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Int Chin J Dent 2008; 8: 21-27.

Three-dimensional finite element analysis of a maxillary central
incisor restored with different post-core materials
Xiao-na Li, DDS, PhD,a Yun-kai Shi, MSD,a Zhen-chun Li, MSD,a Chao-ying Song,
BDS,a Xiao-dong Chen, MSD,a Zhen-qun Guan, MSc,b Hong Guan, PhD,c and
Xiang-tao Chen, BDSda

Department of Prosthodontics, Dalian Stomatological Hiospital, School and Hospital of Stomotology,
Dalian University,b
Key Laboratory of Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian
University of Technology, Dalian, P. R. China,c
Griffith School of Engineering, Griffith University Gold Coast Campus, Queensland, Australia, anddDepartment of Prosthodontics, College of Stomatology, Jiamusi University, Jiamusi, P. R. China
Purpose: To provide a theoretical guidance to post-core choice by analyzing dentinal stress of postrestoration with six types of post-core materials.
Materials and Methods: A three-dimensional (3D) finite element model (FEM) of maxillary central
incisor restored with porcelain fused to metal crown (PFM) was constructed using spiral CT scan
technology. By comparing the restored incisor with PFM as a control model, the stress distribution
pattern in the dentine after post restoration was analyzed upon using six types of post-core materials, cast
Ni-Cr alloy, cast titanium alloy, cast gold alloy, glass fiber reinforced composite resin, and polyethylene
fiber reinforced composite resin, as well as common composite resin.
Results: Compared to the control model, the maximum principal and von Mises stresses in coronal dentin
decreased by 26% and 27.8% respectively, while those in post-apex dentine increased by 152% and 162%
respectively in post-apex when cast Ni-Cr alloy was used as a post-core. Significant change in maximum
stresses was also found in dentin when the first four restoration materials were used as post-core.
Conclusion: Material with low elastic modulus similar to that of dentin, such as polyethylene fiber reinforced
composite, may be more ideal for post restoration with respect to the stress distribution in dentin.
(Int Chin J Dent 2008; 8: 21-27.)
Key Words: dentin, elastic modulus, finite element analysis, post-core material, stress.

Introduction
Post and core build-ups represent an important pre-prosthetic procedure prior to the restoration of an
endodontically treated tooth. The dental practitioner is often presented with the dilemma of selecting post-corematerials from an ever increasing variety of available materials, many of which are harmful or controversial inuse. Materials used for post-core include both metal and nonmetal. Metal post-cores are generally made of gold
alloys, stainless steel, titanium alloys, pure titanium, and brass alloys. Nonmetal post-cores are generally
produced with zirconium oxide,1 composite and other types of fiber reinforced composites. Many researchers
have investigated the physical, chemical and biomedical characteristics of different types of materials andsuggested ideal post-core build-ups by considering their mechanical properties. However, the conclusions arediverse.2,3 Ko et al.2 suggested that the materials with high elastic modulus can be made small in diameter. In
this case, a small amount of dentin is removed so as to retain more usable dentin. On the other hand, Pegoretti etal.3 recommended that it is ideal for the post-core materials to have a similar elastic modulus to that of dentin,
because such materials do not significantly change the stress distribution characteristics of the dentin and areconvenient for re-restoration if the initial restoration is failed.
The finite element method (FEM) is based on a mathematical model which approximates the geometry, loading,and constraint conditions of a structure to be analyzed. Deformations and stresses at any point within the model canbe evaluated and highly stressed regions can then be identified. Research is limited in the area of three-dimensional(3D) finite element analysis (FEA) of stress distribution in post restored teeth.3-6 In particular, little work is21

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Int Chin J Dent 2008; 8: 21-27.

published in relation to the materials used as post-core build-ups in clinical practice. The aim of the present work is
thus to analyze the stress distribution characteristics in dentin with different post-core models. The outcome of thisresearch is to provide a theoretical guidance for the dental clinicians in selecting appropriate post-core materials intheir practice.

