modal analysis for selecting restorative materials in...

73

Journal of Applied and Industrial Sciences, 2013, 1 (2): 73-85, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)

Research Article

*Corresponding author E-mail: [email protected]

Abstract- Modal analysis is an effective tool for assessing the

stability and health of the restored endodontically treated teeth.

Natural frequency depends mainly on the bone osteointegration loss,

hence on the tooth stiffness, which in turn is affected by the selection

of tooth restorative materials. The present work aims to study how

the selection of restorative materials for crowns, cores and posts

affects natural frequency: this allows the restoration construction to

be optimized. For this purpose, the commercial finite element

package ANSYS was utilized. The results indicated that the natural

frequency of the restored tooth depends on the Young's modulus and

mass density of the used materials. In view of the fact that tooth

restoration stability improves as natural frequency increases, the

restorative materials can be rated as the most suitable materials as

follows: Carbon fibres, Glass fibres, Porcelain, Feldspathic Ceramic,

Titanium alloy, Zirconia, and Gold. Natural frequencies also decrease

as the ratio between Young's modulus and mass density decreases.

Index terms: Vibration, Natural frequency, Modal shape, Post,

Crown, Core, Treated teeth, Dental materials

I. INTRODUCTION

ailure of endodontically restored teeth has been related to

the design of the restoration with respect to the selection

of restorative materials and, in particular, natural frequencies.

Endodontic treatments are usually recommended when the

pulp tissue is degenerated or injured. Post and core systems

are commonly used for the restoration of endodontically

treated teeth when the teeth have suffered coronal damage.

Kishen, and A. Asundi[1] studied the stress distribution

patterns in post– core restored teeth and the behavior of dentin

material to fracture propagation was conducted. Digital

photoelastic experiments showed that endodontic post–core

restoration resulted in regions of high tensile stress and stress

concentrations in the remaining dentin structure. There was a

significant correspondence between the plane of stress

concentrations identified in the photoelastic models and in

those of the plane of fracture exhibited by the rehabilitated

tooth specimens. While the fracture of post–core rehabilitated

teeth was consistent, that of control teeth was not as distinct.

The Scanning Electron Microscopy (SEM) highlighted

varying dentin response to fracture propagation at the inner

core and the outer regions. The fractographs showed brittle

and ductile response to fracture propagation.

Roberto Sorrentino et al., [2] presented a Finite Element

Analysis (FEA) of strain and stress distributions in

endodontically treated maxillary central incisors restored with

different post, core and crown materials,. They concluded that

the mechanical properties of the crown and core material

influenced the position of concentration areas of stress and

strain and the level of stress and strain along the

dentin/cement/post interface in addition the higher the rigidity

of the crown and core materials the more apical stress and

strain concentrations along the adhesive interfaces.

S. Joshi et al., [3] studied the mechanical performance of

endodontically treated teeth. They found that posts fabricated

from conventional materials do not reinforce teeth. Rather

they cause areas of stress concentration that may make

endodontically treated teeth susceptible to fracture. The ideal

post material should have stiffness properties close to that of

the dentin. Moreover, the post material should be tailored to

prevent fracture in the existing tooth structure. The failure in

the post should also be gradual. The only class of materials

that can possess all these properties are composites.

A. Pegoretti., et al [4] investigated the Finite Element

Analysis (FEA) of a glass fibre reinforced composite

endodontic post. The results were compared with those

obtained considering either a commercial carbon fibre post or

a gold alloy cast post. A natural tooth, or better a tooth

restored with ideal materials whose stiffness is equal to those

of enamel and dentine, was considered as a reference model.

Modal Analysis for Selecting Restorative

Materials in Endodontically Treated Teeth

Nadia. E. Bondok Department of Technology Development, Academy of Specialized Studies, Workers .University of Esmailia, Egypt

,Faculty of Engineering, University of Gizan , Saudi Arabia

,

(Received May 01, 2013; Accepted May 31, 2013)

F

mailto:%20nana

74


The gold cast post-and core produces the greatest stress

concentration at the post-dentin interface. Except for the force

concentration at the cervical margin, the glass fibre composite

post induces a stress field quite similar to that of the natural

tooth. Stresses at the cervical margins could be lowered using

less stiff crown materials, i.e. composite resins, thus obtaining

an „„integrated‟‟ post core- crown system.

