
0.45
0.33
0.33
0.3
0.3
0.3
0.4

Reference
[20]
[20]
[22]
[23]
[19]
[20]
[19]
[8]
[21]
[25]
[13]
[20]

Fig. 4 Measurement points (a-d)
a, base of the post; b, cervical area;c, end of the post; d, apex of the root

During function, the amount of distortion of the periodontal ligament was larger compared to othercomponents. Therefore, the number of layers of the periodontal ligament was determined as three to improve theaccuracy of finite element analysis results [10]. The model was absolutely restrained at all nodes on the bottom
surface of the cortical bone and cancellous bone. In general, the shape of elements was tetrahedron, but wedeveloped the hexahedral shape of element to increase the precision of finite element analysis results.
The information obtained in previous studies of occlusal force during beef jerky mastication measured withthe three-dimensional occlusal force sensor [10,11] was used in this study. The data of three dimensional
occlusal forces used as reference for the palatal, distal, and apical directions were 23.9 N, 28.9 N, and 164.3 N
respectively [10,11]. That data was applied to a node located at the center of occlusal surface. Stress produced in
the dentin of each root was calculated as von Mises stress, and stress distribution in the root was analyzed.
Magnitude of von Mises stress around base of the post, cervical area, end of the post, and apex of the root werecompared (Fig. 4).

Results
The von Mises stress distributions within the root of seven models during masticating beef jerky were observed(Fig. 5). The von Mises stress around the base of the post, the cervical area, the end of the post, and the apex of3

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the root were analyzed (Table 2).
The magnitude of von Mises stress of composite resin core with four types of prefabricated post models (SP,FP3, FP29, FP45) were higher than that of CP around the cervical area. On the other hand, SP and CP produced
higher stress concentration than composite resin core with three types of fiber post models (FP3, FP29, FP45)
around the base of the post and the end of the post.
Among the vital tooth models, VT showed high-stress values around the cervical area of root compared with
NT. In addition, at almost all of the points, the magnitude of von Mises stress of NT tended to be the lowest
among all models.

Fig. 5 Comparison of von Mises stress distributions for seven models

Table 2 Magnitude of von Mises stress at each analysis point by finite element analysis (MPa)NT
Base of the post
2.1
Cervical area
6.2
End of the post
10.6
Apex of the root
14.5
Abbreviations as in Fig. 5

VT
1.7
15.3
11.2
14.7

FP3
1.9
14.6
4.9
14.5

FP29
6.3
14.3
9.6
14.5

FP45
8.6
14.2
11.8
14.5

SP
25.7
13.4
23.4
14.5

CP
15.5
10.5
16.0
14.6

Discussion
The strain gage methods [6,12,28], loading tests [13,28,29], photoelastic analyses [30,31], and finite element
methods [1,18,32,33] have been used to evaluate the possibility of root fractures. Each method has its own suiteof advantages and disadvantages. With the strain gage method, it is possible to accurately measure the magnitudeof the strain on the teeth or restorations surface under loading; however, it can’t directly measure the internalstrain. Although loading tests can measure failure load and mode, they cannot analyze the stress distribution
within teeth. Photoelastic analyses allow stress distribution to be observed in two or three-dimensional mode, but
it is difficult to make models in detail and to analyze the magnitude of internal stress in teeth accurately.