Materials and Methods
A volunteer with a near standard maxillary central incisor consisting of a dental corona of 11.1 mm and a root of
11.5 mm was selected. The subject was given an informed consent prior to the commencement of this study. The
maxillary bone and tooth of the volunteer were scanned by a spiral CT (GE Medical Systems, Milwaukee, WI,
USA). The image data were saved in a bitmap format and imported into an in-house computer program. Following
a series of process (preprocessing, image subdivision, and outlining), a contour data were obtained andsubsequently imported into the general purpose software SolidWorks (Solidworks Corp., Boston, MA, USA).
Through a sequential processing (lofting, shelling, Boolean calculus, etc.), a solid model of the maxillary central
incisor with PFM was produced. The solid model consisted of nine components; porcelain, metal base, post-core,dentin, cementum, periodontal ligament, gutta-percha, cancellous bone, and cortical bone (Fig. 1). The length anddiameter of the post-core was respectively 2/3 and 1/3 of those of the dental root. The shape of the post-core was
identical to the root canal. A computer aided engineering software FEMAP (UGS Corp., Plano, TX, USA) wasused for mesh generation of the solid model. The complete finite element model contained 126,912 nodes and86,369 tetrahedron elements.

Fig. 1. (left)
Vertical section of solid
model with PFM crown.
1, porcelain;
2, metal base;3, post-core;
4, dentin;
5, cementum;
6, periodontal ligament;
7, cortical bone;
8, gutta-percha;
9, cancellous bone).
Fig. 2. (right)
Loading condition.

To simulate the functional masticatory force, a 100 N load was applied at 45° with respect to the longitudinal
axis of the tooth. The concentrated load was converted to a uniformly distributed load which was applied
through five nodes on the boundary of incisal 1/3 and middle 1/3 in lingual surface (Fig. 2).7,8 A fixed restraint
was applied to all the nodes on the bottom surface of each model.9

All materials were assumed to behomogeneous, isotropic and have linear elastic behavior. The material properties are summarized in Table
1.3,10-13
In this study, six types of post-core materials with different elastic moduli were selected for the finite element
analysis. Amongst the six, three metal materials were often used in clinical practice, cast Ni-Cr alloy, casttitanium alloy and cast gold alloy. The other three nonmetal materials have also been used in recent years, glass22

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Int Chin J Dent 2008; 8: 21-27.

fiber reinforced composite, polyethylene fiber reinforced composite, and common composite. The same modelwith ideal post-core material, whose elastic modulus is equal to dentin, will be considered as a control model.
Table 1. Material properties used in FEA models.
Restoration materials
Modulus of elasticity (GPa)Cancellous bone10
1.37
Cast gold alloy10
96.6
Cast Ni-Cr alloy11
210
Cast titanium alloy12120
Cementum10
13.7
Common composite10
8.3
Cortical bone10
13.7
Dentin10
18.6
Enamel10
84.1
Glass fiber reinforced composite3
45
Gutta-percha10
0.00069
Periodontal ligament10
0.0689Polyethylene fiber reinforced composite13
23.6
Porcelain10
96

Poisson’s ratio
0.30
0.35
0.33
0.33
0.30
0.28
0.30
0.31
0.30
0.32
0.45
0.45
0.32
0.29

A total of seven 3D FEA models including the control model and those with six different post-core materials
were established and analyzed using the finite element software ANSYS (Swanson Analysis Systems, Inc.,
Pittsburgh, PA, USA). The maximum principal (tensile) σ11,max and von Mises stresses σ vM,max in dentine wereobtained for different models with different post-core materials.

Results
Regardless of the model with any post-core material, σ11,max were mainly found in dentin at around coronal
1/3 of the root on the lingual side; whereas σvM,max mainly occurred on the outer layer of dentin at the same
location on both the facial and lingual sides. Details of σ 11,max and σvM,max at around the coronal part of theroot are given in Table 2, while those at the root apex are presented in Table 3. It can be seen that themagnitudes of both σ11,max and σvM,max are higher at around the coronal part of the root than those at the root
apex.

Further, both σ 11,max and σvM,max are considerably low at the root apex for models restored with

polyethylene fiber reinforced composite and common composite. Note that in Table 2, a reduction ratio was
calculated in relation to the stresses of the control model. Table 3, on the other hand, shows an increase rate ascompared to the control model.
Table 2. σ11,max and σvM,max (MPa) in dentin at coronal part of the root.
Restoration materials
σ11,max
Magnitude
Reduction ratio
Magnitude
Control model
37.61
33.46
Cast Ni-Cr alloy
27.84
-26.0
24.15
Cast titanium alloy
31.24
-16.9
27.33
Cast gold alloy
32.32
-14.0
28.44
Glass fiber reinforced
35.25
-6.3
31.42
composite
Polyethylene fiber
37.04
-1.5
32.98
reinforced composite
Common composite
39.25
4.4
34.21