A. Lanza et al., [5] investigated a cemented steel, glass and

carbon posts in a maxillary incisor by Finite Element Analysis

(FEM) . It was found that the more stiff systems (steel and

carbon posts) have been evaluated to work against the natural

function of the tooth. A very stiff post works against the

natural function of the tooth creating zones of tension and

shear both in the dentine and at the interfaces of the luting

cement and the post. The influence of the cement layer

elasticity in redistributing the stresses has been observed to be

less relevant as the post flexibility is increased.

Erik Asmussen et al., [6] analysed the stresses in

endodontically treated, dowel-restored teeth. Within the

limitations of this study, it was found that all investigated

dowel-related factors influenced the stress field generated in

dowel-restored teeth. Bonded dowels and parallel-sided

dowels resulted in less dentin stress than non-bonded and

tapered dowels. Dentin stress was reduced with increasing

diameter and modulus of elasticity of a bonded dowel. A

decrease in dowel length increased dentin stress, but shifted

the maximum stress to a location apical to the dowel.

Franco Maceri et al., [7] investigated the mechanical

behaviour of endodontic restorations with multiple

prefabricated posts by a finite-element approach, when

standard restorative materials and natural tooth are considered.

A risk-analysis of root fracture and interface-failure shows

that cast gold-alloy post produces high stress concentrations at

post-dentin interface, whereas multi post solution leads to a

behaviour closer to the natural teeth, exhibiting some

advantages with respect to single prefabricated composite post

(PCP) restorations.

Fouad K.Wahab,[8] reviewed the restoring of

endodontically treated tooth, concepts and techniques. The

strength of core materials directly affect the clinical success of

posts. Custom cast posts are potentially more conservative in

anterior teeth whilst prefabricated posts are more conservative

in molars. Premolars may be restored with either technique.

Threaded posts that engage dentine are dangerous and

generally not recommended.

Q. Li.etal [9] investigated the fracture resistance and

retention of endodontically treated roots with over-flared

canals restored with different post systems, including one cast

metal post and four fiber posts with/without auxiliary fiber

posts.Within the limitations of this study, it was concluded

that the application of an auxiliary fiber post could

significantly increase the fracture resistance of over-flared

roots; however, no beneficial effects in enhancing retention

were observed.

A.Shetty etal., [10] carried out a comparative study of intra

canal stress pattern in endodontically treated teeth with

average sized canal diameter and reinforced wide canals with

three different post systems - cast post and core, carbon fiber

post, stainless steel post; restored with ceramic crown using

finite element analysis(FEA). Maximum stress was seen on

the inner dentinal wall in case of stainless steel post followed

by cast gold and carbon fiber post, both in the models without

reinforcement as well as in the reinforced models.

N. Meredith., [11] determined the elastic modulus of resin

based materials as a function of resonance frequency during

polymerization. All results showed that a new non-invasive

test method is described which can measure the increase in the

elastic modulus of resin based materials as a function of

resonance frequency. The technique is not sensitive to

temperature, exhibits no drift and does not influence the

polymerisation of the test material.

R. F. Gibson., [12] investigates modal vibration response

measurements for characterization of composite materials and

structures. It is shown that modal testing in either a single

mode or multiple modes of vibration can be used to determine

elastic moduli and damping factors of composites and their

constituents under various environmental conditions. Modal

testing by the use of impulsive excitation methods has been

shown to have the potential to be a fast and accurate approach

not only for the characterization of intrinsic material

properties, but for quality control and inspection as well.

R. Schmidt et al. [13] investigated the applicability of the

impulse excitation technique to non-destructive measurement

of the dynamic Young's modulus of moulding compounds.

This method has the advantage of being fast, highly accurate

and repeatable. The best selection of dental materials, their

resonance frequency as well as the type of loads may allow

preventing dental failures. Modal analysis is a good tool for

evaluating stability and health of endodontically treated teeth.

From the previous literature survey it is clear that natural

frequency depends on the tooth stiffness, which in turn is

affected by the selection of tooth restorative materials. For

these reasons, the present work aims to study how the

selection of restorative materials for crowns, cores and posts

may affect natural frequency: this will allow restoration

constructions to be optimized.

