Journal
of
Dentistry
Journal of Dentistry 29 (2001) 63±73
www.elsevier.com/locate/jdent
A comparison of the mechanical behavior of posterior teeth with amalgam
and composite MOD restorations
D. Arola a,*, L.A. Galles a, M.F. Sarubin b
a
Department of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
b
Sarubin Family Dental Associates, 3110 Timanus Lane, Suite 100, Baltimore, MD 21224, USA
Received 19 July 1999; revised 13 March 2000; accepted 30 June 2000
Abstract
Objective: To compare the mechanical behavior, and infer differences in fracture resistance, of mandibular molars with amalgam and
composite MOD restorations to that of an unrestored molar.
Method: Finite element models were developed for an unrestored molar and molars with MOD amalgam and composite restorations. The
location and magnitude of maximum principal stress resulting from simultaneous mechanical and thermal loads were determined for each
molar using a series of designed experiments. An analysis of variance was conducted with the components of stress to distinguish the relative
in¯uence of oral parameters and restoration on the stress distribution in each molar.
Results: The maximum principal stress in the unrestored molar was the largest of all three molars examined and occurred within the dentin
along the pulpal wall. Maximum principal stresses in the molars with amalgam and composite restorations both occurred along the cavosurface margin. Maximum principal stresses in the molar with amalgam restoration occurred at the pulpal ¯oor and lingual wall junction and
resulted from large occlusal loads. Although occlusal loading had minimal effects on the stress distribution within the molar with composite
restoration, low oral temperatures were responsible for the maximum principal stresses, which were found at the lingual margin and occlusal
surface junction.
Conclusion: There was no signi®cant difference in the magnitude of maximum stress that occurred in the molars with amalgam and light
curing composite restorations. However, the location and orientation of maximum stress in the restored molars were largely dependent on the
restorative material. Although clinical studies report that tooth fracture occurs predominately to restored molars, the unrestored molar
experienced the highest stress in this investigation. Therefore, the reduction in fracture resistance of restored posterior teeth appears to result
from changes in the location of maximum stress resulting from mastication and temperature changes. q 2001 Elsevier Science Ltd. All
rights reserved.
Keywords: Amalgam; Posterior composites; Cusp; Fracture; Restoration
1. Introduction
The failure of dental restorations through recurring caries,
marginal discrepancies, and tooth fracture are topics of
substantial clinical signi®cance. Although not the primary
cause for failure, tooth fracture may be most detrimental
because it often results in extraction [1]. Therefore, the
fracture of restored teeth is a signi®cant problem, which
warrants further study.
According to a reported clinical survey of 100 fractured
teeth, 92 cases involved teeth that had been previously
restored [1]. Furthermore, from a clinical examination of
206 fractured posterior teeth, Eakle et al. [2] found that
over 93% were restored with amalgam, 82% of which
* Corresponding author. Tel.: 11-410-455-3310; fax: 11-410-455-1052.
E-mail address: [email protected] (D. Arola).
were Class II restorations. An independent cross-sectional
survey of amalgam restorations revealed that the probability
of failure may reach over 40% [3]. Although still considered
the primary posterior restorative material, amalgam restorations are considered more susceptible to tooth fracture due
to their inability to provide tooth reinforcement [4,5]. In
contrast, cusp reinforcement can be achieved through dentin
and enamel bonding of light cured composites [5]. Nevertheless, clinical evaluations of Class I and II composite
restorations have shown that the incidence of failure is
near that for dental amalgam [6,7].
Several in vitro studies have been performed using
destructive methods of evaluation to compare molars that
have received composite and amalgam restorations [8±15].
While some have found that composites increase the fracture resistance of molars with Class I [15] and Class II
restorations [13], others contend that the fracture resistance
0300-5712/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved.
PII: S 0300-571 2(00)00036-1
64
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
Fig. 1. Schematic diagrams (proximal view) of the ®nite element models for the unrestored and restored molars. (a) unrestored, (b) amalgam restoration, and
(c) composite restoration.
is sacri®ced by the preparation and is independent of the
restorative material [6,8,14]. In vitro evaluations of tooth
fracture resistance provide little understanding of restorative
material effects on differences in mechanical behavior under
typical oral conditions. No study has compared the stress
distribution in an unrestored molar to that in molars with
amalgam and composite restorations, to understand the
differences in fracture resistance.