σvM,max
Reduction ratio
-27.8
-18.3
-15.0
-6.1
-1.4
2.2

Reduction ratio (%) = (maximum stress of restored model - maximum stress of control model) x 100/ maximum stress of control
model

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Table 3. σ11,max and σvM,max (MPa) in dentin at root apex.
Restoration materials
σ11,max
Magnitude
Increase rate
Control model
9.2
Cast Ni-Cr alloy
24.11
162.0
Cast titanium alloy
20.84
127.0
Cast gold alloy
18.30
99.0
Glass fiber reinforced
15.76
71.3
composite
Polyethylene fiber
14.08
53.0
reinforced composite
Common composite
13.55
47.3

Magnitude
7.53
18.95
16.52
12.12

σvM,max
Increase rate
151.8
119.0
61.1

10.60

40.9

4.82

-36.0

3.09

-59.0

Increase rate (%) = (maximum stress of restored model - maximum stress of control model) x 100 / maximum stress of control
model

Fig. 3.

a

b

c

d

e

f

Stress distribution contour of maxillary central incisor in different models.
a, Control model (σ11); b, Ni-Cr post (σ11); c, Polyethylene fiber reinforced composite post (σ11);d, Control model (σvM); e, Ni-Cr post (σvM); and f, Polyethylene fiber reinforced composite post (σvM)

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Int Chin J Dent 2008; 8: 21-27.

When cast Ni-Cr alloy was used as a post-core, the σ 11,max and σ vM,max in dentin at around the coronal 1/3 ofthe root decreased by 26% and 27.8% respectively, while significantly increased by 151.8% and 162%
respectively at the root apex, as compared to the control model. When the post-core material was glass fiber
reinforced composite, cast gold alloy and cast titanium alloy, the σ 11,max and σ vM,max decreased by 6.3%-16.9%
and 6.1%-18.3% respectively at the coronal part of the root whereas increased by 40.9%-119.0% and71.3%-127% respectively at the root apex. However, when the nonmetal materials, the polyethylene fiber
reinforced composite or the common composite was used, both σ11,max and σvM,max had little change at around thecoronal part of the root. Note that σ vM,max had a small increase at the root apex (13.55 MPa and 14.08 MPa
versus 9.2 MPa in the control model); but such an increase (47.3%-53.0%) was insignificant as compared tometal post-core models (99.0%-163% increase). Further, σ 11,max at the root apex decreased showing negative
increase rates (-36.0% and -59.0% for polythene fiber reinforced and common composites, respectively).
Fig. 2 shows the stress distribution patterns of the control model, the cast Ni-Cr alloy and the polyethylene
fiber reinforced composite post models. Shown in Figs. 2(a) and (d) are the distribution of σ11 and σvM for thecontrol model. The σ 11,max were mainly found in the outer layer of the coronal dentin - at around coronal
1/3 of the root on the lingual side; whereas the σvM,max mainly occurred at the same location on both thefacial and lingual sides.

The maximum stress locations were similar in models with Ni-Cr andpolyethylene fiber reinforced composite posts, except that the maximum stress regions expanded towards the
apex in the Ni-Cr post models.

Discussion
The FEM has been used extensively in dental biomechanics research. The method is powerful and versatile inthat it can provide detailed information on stresses, strains and displacements within complex structures such as
teeth and restored teeth with post-core materials. Previous research3-6 has demonstrated that 3D modeling iseffective in analyzing stress distribution characteristics in dentin and post, and such a technique is used in thisstudy.
In this study, six types of representative post-core materials were selected and their elastic moduli ranged from
8.3 GPa to 210 GPa, covering a wide range of available post-core materials used in clinical practice. The
post-core systems studied herein consisted of components (dentin and the post-core material) of different elastic
moduli. This study has demonstrated that the stress distribution patterns in dentin of a restored tooth are similar
if the elastic modulus of the post-core material is close to that of dentin. Hence the elastic modulus is one of theimportant parameters to evaluate when choosing an appropriate post-core material for dental restoration. The
outcome of this study can be used as a reference when other materials are chosen to be post-cores, for example
carbon fiber reinforced composites, pure titanium, and zirconium oxide.
The study also demonstrated that when the elastic modulus of the post-core material increased, the maximum
stresses in the coronal part of the root dentin deceased, whereas the maximum stresses in the post-apex increased.
It is evident from the stress distribution contour shown in Fig. 3 that the post-core with high elastic modulus
reduced the maximum stress values in the coronal part of the root dentin, but the highly stressed region expanded
along the surface of the root towards the apex. The higher the elastic modulus of the post-core material, thelarger the expanded high stress region and more stress concentration at around the post-apex. When the cast
Ni-Cr alloy (with the highest elastic modulus) was used as post-core, the highly stressed region on the root25