II. MATERIALS AND METHODS

Description of model

According to the Canadian Academy of Enododontic

(CAE1998) [14] the procedure of an endodontic treatment

includes several steps. The infected Pulp tissues inside the

tooth are first removed. Once the root canal space is cleaned, a

material called gutta percha is placed to fill and seal the canal.

A post-core system is commonly used to restore the tooth. on

the top of the core, a crown is placed. In this work, the

physical model of a post-core restored endodontically treated

tooth is the maxillary central incisor which includes seven

components: the bone supporting the tooth, periodontal

75


ligament (PDL), root dentin, gutta-percha, post, core, crown,

and. The structure of post-core restored endodontic treated

tooth (geometry of the physical model) is shown in Figure (1).

The boundary conditions at the bottom end of the bone

were restrained in all degrees of freedom to simulate the

alveolar bone holding the tooth, i.e., the outside surface of the

bone is fixed which allows zero displacement.

Some assumptions have been made regarding the material

properties of each part and its geometry.

-The geometry of the post and core restored incisor is

simplified in that all components are Modeled to be axi-

symmetric along the vertical centerline.

- An ideal dental post have parallel geometry without taper,

where tapered posts exhibit Wedging effect at root canal and

produce stress concentration around the tip of post.

- Since any cement (lutting agent) layer between any of the

restorative materials, or between these materials and tooth

structure is very thin , the cement layer is regarded as part of

dentin especially cement with modulus of elasticity equal

18.6MPa [5] was used in this model.

- No gap exists between the components, and all

components are assumed to be perfectly bonded.

- Pre- stress due to the endodontic treatment is neglected

Axi- symmetric models are appealing for resonance analysis,

therefore an axisymmetric model is used in this study with

the commercial software ANSYS. In an axi-symmetric model,

the elements are represented by 2D elements, but a 3D

structures is implied.

One should, point out that two-dimensional software

assumes that the model‟s geometry remains unchanged in all

sections parallel to the plane of the model. Amarante et al [27]

found that axi-symmetric models are therefore more

representative and three-dimensional (3D) models would

represent the most faithful simulation of clinical situations.

Three-dimensional models are surely more accurate in

describing the actual state of stress but, at the same time, much

more complicated to realize and they do require a much

extensive computing time to be resolved. Papadopoulos et al

[28] designed a two dimensional finite element model in order

to simulate their experimentally obtained results. Their

numerical and experimental results nearly coincided.

Vibration and Finite Element Analysis:

Mechanical vibration analysis is a non-destructive

testing method widely used by mechanical engineers to

inspect structural integrity. The potential application of this

technique in the area of dental restoration has been proven

able to augment information available from clinical

radiography, scintography and orthography. The natural

frequency of a model reproducing a single degree of freedom

system mounted as a cantilever beam is:

Figure (1) structure of post- core restored endodontic treated

tooth

m

kf

2

1 (1)

where m is the mass of the material and k is the stiffness of the

structure. If model dimensions are constant, the resonance

frequency can be expressed as:

ECf (2)

where C is a constant, E is the Young's modulus of the

material, is the mass density. Equation (2) shows that the

resonance frequency depends on the ratio between the Young's

modulus and density of materials used for core, post and

crowns. As the ratio E/ increases, the resonance frequency

becomes higher. In this study, the material of each component

included in the finite element model of post-core restored

endodontically treated tooth was assumed to be homogeneous,

isotropic/anisotropic, and linearly elastic. Table 1 lists the

material properties used for all components. Finite element

models and analysis were performed with the commercial

software ANSYS. The quadratic element (PLANE82) was

utilized for meshing the tooth model: it includes eight nodes

each with two degrees of freedom, the translations in the

coordinate directions x and y-directions defined in the local

reference system of the element. PLANE82 has plasticity,

creep swelling, stress stiffening, large deflection, and large

strain capabilities.

Figure 2 shows the seven parts of which the solid model of

maxillary central incisor is comprised. Figure 3 shows the

finite element model generated by ANSYS.