The objective of this study was to identify differences in
the mechanical behavior of an unrestored molar with that of
a molar with a Class II amalgam or composite mesial occlusal distal (MOD) restoration with dentin and enamel bonding. The hypothesis to be tested was that the restoration has
a signi®cant effect on the magnitude and location of maximum stress in molars subjected to simultaneous occlusal
and thermal loads.
2. Methods
Previous studies have shown that the incidence of tooth
fracture is highest in ®rst permanent mandibular molars
[1,4,16]. Therefore, ®nite element models for restored and
unrestored ®rst permanent mandibular molars were developed.
2.1. Finite element models
Three individual ®nite element models were developed in
this study including an anatomical crown model of an
unrestored molar and one each of the same molar with
amalgam and composite MOD restorations as shown in
Fig. 1. The solid models were constructed using a commercial computer aided design and ®nite element software 1
according to summaries for permanent dentition in the
literature [17]. The restoration size, location, and cavosurface line angles were chosen to conform with standard
1
I-DEAS, Masters Series 5.0, Structural Dynamics Research Corporation, Ohio, 1990.
cavity design for amalgam preparations [18]. Both the amalgam and composite MOD preparations were modeled with
an isthmus width exceeding 1/3 the inter-cuspal distance
and a depth of 3.0 mm due to the incidence of failure associated with these dimensions [2]. For consistency, the maximum width of both the composite and amalgam
preparations was 3 mm; the line angle radius of curvature
for both preparations was 0.3 mm and would result from
®nishing with a #245 or #329 pear bur 2. Though different
preparations are used when placing amalgam and composite
restorations in teeth with virgin lesions, it was essential to
maintain consistent cavity dimensions for a basis of comparison. The tooth and restoration were meshed with four node
isoparametric plane strain elements. A plane strain analysis
was used due to the extent of deformation occurring in the
buccal-lingual plane in comparison to that along the mesialdistal axis (x33). Mesh re®nement was maintained along the
cavosurface margin of each restored molar, as evident in
Fig. 1, to account for the expected contact stress gradients.
A convergence study was performed prior to the ®nite
element analysis to ensure adequate mesh density for each
model. Differences in stress distribution and mesh convergence results for each molar necessitated the use of unique
mesh con®gurations for the three models. Since each model
is treated as a molar with plane strain response, the 3D stress
state for a molar with a MOD restoration was accurately
obtained. However, results from the model may not be
representative of mesial-occlusal or distal-occlusal Class
II preparations with minimal extension.
Each solid model was translated to a second commercial
®nite element code 3 that permitted treatment of surface
interaction expected along the margins. Boundary conditions for each molar were speci®ed to maintain consistency
with physiological conditions. Vertical displacement along
the base of each crown model was restricted due to support
from the alveolar socket. Horizontal displacement of the
2
3
Brasseler USA, Dental Rotary Instruments, Savannah, GA.
Abaqus, Version 5.7, K.A.S. Hibbit Inc., Rhode Island, 1998.
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
P
θ
T(t)
T(t)
x22
x11
x33
Fig. 2. Boundary conditions and description of the oral parameters considered in the analysis. T(t) is the time dependent temperature, P is the resultant occlusal load, and u is the occlusal load orientation.
crown was also ®xed without restricting Poisson's (transverse) expansion. Similarly, the cavosurface margin of each
restored molar was modeled according to clinical practice.
The molar with a MOD composite was assumed to have
been restored with dentin and enamel bonding, which
requires that the tensile and compressive stress components
remain continuous across the cavosurface margin. In
contrast, the molar with amalgam restoration was modeled
with unbonded margins to permit ®nite sliding interaction
while maintaining compressive stress continuity. A study of
interfacial friction between the amalgam and margins has
not been reported. Therefore, a coef®cient of friction (m ) of
0.5 was arbitrarily chosen to account for interfacial friction
along the unbonded margins of the molar with an amalgam
restoration. It was expected that the actual value would be
between 0.25 and 0.75 according to the standard range
reported for dissimilar materials with rough surfaces [19].