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The results of finite element analyses depend on its modeling methods, values assigned to the material
properties, the position of restraint and the direction of occlusal force. However finite element analyses havebeen 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 and the distribution and magnitudeof stress at any point within the root can be precisely analyzed. In this study, finite element analyses wereselected to investigate stress distributions within the root in three dimensions.
The probability of root fracture of endodontically treated teeth is higher than that of vital teeth. In clinicalrestorations, composite resin cores with prefabricated posts sometimes caused horizontal root fracture which isrepairable, but cast posts and cores sometimes caused vertical root fracture which leads to extraction of the teeth.
To prevent catastrophic vertical root fracture, it is important to investigate stress distribution within the rootin various kinds of post materials, especially around the end of the post because of vertical root fracture surface
included around the end of the post [13,28,29]. This means there are stress concentrations around the end of thepost. Horizontal root fracture is also undesirable incident for patients and dentists, although the horizontal root
fracture can be retreated [4] in many cases. Therefore, it is necessary to investigate the stress distribution within
the root around the cervical area also because stress around this area might be related to horizontal fracture. In
this study, the magnitudes of von Mises stress of cast metal post and core and composite resin cores with three
types of glass fiber posts and stainless steel post during function were calculated. The natural tooth model was
assumed to be a control.
Composite resin core models with four types of prefabricated post material (FP3, FP29, FP45, SP) and VT
produced higher stress levels around the cervical area compared with CP and NT. This result was corresponding
to the previous reports [10,11]. It suggested that composite resin core cause to the horizontal root fracture
regardless of prefabricate post materials. To prevent the horizontal root fracture, stress concentration around thecervical area should be reduced. Taking into consideration that there were no differences in the magnitude of vonMises stress around the cervical area among the composite resin core with four types of prefabricated post
material models (FP3, FP29, FP45, SP), the crown materials, luting agent [11] and ferule [34] would affect themagnitude of stress.
In reconstructing endodontically treated teeth, the kind and combination of materials for restoration andmarginal shape and position is important to prevent the root fracture [35]. For VT, the stress concentration
around the cervical area cause to wedge-shaped defect which produce pain, thus there would to be little case ofserious root fracture. SP and CP which were the models with metal cast posts, produced high stressconcentration around the base of the post and the end of the post. In the case of SP and CP, there is a highpossibility of root fracture compared with other restorations. Especially, SP produced the high stressconcentration around both cervical area and the end of the post. This suggested that SP was at the greatest risk ofvertical and horizontal root fracture in this study.
Among composite resin core models with three types of glass fiber post (FP3, FP29, FP45), stressconcentration around the base of the post and the end of the post was decreased as the Young's modulus of glass
fiber posts became small. That is, the model with the lowest Young’s modulus of glass fiber posts (FP3) showed
the lowest stress concentration around the base of the post and the end of the post. This also meant that FP
reduced the most possibility of vertical root fracture. In the case of FP, stress distribution within the root of
restored tooth was similar to that of NT and the risk of root fracture would be reduced. If the Young’s modulus

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Asian Pac J Dent 2016; 16: 1-7

of fiber post is under 29,000 MPa, it might prevent root fracture since magnitude of von Mises stress of FP29
around end of the post was lower than NT.
In this study, it was assumed that the prefabricated post materials adhered completely to composite resin andthe cast post and core adhered completely to the luting agent. The adhesive properties might have an effect of on
the distribution of stress within the root [36-41]. Furthermore, the stress concentration to composite resin andluting agent might cause to interfacial failure between composite resin or adhesive agent and post materials.
Therefore, it was necessary to consider not only adhesive properties, but Young’s modulus and Poisson’s
ratio of materials as choosing composite resin and luting agents. Result of this study revealed that the Young’s
modulus of post and core materials might affect distribution of stress within the root. Within the limitation ofthis study, FP3 (the lowest Young’s modulus of glass fiber posts), was found to be the most suitable candidate in
the viewpoint of avoiding catastrophic vertical root fracture. Also, the following conclusions were obtained:
1.

Around base of the post, SP and CP gave rise to higher stress concentration and the magnitude of vonMises stress of VT and FP3 was about the same as that of NT.

2.

As for VT, a larger stress was also concentrated around cervical area.

3.

SP and CP produced high stress concentration around end of the post. It suggested that SP and CP cause to
the vertical root fracture.

4.

Composite resin core models with any post material produced high stress levels around cervical area.
Consequently, it suggested that composite resin core cause to the horizontal root fracture.

5.

Among composite resin core models with three types of fiber post, with a higher Young’s modulus of glass
fiber post, a larger stress tended to be concentrated around end of the post.

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Correspondence to:
Dr. Daizo Okada
Fixed Prosthodontics, Department of Restorative Sciences, Graduate School,
Tokyo Medical and Dental University
1-5-45, Yushima, Bunkyo-ku, Tokyo 113-8549, Japan
Fax: +81-3-5803-0201 E-mail: d.okada.fpro@tmd.ac.jp
Copyright ©2016 by the Asian Pacific Journal of Dentistry.

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Accepted January 7, 2016.
Online ISSN 2185-3487, Print ISSN 2185-3479