76


Table (1). Elastic properties of the isotropic materials utilized for the FE analysis

Material

Young's modulus

(E,GPa)

Poisson'sRatio(υ) Density(ρ) , kg/m

3

E/ ρ* (109)

(N.m/kg)

Feldspathic Ceramic[2] 69 0.3 2600 0.025

Porcelain [16] 96 0.29 2400 0.04

Gold [17] 96.6 0.35 12800 0.0078

Zirconia [18] 75 0.278 5600 0.01

Carbon Fiber[19] 125[8.5] 0.25 [0.32] 1500 0.083

Glass Fiber [20] 85 0.22 2000 0.0425

Composite resin [14] 16.6 0.24 2000 0.00825

Titanium Alloy [21] 54 0.35 4500 0.012

Cortical bone[22,23] 13.7 0.3 2000 0.0068

Dentine[2],[15],[29] 18.6 0.32 2100 0.0087

Adhesive cement resin (high modulus)

(Panavia, Kuraray, Japan) [5] 18.6 0.28 2100 0.0087

Gutta percha[17,24 ,25] 0.00069 0.45 1000 0. 69*10-6

Periodontal ligament[14,26] 0.05 0.45 1100 45*10-6

1

X

Y

Z

FGBM dental implant

APR 10 2010

21:43:55

ELEMENTS

/EXPANDED

MAT NUM

Figure 2. Solid models of the parts included in the restored tooth

1

X

Y

Z

FGBM dental implant

APR 10 2010

21:43:02

ELEMENTS

/EXPANDED

MAT NUM

1

X

Y

Z

FGBM dental implant

APR 10 2010

21:42:49

ELEMENTS

/EXPANDED

MAT NUM

1

FGBM dental implant

APR 10 2010

21:41:37

ELEMENTS

/EXPANDED

MAT NUM

1

FGBM dental implant

APR 10 2010

21:40:30

ELEMENTS

/EXPANDED

MAT NUM

(e)Post

(b)PDL

(a) Dentin

(f) crown

(c) Cortical bone

(d) core

1

X

Y

Z

FGBM dental implant

APR 10 2010

21:42:00

ELEMENTS

/EXPANDED

MAT NUM

1

FGBM dental implant

APR 10 2010

21:44:20

ELEMENTS

/EXPANDED

MAT NUM

(e) gutta percha

77


Figure 3. Finite element model of the restored tooth.

III. RESULTS AND DISCUSSION

The effect of the different materials used for tooth

restoration on natural frequency and modal shape was studied.

Preliminary tests indicated that only the first mode of vibration

is affected by the different combinations of crown, post and

core materials. The first cycle of finite element analyses

served to study the effect of combining post and crown

materials when the core material (composite resin) does not

change. The values of first natural frequency obtained for

different materials are reported in Table2. It appears that

natural frequency is more sensitive to crown materials. This is

proven by the largest dispersion with respect to the mean

value of frequency. This result can be explained in view of the

shape size, and geometry of the crown. Figure 4 shows the

frequency values obtained by choosing post and crown made

of the same material: the minimum value corresponds to the

gold restoration for which the ratio between Young's modulus

and density also is the least. It can be concluded that the

crown-post core system stiffness drives the frequency

response of the restored tooth.

Figure 5 shows some modal shapes obtained for different

combinations of crown and post materials with the same

composite resin core, while Figure (6) indicates that modal

shapes usually are of the compression-bending type when post

and crown materials are the same.

Carbon fiber

Glass fiber

Porcelain

Feldspathic Ceramic

Titanium Allo

y

Zirconia

Gold

0

100

200

300

400

500

600

700Frequency

Frequency

Figure (4). Natural frequency values computed with

composite resin core when the post and crown are made of

the same material.

Crown vibration was dominantly present in the natural

modes.Under the impact of chewing force, the tooth vibration

will be mostly dominated by the first vibration mode shape.

Chewing force on maxillary central incisor tooth is transferred

along its axis and will be cushioned by the periodontal

ligament. The results of Li, Ming-Yong et al.[24] showed that

the first natural frequency of maxillary central incisor tooth

was 879.65 Hz and the vibration mode was whole tooth

vibration along its axis in crown to root direction, so according

to the present results in table 2 the first natural frequency of

the restored tooth when restored the post and crown from

porcelain, is approximately near to that reported by this

reference .