Occlusal loads were distributed along the buccal or
lingual cusp in separate analyses as shown for the molar
with an amalgam restoration in Fig. 2 and were varied
from 0 to 300 N [20]. The total load was distributed over
ten occlusal surface nodes beginning at the ®rst node near
the tooth central axis (within 0.1 mm) and extending over
65
1 mm. The complete occlusal load was located within the
preparation margins; a preliminary study showed that occlusal load placement did not cause large variations in the
resulting stress state unless placed at the cusp tip. The occlusal load was applied through a range of orientations
(458 # u # 908) to accommodate variations encountered
with routine mastication. Thermal loads were applied
along the entire anatomic crown by specifying a node
temperature for a period of time. Temperatures from 5 to
558C, with exposure time between 1 and 10 s, were considered. Although oral cavity temperatures do not remain
constant and approach the intra-oral environment (378C)
with time, the crown nodal temperatures were assumed to
remain constant over the prescribed time period. Changes in
the oral temperature with time would depend on the thermal
properties, density, and volume of consumed substance and
were neglected for simplicity.
All of the mechanical and physical properties for the
molar and restoration were obtained from the literature
and are reported in Table 1. Properties for the dentin and
pulp were assumed to exhibit isotropic behavior as reported
in Refs. [21±23], whereas the enamel was considered anisotropic according to the work of Spears et al. [24]. The
enamel prism orientation was considered to extend radially
through the enamel with an origin located within the pulpal
core. Although dentin exhibits anisotropic structure, an
experimental evaluation showed that mechanical anisotropy
is minimal [25]. All the physical properties of the tooth
required for a thermal analysis were obtained from the
literature and were assumed isotropic [26,27]. Mechanical
and physical properties for the restorative materials were
also obtained from recent published values [18,23]. Properties for the composite were derived from an average of
values reported for posterior materials, and properties for
the amalgam were obtained from an average of admixed
materials.
2.2. Design of numerical experiments
A three-level, four-factor, nine-run design of experiments
(DOE) was adopted in which crown temperature (T ), time
Table 1
Material properties used in the ®nite element analysis
Property
Mechanical [18, 21±24]
E1 (MPa)
E2, E3 (MPa)
v12
v13, v23
Thermal [26,27]
r (kg/m 3)
cp (J/(kg 8C))
k (J/(m s 8C))
a ((m/m)/8C)
Amalgam
n/a
n/a
50.0 £ 10 3
0.29
10500
240
22.70
2.50 £ 10 25
Composite
Dentin
19.0 £ 10 3
n/a
0.24
n/a
20.0 £ 10 3
n/a
0.31
n/a
2830
825
1.09
3.94 £ 10 25
1960
1600
0.59
1.01 £ 10 25
Enamel
80.0 £ 10 3
20.0 £ 10 3
0.30
0.08
2800
712
0.93
1.15 £ 10 25
Pulp
n/a
n/a
2.07
0.45
1000
4200
0.67
1.01 £ 10 25
66
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
Table 2
Levels of the oral parameters used in the numerical analysis
Level
Low (2)
Medium (o)
High (1)
Oral parameters
Crown temperature T (8C)
Time t (s)
Occlusal load P (N)
Orientation u (8)
5
30
55
1
5
10
0
150
300
90
67.5
45
of thermal loading (t), resultant occlusal force (P), and the
occlusal force orientation (u ) were considered as independent variables. The three levels of each independent variable, which span the oral parameter space, are listed in
Table 2. To insure consistency in the numerical results,
three sets of nine runs, consisting of a low, medium, and
high level nine-run set, were performed (27 experiments). A
full factorial analysis (all possible combinations) would
require 81 simulations for each occlusal load placement
(buccal or lingual cusp). A summary of the oral conditions
used in the high level nine-run array is listed in Table 3. The
experimental arrays were performed separately for each
molar to consider occlusal loading of the buccal and lingual
cusps. In total, 54 separate numerical simulations were
conducted with each tooth (two loading cases £ 27 experiments); the entire study consisted of 162 numerical experiments (three models £ 54). Additional information on the
DOE is located in Appendix A.