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Int Chin J Dent 2008; 8: 21-27.

surface covered form the coronal part of the root dentin all the way to the level of post-apex. This, together withthe two stress concentration areas, formed a large highly stressed region over the entire cross section of the root
(Fig. 3(e)). This in turn increased the likelihood of fracture of the dentin. The post with low elastic modulus, on
the other hand, did not reduce the maximum stress values of the coronal part of the root dentin; neither caused
stress concentration at the post-apex. When the polyethylene fiber reinforced composite, of which the elastic
modulus was similar to that of a dentin, was used as a post-core, the stress distribution characteristics were very
similar to those of the control model restored with PFM.
The above FEM results can be elaborated from the mechanics point of view. When the elastic modulus of thepost is high, the load carrying capacity of the post itself is also high. In other words, the post absorbs more
loading which in turn reduces the stress in dentine at the post level, and shifts the stress concentration region to
the post-apex level. Considering the fact that the coronal part of the root dentin is much thicker than the
post-apex, the likelihood of fracture of the post-apex is much higher than the coronal part under the same stresscondition. Hence it is more important to reduce the stresses in the post-apex region.
The placement of the post-core changes the stress distribution patterns within the dentin, which largely
correlated with the elastic modulus of the post. Before post restoration, the induced stresses transfer from thecoronal part to the apex along the surface of the root. The interior part of the root where the post is placed islowly stressed. This situation is changed when placing a post with high elastic modulus where the post itself
attracts a large amount of the load. As a result, the stresses within the root decrease except the post-apex region.
When the elastic modulus of the post is low, the load absorbed by the post is small and the remaining load mustbe supported by the out layer of the dentin. This study showed that, when the elastic modulus of the post was
high, the primary load supporting element is the post and stress concentration was high. When the elastic
modulus of the post was small, the post did not attract much load which caused little change on the stress
distribution within the root dentin. The finding of this study is also supported by the work of Albuquerque etal.14 and Toparli et al.15 who claimed that stainless steel posts presented the highest level of stress concentration.
Although the stress distribution characteristics in root dentin restored with different post-core materials havebeen successfully evaluated in this study, certain limitations are recognized by the authors. These include theassumptions made on the properties of the post materials and tissues used in the finite element analysis, as wellas the simplified loading scenarios. Note that this study was not intended to determine the absolute numericalstress levels created within the restoration but to examine the stress distribution patterns due to different
post-core materials. Note also that failure of the models was outside the scope of this study, therefore themagnitude of the load would only proportionally alter the magnitude of the stresses. Moreover, the theoretical
study conducted herein should be validated in relevant clinical and in vitro experimental work, which will help
further develop key principles for post restoration.
In conclusion, this study successfully demonstrated that the FEM was effective in analyzing stress distribution
characteristics in dentin and post. The study has verified that the elastic modulus is one of the importantparameters to evaluate in post restoration. The results have provided some useful guidance for clinical practice.
Within the limitations of this study, the results suggested that the polyethylene fiber reinforced composite withelastic modulus similar to that of a dentin is more suitable for post-core restoration. The extensively used cast
Ni-Cr alloy, cast titanium alloy, and cast gold alloy are considered to be less appropriate. Results of this study
further confirmed the principle that the elastic modulus of the restoration material should be as close as that of a26

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Int Chin J Dent 2008; 8: 21-27.

dentin. This is supported by the recent move of the dentists who have changed from using very rigid materials to
those that closely resemble dentin in an attempt to produce a mechanically homogenous unit.16,17
Acknowledgment
The assistance of Emeritus Professor Kunhao Fang of Sun Yat-Sen University, China in improving the technical discussion is gratefully
acknowledged.

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Correspondence to:
Dr. Xiao-na Li
Department of Prosthodontics, Dalian Stomatological Hiospital
School and Hospital of Stomotology, Dalian University
No. 935 Changjiang Road, Shahekou District, Dalian, 116021, P. R. China.
Fax: +86-0411-8464-4794 E-mail: lixn0217@163.com
Received January 22, 2008. Accepted May 31, 2008.
Copyright ©2008 by the International Chinese Journal of Dentistry.

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