Titanium post with gold crown

Titanium post with Porcelain crown

Frequency

(HZ)

Figure 5: first mode shapes of the Titanium post, Composite resin core with gold

and Porcelain crown respectively

78


Table (2). Frequency values with composite resin core and different Crown and post materials combinations

Post and crown Gold

Post and crown Feldspathic Ceramic

post and crown porcelain alumina

Post and crownTitanium

Figure 6. Mode shapes of restored teeth with composite resin core the post and crown made of porcelain alumina and Titanium

respectively.

Post material Mean Standard

Deviation

Glass

fiber

Feldspathic

Ceramic

Gold

Titanium

Alloy

Porcelain

Carbon

fiber

Zirconia

Cro

wn

mat

eria

ls

Glass fiber 646.82 648.35 611.9 642.8 651.58 648.64 641.6 641.67 13.57368

Feldspathic

Ceramic 625.2 626.03 593.23 620.85 628.55 626.85 619.31 620 12.256

Gold 397.48 399.6 391.65 399.31 401.44 397.78 400.49 398.25 3.22784

Titanium 555.25 556.58 533.7 553.5 558.9 556.33 553.1 552.48 8.51112

porcelain 635.57 636.16 601.76 630.57 638.59 637.33 628.68 629.8 12.87986

Carbon fiber 679.97 674.8 633.6 668.2 678.12 675.69 666.47 668.12 16.00369

Zirconia 524.95 526.49 507.16 523.28 528.6 525.83 523.86 522.88 7.15282

Mean 580.7 581.14 553.2 576.9 583.6 581.2 576.2

Standard Deviation 97.076 95.63671 84.1314

5 93.498 96.105 96.6422 92.363

79


The second cycle of FE simulations studied the sensitivity of

first natural frequency to different core and post material

combinations when the crown material (Feldspathic ceramic)

remained the same. Table 3 indicates that the effect of core

material on the natural frequency is more significant than for

the post materials: this is confirmed by the largest dispersion

with respect to the mean value. Figure 7 shows some

examples of modal shapes obtained for different combinations

of core and post materials while Figure 8 is relative to similar

material combinations. Again, modal shapes are in

compression-bending modes. It can be concluded that the

effect of the different tooth parts on the mode frequencies and

shapes can be ranked as follows: 1) Crown; 2) Core; 3) Post.

As expected, the material with the smallest ratio between

Young's modulus and mass density also has the minimum

frequency. Some modal shapes are presented in Figure (9).

The influence of the bone material properties (e.g. Young's

modulus and mass density of dentine) on the first five modes

were studied using material properties listed in Table 4. As

expected, natural frequencies become higher as the Young's

modulus increases. The trend becomes nearly asymptotic

when the Young's modulus is larger than 5 GPa (see Table 5

and Figure 9).

Table 3. Modal frequencies with Alumina Crown and different core and post materials

Post materials Mean Standard

Deviation

Glass ceramic gold Titanium

alloy porcelain

Carbon

fiber zirconia

Core

materials

Glass 576.87 577.9 552.2 574.08 580.1 578.11 573.1 573 9.5661

ceramic 565.99 567.26 542.47 563.64 569.5 567.15 563.02 562.7 9.20051

Gold 434.09 436.17 425.44 435.39 438 434.52 436.29 434 4.10125

Titanium 532.63 534.22 513.91 531.56 536.42 533.56 531.38 530.5 7.52669

Porcelai

n 570 571.36 546.36 567.75 573.43 571.29 566.99 566.7 9.25435

Carbon

fiber 587.24 588.18 561.08 584.02 590.33 588.57 582.83 583.2 10.09039

zirconia 515.9 517.66 499.23 515.4 519.86 516.75 515.49 514.3 6.83729

Mean 540.3 541.8 520 538.8 543.9 541 538.4

Standard

Deviation 53.2564 52.8744 47.142 51.7015 52.98149 53.575 50.99385

Titanium post, Gold core, Alumina crown

Titanium post Porcelain core, Alumina crown

Figure 7. Mode shapes of restored teeth with, Titanium post, Alumina crown, Gold and Porcelain core materials.