For each numerical experiment, the location, magnitude,
and orientation of maximum principal stress (s 1) within the
tooth model were identi®ed and recorded. The maximum
principal stress represents the largest normal stress acting
on a plane of no shear stress and is determined from components of stress in the buccal-lingual plane according to the
following equation [28].
s 1 s 22
1
s 1 ˆ 11
2
"
s 11 2 s 22
2
2
1…s 12 †
2
#1=2
…1†
The direction (xij) of individual stress components (s 11, s 22,
and s 33) is shown in Fig. 2. Note that since the analysis is
conducted with a plane strain model, which assumes that
strain in the mesial-distal direction (x33) is negligible with
respect to that in the buccal lingual plane …e 33 < 0†; the out
of plane stress (s 33 ) is obtained from Hookes law [28],
where y is Poisson's ratio.
s 33 ˆ y…s 11 1 s 22 †
…2†
An analysis of variance (ANOVA) was conducted with
results from each nine-run design array to determine the
relative effects of oral parameters on the resulting stress
distribution within each molar. An ANOVA can be used
to distinguish the relative contribution of each oral independent variable on the dependent variable of interest, namely
the individual stress components. The relative percent effect
of each oral parameter was calculated by the ratio of the
individual parametric sum of squares to the total sum of
squares of all parameters. A review of ANOVA is available
in Wheeler, 1989 [29].
3. Results
A ®nite element analysis of an unrestored ®rst permanent
mandibular molar and a restored molar with amalgam and
composite Class II MOD restorations was conducted. Each
molar was subjected to simultaneous mechanical and thermal loads according to the three-level, four-factor experimental design.
3.1. Amalgam restoration
An example of the distribution in s 1 within the restored
molar that resulted from simultaneous mechanical and thermal loading is shown in Fig. 3. The stress distribution in this
®gure resulted from experiment H6 of Table 3, which
consisted of a 150 N occlusal load at 458 orientation, and
Table 3
The nine-run high level array of the design of experiments
Experiment
Temperature (8C)
Time (seconds)
Load (N)
Orientation (8)
H1
H2
H3
H4
H5
H6
H7
H8
H9
55
55
55
5
5
5
30
30
30
10
1
5
5
10
1
1
5
10
300
0
150
300
0
150
300
0
150
45
90
67.5
90
67.5
45
67.5
45
90
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
σ1
67
Pa
1
2
3
4
5
6
+5.00E+06
+1.00E+07
+1.50E+07
+2.00E+07
+2.50E+07
+3.00E+07
1
1
1
1
6
62 4
5 6
1 45
2 3 2
1
1
1
1
1
1
1
1 6
1
1
1
1
1
1
1
1
45
23
1
1
1
2
3
2
1
1
1
1
1
1
1
2
1
1
1
1
2
3
4
2
3
4
1 23
a) buccal cusp loading
1
2
3 3 2
2 4 1
2
1
6
1
4 2
4
6 5
5
6 1
3
2
1
1
1
2
1
2
1
2 2
3 2
4 2
1
1
2 1
1
b) lingual cusp loading
Fig. 3. Distribution of maximum principal stress resulting from simultaneous mechanical and thermal loading of the molar with amalgam restoration.
Load ˆ 150 N at a 458 orientation, T ˆ 58C for 1 s. (a) buccal cusp loading, (b) lingual cusp loading.
a crown temperature of 58C for 1 s. Fig. 3(a) and (b) correspond to the stress resulting from occlusal loading of the
buccal and lingual cusps, respectively. The location of
maximum stress resulting from occlusal loading of the
buccal cusp was found to occur predominantly at the pulpal
¯oor and buccal wall junction. Similarly, lingual loading
resulted in maximum stresses near the junction of the pulpal
¯oor and lingual wall as evident in Fig. 3(b). In the absence
of occlusal loads, changes in oral temperature resulted in the
development of maximum stresses at these locations as
well.
For each numerical experiment, the 3D state of stress
(including s 11, s 22, s 12, and s 33) was recorded at the location of maximum stress. Hence, the maximum principal
stress that resulted from numerical simulations comprised
of loading the lingual (buccal) cusp was recorded at the
junction of the pulpal ¯oor and lingual (buccal) margin. A
summary of s 1 resulting from occlusal loading of the buccal
cusp and recorded at the location of maximum stress is
listed for the high level nine-run array in Table 4. As
expected, the largest principal stress resulted from the maximum occlusal load (300 N) and maximum oral temperature
(558C). Occlusal loading of the lingual cusp generally
resulted in larger principal stresses within the restored
molar than that resulting from buccal cusp loads.
An analysis of variance (ANOVA) was conducted with
the recorded stress components to identify the signi®cance
of oral conditions to variations in stress. A separate
ANOVA was conducted with the results from each ninerun set of experiments (low, medium, and high). Results
Table 4
The maximum principal stress within each molar resulting from occlusal loading of the buccal cusp according to the high level nine-run array
Experiment
MOD amalgam s 1 (MPa)
MOD composite s 1 (MPa)
Unrestored s 1 (MPa)
H1
H2
H3
H4
H5
H6
H7
H8
H9
35.7
7.4
15.4
28.1
9.5
26.8
35.1
2.3
13.1
18.6
11.8
13.0
21.9
20.6
20.6
6.1
4.7
4.7
82.1
2.2
22.8
13.9
8.3
39.4
42.7
1.9
7.0
Avg.
19.3
13.6
24.5
68
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
Table 5
The relative in¯uence of oral parameters on the maximum principal stress variation in each molar that occurred in the design of experiments. The nominal sum
of each column is 100%. (The sum of effects from each oral parameter on maximum principal stress is equal to the total observed variation)
Parameter
Buccal loading
Temperature
Time
Load
Orientation
Lingual loading
Temperature
Time
Load
Orientation
Percentage effect of oral parameter on s 1
MOD amalgam (%)
MOD composite (%)
Unrestored (%)
6.0
3.3
81.4
9.3
45.9
7.3
35.6
11.2
10.9
6.7
66.0
16.4
14.0
12.0
41.6
32.4
64.2
14.9
11.2
9.7
7.9
6.0
72.5
13.6
from the three arrays were averaged and are listed in Table
5, which correspond to the parametric effects for buccal and
lingual loading, respectively. The quantities in Table 5
represent the relative percentage in¯uence of the individual
oral parameters on the total change in maximum principal
stress that occurred over all experiments of the DOE. As
evident from Table 5, the occlusal load and its orientation
had the greatest effect on principal stress variations in the
molar with an amalgam preparation over the range in oral
parameters considered. Regardless of placement (buccal or
lingual cusp) the occlusal load and orientation accounted for
over 70% of the variation in s 1. In contrast, changes in
crown temperature and time of thermal loading had limited
in¯uence on the magnitude of s 1; only 14% of the total
variation in s 1 was attributed to changes in crown
temperature.
3.2. Composite restoration
As evident from Table 4, maximum principal stresses
within the molar with a MOD composite restoration were
generally of lower magnitude than those within the molar
with amalgam. An example of the principal stress distribution in the molar with composite preparation resulting from
experiment H6 (Table 3) is presented in Fig. 4. The stress
distribution in Fig. 4(a) and (b) resulted from occlusal loading of the buccal cusp and lingual cusp, respectively; stresses within the molar with amalgam preparation resulting
σ1
Pa
1
2
3
4
5
6
3 4
1
2
2
1
6
54 3
6
5
5
4 4 6 4
3
3
2
2
1
1
1
+5.00E+06
+1.00E+07
+1.50E+07
+2.00E+07
+2.50E+07
+3.00E+07
3 4
1
2
1
2
1
2
1 2
1
56
6
3
1 5
4
3
2
1
6
54 3
2
1
1
4
3
2
1
2
1
3 21
1
1
1
1
2
4
3
1
3
1
1
1
2
2 3
1
4
5
2
1
21
2
21
a) buccal cusp loading
2
1
4
3
1
3
1
3
1 2 4
4
2
2
2
1
2
2 3
1
3
1
1
2
1
1
2 2
3
2
1
4
1
2
3
1
2
1
b) lingual cusp loading
Fig. 4. Distribution of maximum principal stress resulting from simultaneous mechanical and thermal loading of the molar with composite restoration.
Load ˆ 150 N at a 458 orientation, T ˆ 58C for 1 s. (a) buccal cusp loading, (b) lingual cusp loading.