80


Porcelain post and core, Alumina Crown

Titanium post and core ,Alumina Crown

Table 4. Young's modulus of different types of Dentin [27]

Young's modulus

(E,MPa)

Poisson's Ratio (υ) Density

(ρ , kg/m3) E/ ρ*10

6

10 0.3 1000 0.01

100 0.3 1000 0.1

300 0.3 1000 0.3

500 0.3 1000 0.5

1000 0.3 1000 1

5000 0.3 2000 2.5

10000 0.3 2000 5

15000 0.3 2000 7.5

20000 0.3 2000 10

Table 5. Effect of Dentin material properties on the modal frequencies.

Titanium post, porcelain crown, composite resin core

Different dentin properties

Density = 1000 kg/m3 Density = 2000 kg/m

3

E = 10

Mpa

E = 100

Mpa

E = 500

Mpa

E =

1000

Mpa

E =

5000Mpa

E =

10000 Mpa

E= 15000

Mpa

E= 20000

Mpa

f1 67.121 195.916 365.568 449.45 563.73 609.69 621.8 642.77

f2 306.5 834.9 887.3 893.4 899.3 900.6 901.2 901.6

f3 375.7 903 1140 1150 1159 1161 1161 1162

f4 418 1067 1417 1429 1439 1441 1441 1442

f 5

462 1119 1569 1636 1644 1645 1646 1646

Figure 8. Mode shapes of restored teeth with the Porcelain and Titanium (Post and core), and alumina crown

Porcelain post and core, Alumina Crown

81


0

200

400

600

800

1000

1200

1400

1600

1800

0 5000 10000 15000 20000

Dentin Young's modulus (Mpa)

Fre

qu

en

cy (

Hz)

Mode1

Mode2

Mode3

Mode4

Mode5

Figure 9. Natural frequencies for different material properties of Dentin

Figures (10 and 11) show that the first five mode shapes are

affected when modulus of elasticity equal 10 MPa,100MPa

respectively, while Figures (12 – 15) indicated that the first

mode shape is the most sensitive mode to changes in dentin

elastic properties. The other mode shapes do not change

significantly if the Young's modulus is larger than 1 GPa.

Finite element results reported by Ho et alquated by Amarante

et al [27] on a maxillary central incisor with and without post

restoration indicated that, despite the simplifications of the 2D

models, the locations of the peak dentinal stresses in the two-

and three-dimensional models were similar. In addition, the

3D models demonstrated that these peak stresses, generated in

the tooth due to masticatory or traumatic loading, were

reduced by an average of about 10% as a result of using gold

or stainless steel restoration posts. However, these reductions

were slightly greater than those predicted by two-dimensional

and axisymmetric models, which amounted to an average of

approximately 5%. This comparison seems to indicate that

two-dimensional models are more conservative than their

three-dimensional counterparts.

Also results obtained by Meira et al.,[quated by Amarante

et al [27] have indicated that the axisymmetric model presents

stress vectors with similar orientation but lower in magnitude

than those detected by 2D analysis for elements in the vicinity

of restoration post, and stress levels can therefore be

overestimated by adopting 2D finite element analysis. It is

worth mentioning that, despite eventual approximations due to

the adoption of 2D rather than 3D analysis, the comparison

between the models is considered to be valid, specifically in

regard to the identifi- cation of critical regions where cracks

can nucleate and eventually propagate leading to the loss of

structural integrity and finally ultimate fracture of the restored

tooth. Papadopoulos et al.,[28] investigated an experimental

and numerical determination of the mechanical responsponse

of teeth with reinforced posts, mechanical testing rvealed that

teeth restored with titanium posts exhibited the highest

fracture strength. Depending of the core was the main failure

mode observed in glass fiber posts, whereas vertical root

fractures were observed in between the post,dentin, and the

composite core cortical regions. Kaur et al.,[10] studied a

comparative study of intra canal stress pattern in

endodontically treated teeth with average sized canal diameter

and reinforced wide canals with three different post systems

using finite element analysis. They found that Stress pattern

seen in the tooth-root surface were similar in nature,

irrespective of the post material used. Maximum stress was

seen in case of stainless steel post followed by cast gold and

carbon fiber post. The stress generated on the root surface

could be co-related to the Young's modulus of elasticity of the

material used for the post system. It can be concluded that in

widened root canal reinforcement with suitable material, use

of carbon fiber post is better than stainless steel post or cast

gold post.

82


Fi First mode

Second mode

Third mode

Fourth mode

Fifth mode

Figure10. First five mode shapes with E dentin=10 MPa

83


First mode

Second mode

Third mode

Fourth mode

Fifth mode

Figure 11. First five mode shapes with Edentin=100 MPa

84


Figure 12. First five mode shapes with Edentin =500 MPa

IV. CONCLUSION

The effect of the different materials used for tooth

restoration on natural frequency and modal shape was studied.

It was found that for crown, core and post, only the first

natural frequency was affected by the type of material. Finite

element analysis results indicated that the natural frequency

increases as the ratio between material Young's modulus and

mass density increases. The structural response is dominated

by the crown material, the core material has an intermediate

effect, while the effect of post material is less significant.

Natural frequencies also increase when the bone material is

stiffer. However, values becomes nearly asymptotic as the

Young's modulus is larger than 5 GPa. With respect to tooth

restoration stability which is related to the value of natural

frequency, the restorative materials can be rated as follow:

Carbon fibres, Glass fibres, Porcelain, Feldspathic Ceramic,

Titanium alloy, Zirconia, Gold.

REFERENCES [1] A. Kishen, A. Asundi,. (2002). Photomechanical

investigations on post endodontically rehabilitated

teeth",Journal of Biomedical Optics,Vol.7, PP. 262–270.

[2] R. Sorrentino,R. Aversa,V. Ferro, T. Auriemma, F.

Zarone, M. Ferrari, A. Apicella .(2007) Three-

dimensional finite element analysis of strain and stress

distributions in endodontically treated maxillary central

incisors restored with different post, core and crown

materials”, Dental Materials Vol.2 3,PP.983–993.

[3] S. Joshi, A. Mukherjee, M. Kheur, A. Mehta, (2001).

Mechanical performance of endodontically treated

teeth", Finite Elements in Analysis and Design,Vol.

37,PP. 587-601,

[4] A. Pegoretti, L. Fambri, G. Zappini,M. Bianchetti, (2002).

Finite element analysis of a glass fibre reinforced

composite endodontic post" Biomaterials, Vol

23,PP.2667–2682.

[5] A. Lanza, R. Aversa, S. Rengo, D. Apicella, A. Apicella,

(2005) .3D FEA of cemented steel, glass and carbon

posts in a maxillary incisor, Dental Materials, Vol. 21,PP.

709–715.

[6] E. Asmussen, C.Scient, DrOdont, A.Peutzfeldt, D.Odont,

A. Sahafi., , (2005). Finite element analysis of stresses in

endodontically treated, dowel-restored teeth", The Journal

of Prosthetic Dentistry,Vol 94 .

[7] F. Maceri, M. Martignoni, G. Vairo, (2007). Mechanical


prefabricated posts: A finite-element approach", Journal of

Biomechanics, Vol. 40 PP.2386–2398,

[8] F. K. Wahab, (2004). Restoring of endodontically treated

tooth. Concepts and techniques", The Saudi Dental

Journal, Vol. 16, No. 2.

[9] Q.Li,B.XU,Y.Wang,Y.Cai (2011).Effects of Auxiliary

Fiber Posts on Endodontically Treated Teeth With

Flared Canals", Operative Dentistry, Vol.(Zero),in press

[10] A.Kaur,N.Meena, N.Shubhashini,A. Kumari,A.Shetty,

(2010). comparative study of intra canal stress pattern in

endodontically treated teeth with average sized canal

diameter and reinforced wide canals with three different

post systems using finite element analysis", Journal of

Conservative Dentistry Vol.13,PP.28-33.

[11] N. Meredith., (1999). Determination of the elastic

modulus of resin based materials as a function of

resonance frequency during polymerization."., Dental

Materials,Vol.15, PP.98 -104.

[12] R.F.Gibson., (2000). Modal Vibration Response

Measurements for Characterization of Composite

Materials and Structures", Journal of Composites Science

and Technology.Vol.60, PP. 2769- 2780.