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
σ1
Pa
1
2
3
4
5
6
2
+5.00E+06
+1.00E+07
+1.50E+07
+2.00E+07
+2.50E+07
+3.00E+07
2
1
1
1
1
1
1
2
69
3
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
45
6
1
2
3
2
2
1
1
1
3
1
1
1
1
a) buccal cusp loading
3
4
1
2
3
2
34
2 4
4
1
1
1
1
2
3
1
2
1
1
2
2
1
b) lingual cusp loading
Fig. 5. Distribution of maximum principal stress resulting from simultaneous mechanical and thermal loading of the unrestored molar. Load ˆ 150 N at a 458
orientation, T ˆ 58C for 1 s. (a) buccal cusp loading, (b) lingual cusp loading.
from these oral conditions were presented in Fig. 3.
Regardless of occlusal load placement (lingual or buccal
cusp), s 1 within the molar with a composite restoration
occurred at the lingual margin. The magnitude of s 1 at
this location resulting from numerical experiments of
the high level orthogonal array with buccal loading is
listed in Table 4. Stresses located along the pulpal ¯oor
were much lower than those within the molar with
amalgam restoration. In contrast to the molar with amalgam, variations in the occlusal load and orientation had
little in¯uence on the maximum principal stress. As
evident in Table 4 (experiments H4±H6), s 1 was
found to be largest during oral conditions comprised
of low temperature (58C).
Following the ®nite element analysis, an ANOVA
was conducted with stresses in the molar with a composite restoration to identify the in¯uence of oral conditions; the analysis was conducted with components of
stress recorded at the junction of the composite margin
and occlusal surface highlighted in Fig. 4(b). A separate
ANOVA was conducted with each set of nine-run
experiments. Results from each of the nine-run DOEs
were averaged and are listed in Table 5. Changes in
oral temperature had the most in¯uence on stresses
within the molar with a composite restoration and
accounted for 46 and 64% of the total variation in
principal stress with buccal and lingual cusp loads,
respectively. In comparison, the occlusal load had far
less in¯uence on the magnitude of principal stress
regardless of load placement (buccal or lingual cusp).
3.3. Unrestored molar
The maximum principal stress distribution in the unrestored molar resulting from a 150 N occlusal load with 458
orientation and crown thermal load of 58C for 1 s (H6 of
Table 3) is shown in Fig. 5. Results from loading the buccal
and lingual cusps are shown in Fig. 5(a) and (b), respectively. In general, the maximum principal stress for all oral
conditions occurred along the pulpal wall. The magnitude of
s 1 resulting from all conditions of the high level orthogonal
array was recorded at the location of maximum principal
stress and are listed in Table 4. Surprisingly, occlusal loading of the buccal cusp resulted in principal stresses much
larger than those resulting from lingual cusp placement. In
fact, principal stresses within the unrestored molar exceeded
those within either restored molar for conditions comprised
of large occlusal loads at shallow angles (u , 908). The
largest maximum principal stress for all oral conditions
resulted within the unrestored molar and was found to be
82 MPa.
Due to variations in location of maximum principal stress
within the unrestored molar, the stress distribution resulting
from all numerical simulations was recorded at approximately the same site of maximum stress identi®ed for the
molar with amalgam restoration. An ANOVA was
conducted with the stresses at these respective locations
resulting from buccal and lingual loading, and the results
are listed in Table 5(a) and (b), respectively. As evident
from the parametric effects outlined in these tables, the
occlusal load and its orientation were responsible for over
70
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
Fig. 6. Location and orientation of the maximum principal stress within the molar. Load ˆ 150 N at a 458 orientation, T ˆ 58C for 1 s.
80% of the total variation in s 1. In comparison, thermal
loads imposed by variations in crown temperature were of
little importance. Furthermore, according to the consistency
in results from the ANOVA with lingual and buccal loading,
occlusal load placement had a negligible in¯uence on the
extent of variation in s 1 within the unrestored molar.