[13] R. Schmidt, V. Wicher, R. Tilgner, (2005). Young‟s

modulus of moulding compounds measured with a

resonance method", Polymer Testing.Vol.24,PP. 197–203.

http://www.sciencedirect.com/science/journal/02663538

http://www.sciencedirect.com/science/journal/02663538

85


[14] G.Q. Song , (2005).“Three dimensional finite element

analysis of post core restored endodontically treated

teeth.”, Master of Science, University of Manitoba,

Winnipeg, Manitoba (Canada),

[15] W.Jiang,H.Bo,G.Y. Chun,N.L.Xing .(2010). Stress

distribution in molars restored with inlays or onlays

with or without endodontic treatement: A three

dimentional finite element analysis", The Journal of

Prosthetic dentistry Vol. 103,PP.6-12

[16] X. N. Li, Y. K. Shi, Z. C.Li, C.Y. Song, X.D. Chen,

Z.Q. Guan, H.G.Xiang ,T.Chen, .(2007). Three

dimentional finite element analysis of a maxillary

central incisor restored with different post- core

materials”,Int. Chin J. Dent Vol.8 ,PP. 21–27

[17] S.D. Heintze, A. Cavalleri, G. Zellweger, A. Bu¨ chler,

G. Zappini.(2008).Fracture frequency of all-ceramic

crowns during dynamic loading in a chewing simulator

using different loading and luting protocols”, Dental

Materials, Vol. 24, PP.1352–1361.

[18] G.H. Zhou , S.W Wang, J.K.Guo, Z.Zhang, (2008). The

preparation and mechanical properties of the

unidirectional carbon fiber reinforced zirconia

composite”, Journal of the European Ceramic Society,

Vol. 28, PP.787–792.

[19] A. Pegoretti, L. Fambri, G. Zappini, M. Bianchetti.

(2002).Finite element analysis of a glass fibre

reinforced composite endodontic post”, Biomaterials,

Vol.23,PP. 2667–2682.

[20] X. Li, , B. Bhushan, P.B.McGinnis., (1996). Nanoscale

mechanical characterization of glass fibers”, Materials

Letters, Vol. 29 ,PP.215-220,

[21] G. He, M. Hagiwara., (2005) Bimodal structured Ti-base

alloy with large elasticity and low Young‟s modulus”,

Materials Science and Engineering C ,Vol. 25 PP. 290 –

295.

[22] L. Capek, , A. Simunek, R. Slezak, L. Dzan , (2009)

Influence of the orientation of the Osstell® transducer

during measurement of dental implant stability using

resonance frequency analysis: A numerical approach”,

Medical Engineering & Physics, Vol 31 ,PP. 764–769.

[23] V.Pattijn, C.Van Lierde,G.Van Der Perre, I.Naert,

J.Vander Sloten (2006).The resonance frequencies and

mode shapes of dental implants: Rigid body behaviour

versus bending behaviour. A numerical approach”,

Journal of Biomechanics. Vol. 39 PP.939–947.

[24]Li,.M.Yong,Li,Bin,Yan,Hong,Li,Y.Long,Zhao,L.Cheng,

Yan,Z.Qiang,Li, Zhun, Ma, X.Xiang, “Modal analysis of

maxillary central incisor tooth”, African Journal of

Biotechnology Vol. 8 (19),PP. 5088-5096, (2009)

[25] K.Genovese,L. Lamberti, C.Pappalettere,”Mechanical


prefabricated posts: A finite-element approach”, Journal

of Biomechanics Vol.40, PP. 2386–2398, (2007).

[26] L.K.Shen,H.M Huang, J.J.Yu, S.Y.Lee, C.M.Lee, S.C.

Hsieh, (2009). “Effects of periodontal bone loss on the

natural frequency of the human canine: a three-

dimensional finite element analysis”, Dental Materials,

Vol.4(2),PP. 81−86

[27] M.V. Amarantea, M.V. Pereirab, F. A. Darwishc, A.

F.Camarãod, (2011). Stress Prediction in a Central

Incisor with Intra-radicular Restorations", Materials

Research, Vol.14,No(2) PP.189-194

[28] T.Papadopoulos, D. Papadogiannis, D. E Mouzakis, K.

Giannadakis ,G. Papanicolaou, (2010) Experimental and

numerical determination of the mechanical response of

teeth with reinforced posts", Biomedical materials,

Vol.(5)No.(3),.

[29] S.Belli,O.Eraslan,G.Eskitascioqlu,V.Karbhari. (2011).

Monoblocks in root canals: a finite elemental stress

analysis study", International Endodontic

Journal,Vol.44(9),PP.817-826

modal analysis for selecting restorative materials in...

Documents