4. Discussion
The magnitude and location of maximum principal stress
(s 1) were different in all three molars examined. The largest
maximum principal stress occurred in the unrestored molar
and resulted from a 300 N occlusal load placed on the
buccal cusp at an orientation of 45 and 558C crown temperature (experiment H1). In contrast, the molar with an amalgam restoration generally experienced larger principal
stresses when occlusal loads were placed on the lingual
cusp, in which case the maximum stress developed along
the pulpal ¯oor and lingual margin. Consistent with that
observation, Eakle et al. [2] reported that the lingual cusps
of mandibular molars exhibited the highest frequency of
fracture. While occlusal loading was the most important
oral parameter to the unrestored molar and molar with an
amalgam restoration (Table 5), occlusal loads had little
effect on the molar with a composite restoration. The
molar with a composite restoration was less sensitive to
mastication due to cusp reinforcement achieved by dentin
and enamel bonding. However, oral temperature variations
(especially cold temperatures) were found responsible for
signi®cant changes in the stress distribution. Though principal stresses in the molar with a composite restoration
increased with either an increase or decrease in oral
temperature from 378C, the principal stresses generated at
58C were clearly of largest magnitude. An increase in s 1
with all temperature changes occurs due to the dependence
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
of s 1 on s 11, s 22 and s 12 according to Eq. (1) and the unique
changes in each of these three components of stress with
change in oral temperature. Therefore, although marginal
bonding of composite restorations served to reduce stresses
resulting from occlusal loading, ®nite element results
suggested that stresses resulting from thermal variations
are ampli®ed. A previous study has shown that marginal
bonding also reduced stresses resulting from occlusal
loads in molars with MOD amalgams but results in large
stresses under elevated oral temperatures [30].
It is important to recognize that the ®nite element analysis
of the molar with a composite restoration ignored residual
stresses resulting from polymerization shrinkage. Tensile
stresses resulting from shrinkage acting perpendicular to
the cavosurface margin have been found to reach as high
as 25 MPa [31]. A superposition of stresses resulting from
oral conditions and residual stresses related to curing in the
molar with a MOD composite would result in principal
stresses as large as 50 MPa and an average stress over all
conditions near 38 MPa. The average and largest principal
stress documented within the molar with a MOD amalgam
restoration was 19 and 56 MPa, respectively. Therefore, the
fracture resistance of molars restored with composites could
be inferior to that of molars with amalgam restorations if
large residual stresses result from the polymerization
process. This statement assumes that the fracture resistance
is only a function of the magnitude and location of maximum stress and is not dependent on differences in mechanical properties of the restorative material.
Although introducing a restoration may change the location and orientation of maximum principal stress within a
molar, the largest principal stress among the three molars
occurred in the virgin molar. This does not imply that all
teeth should be restored to reduce stresses incurred from
mastication and temperature variations. Interestingly, Gher
et al. [1] found from a clinical survey of fractured teeth that
92% had been restored. Similarly, Cameron [32] reported
that of 102 fractured teeth, only ®ve were unrestored.
Results from the present study therefore suggest that the
magnitude of stress within a tooth is not the primary source
for tooth fracture. Rather, differences in fracture resistance
between restored and unrestored posterior teeth appear to be
based more on the location of maximum stress.
A summary of the location and orientation of maximum
principal stress in the molar with an amalgam and a composite restoration (for experiment H6) is highlighted in Fig.
6(a) and (b), respectively. Note that the maximum principal
stress for both restored molars was located along the cavosurface margin which is most likely to contain ¯aws resulting from cavity preparation. Indeed, Bell et al. [33] found
from an examination of molars and premolars with MOD
amalgam restorations that cusp failures appeared to originate at the junction of the pulpal ¯oor and lingual margin.
Although the magnitude of stress was undoubtedly an
important concern, the location of maximum stress and
presence of ¯aws (cracks, craze lines, etc.) introduced
71
during cavity preparation may be a primary factor contributing to restoration failure. The orientation of s 1 in the molar
with amalgam restoration in Fig. 6(a) was inclined from the
pulpal ¯oor towards the lingual surface. Cracks that initiate
from ¯aws along the margin would propagate along the
plane of principal normal stress at an orientation as
shown. The fatigue life of molars with MOD amalgam
restorations was recently estimated using the Paris Law
for cyclic fatigue crack growth [34]. It was found that
molars with MOD amalgam restorations could undergo
cusp fracture within 25 years if ¯aws greater than 25 mm
were distributed along the margin. This would explain the
general tendency for restored teeth to fail much more
frequently than unrestored teeth.
Principal stresses in the molar with a composite restoration were found located along the lingual margin and
oriented perpendicular to the occlusal surface as shown in
Fig. 6(b). Hence, crack growth would tend to initiate from
the occlusal surface and propagate towards the pulpal ¯oor
under the maximum opening mode stress. Large normal
stresses were also found to develop on the occlusal surface
of the composite as shown for results from experiment H6 in
Fig. 4. Consequently, cyclic crack growth in the molar with
composite preparation would likely initiate from occlusal
surface ¯aws and extend towards the pulpal ¯oor as
shown in Fig. 6(b). Therefore, a determination of the cyclic
fatigue crack growth properties of enamel, dentin, and
restorative composites is needed to further understand the
effects of restorative dentistry on the long-term mechanical
behavior and fracture resistance of restored posterior teeth.
5. Conclusions
The stress distribution within mandibular molars with
amalgam and composite MOD restorations was evaluated
using a ®nite element analysis and compared with that of an
unrestored molar. The following conclusions were drawn
based on the stress distribution in each tooth resulting
from simultaneous mechanical and thermal loads and an
analysis of variance:
1. The maximum principal stress resulting from simultaneous mechanical and thermal loads occurred within
the unrestored molar. Stresses were found to be primarily
dependent on the occlusal load, whereas changes in the
crown temperature were of minimal importance.
2. Stresses within the molar with amalgam restoration were
lower than those resulting in the unrestored molar. The
maximum stress occurred along the pulpal ¯oor and
lingual or buccal margin junction and was in¯uenced
primarily by the magnitude of occlusal load.
3. Stresses in the molar with a composite restoration were
in¯uenced primarily by the crown temperature. Principal
stresses were highest along the occlusal surface and
lingual margin, were maximized at low temperatures,
72
D. Arola et al. / Journal of Dentistry 29 (2001) 63±73
Table A1
The low level nine-run experimental design array. The terms 2, o, and 1 represent the low, medium, and high level of the oral parameters as distinguished in
Table 2
Experiment
L1
L2
L3
L4
L5
L6
L7
L8
L9
Oral parameters
Crown temperature T (8C)
Time t (s)
Occlusal load P (N)
Orientation u (8)
2
2
2
o
o
o
1
1
1
2
o
1
1
2
o
o
1
2
2
o
1
2
o
1
2
o
1
2
o
1
o
1
2
1
2
o
but were of lower magnitude than those within the molar
with an amalgam restoration.
4. A comparison of the stress distribution in molars with
MOD composite and amalgam restorations indicated
that there is little difference in the magnitude of maximum principal stress in the tooth. The reduced fracture
resistance of restored molars in comparison to those
which are unrestored appears to be attributed to changes
in location of maximum principal stress that arise from
presence of the restoration.
Appendix A
The three-level, four factor, nine-run design of experiments (DOE) used in this study was constructed according
to a Plackett Burman design array [29]. Generally used as a
screening design, it is a fractional factorial design that
allows the main effects resulting from variation in the independent parameters to be determined from minimum experimentation. The four oral factors selected for the DOE
include the thermal load, time duration, occlusal load, and
its orientation. Expected variations in the oral environment
were used to divide the total range of each oral parameter
into three levels (low, medium, and high) as shown in Table
2. Although a full factorial study (all possible parameter
combinations) comprised of four factors with three levels
would require 81 experiments (3 4), the relative effects from
independent variables on the maximum principal stress (s 1)
within the tooth may be determined from only nine experiments. There are three basic nine-run Plackett Burman
arrays that are referred to as the low, medium, and high
Level set. The low nine-run array is listed in Table A1
where 2, o, and 1 refer to the low, medium and high
level of each parameter, respectively. The medium level
array can be obtained by incrementing the level of each
parameter in the low level array (Table A1) by one. Similarly, the high level array can be obtained by incrementing
parameters of the medium level array and was shown in
Table 3. In this study all three nine-run sets of experiments
were performed for each tooth and occlusal load placement;
results from the three nine-run arrays were compared for
consistency to detect random variation, then averaged and
reported. An analysis of variance (ANOVA) was conducted
with the dependent variable (s 1) by calculating the estimated contrasts and sums of squares for each oral parameter. Relative effects of each independent variable on s 1
in all three teeth were determined from the ratio of the sum
of squares for the parameter of interest to the total sum of
squares for each nine-run array. Further details regarding
the computation of contrasts and sum of squares for a fractional factorial experimental design can be found in
Wheeler, 1989 [29].
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