


DENTAL SCIENCE  ORIGINAL ARTICLE 

Year : 2012  Volume
: 4
 Issue : 6  Page : 384389 


Finite element analysis of stresses in fixed prosthesis and cement layer using a threedimensional model
Arunachalam Sangeetha^{1}, Thallam Veeravalli Padmanabhan^{2}, R Subramaniam^{3}, Vivekanandan Ramkumar^{1}
^{1} Department of Prosthodontics, Vivekanandha Dental College for Women, Elayampalayam, Tiruchengodu, India ^{2} Department of Prosthodontics, Sri Ramachandra Medical University, Porur, Chennai, India ^{3} Department of Prosthodontics, Nooral Islam College of Dental Science, NICE Garden, Aralummood, Neyyatinkara, Kerala, India
Date of Submission  01Dec2011 
Date of Decision  02Jan2012 
Date of Acceptance  26Jan2012 
Date of Web Publication  28Aug2012 
Correspondence Address: Arunachalam Sangeetha Department of Prosthodontics, Vivekanandha Dental College for Women, Elayampalayam, Tiruchengodu India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09757406.100291
Abstract   
Context: To understand the effect of masticatory and parafunctional forces on the integrity of the prosthesis and the underlying cement layer. Aims: The purpose of this study was to evaluate the stress pattern in the cement layer and the fixed prosthesis, on subjecting a threedimensional finite element model to simulated occlusal loading. Materials and Methods: Threedimensional finite element model was simulated to replace missing mandibular first molar with second premolar and second molar as abutments. The model was subjected to a range of occlusal loads (20, 30, 40 MPa) in two different directions  vertical and 30° to the vertical. The cements (zinc phosphate, polycarboxylate, glass ionomer, and composite) were modeled with two cement thicknesses  25 and 100 μm. Stresses were determined in certain reference points in fixed prosthesis and the cement layer. Statistical Analysis Used: The stress values are mathematic calculations without variance; hence, statistical analysis is not routinely required. Results: Stress levels were calculated according to Von Mises criteria for each node. Maximum stresses were recorded at the occlusal surface, axiogingival corners, followed by axial wall. The stresses were greater with lateral load and with 100μm cement thickness. Results revealed higher stresses for zinc phosphate cement, followed by composites. Conclusions: The thinner cement interfaces favor the success of the prosthesis. The stresses in the prosthesis suggest rounding of axiogingival corners and a wellestablished finish line as important factors in maintaining the integrity of the prosthesis. Keywords: 3D FEA, cement interface, occlusal loading, parafunctional forces, stress in fixed prosthesis
How to cite this article: Sangeetha A, Padmanabhan TV, Subramaniam R, Ramkumar V. Finite element analysis of stresses in fixed prosthesis and cement layer using a threedimensional model. J Pharm Bioall Sci 2012;4, Suppl S2:3849 
How to cite this URL: Sangeetha A, Padmanabhan TV, Subramaniam R, Ramkumar V. Finite element analysis of stresses in fixed prosthesis and cement layer using a threedimensional model. J Pharm Bioall Sci [serial online] 2012 [cited 2019 Feb 18];4, Suppl S2:3849. Available from: http://www.jpbsonline.org/text.asp?2012/4/6/384/100291 
Parafunctional forces are more detrimental to the prosthesis and cement layer as there is an average of 25 times increase in stresses compared to the masticatory load. Sufficient axial reduction, rounding of axiogingival corner, and uniform margins prevent stress concentration and dislodgement of the prosthesis. Thinner cement interface increase the longevity of the restoration. Polycarboxylate and glass ionomer cements withstand stresses better than resin or zinc phosphate cements. The masticatory load is insufficient to cause cement microfracture or dislodgement of the prosthesis.
In fixed prosthodontics, stresses induced by masticatory and parafunctional forces influence the distortion and fracture potential of prosthesis and the underlying cement layer. Stress analysis methods like strain gauge and photoelastic methods are extremely limited in their scope as it is impossible to proportion the model stiffness and are inappropriate to dental structure that are of an irregular structural form. ^{[1]}
Finite element method is a modern technique of numerical stress analysis and can be applied to solids of irregular geometry and heterogeneous material properties. In twodimensional finite element modeling, tooth cannot be represented in a twodimensional space as it is irregular and the actual loading cannot be simulated without taking the third dimension into consideration. ^{[2]} Earlier, finite element studies ^{[3],[4]} had analyzed stresses in crowns and fixed prosthesis, but with twodimensional models. Dental reports on cements, ^{[5],[6]} have focused primarily on retentive failures and failures due to microleakage. Studies on stresses in the cement layer and the comparative clinical performance are minimal. ^{[7]}
Considering the above facts, the stresses in components of fixed prosthesis and cement layer were determined with a three dimensional finite element model (zinc phosphate, zinc polycarboxylate, glass ionomer cement, and composite resin cement) in two different thicknesses (20 and100 μm).
Materials and Methods   
In this study, a threeunit fixed dental prosthesis, replacing the missing first molar in the mandibular quadrant, was considered as it was the most common clinical condition observed. ^{[8]} Threedimensional finite element model of fixed dental prosthesis was modeled, with second molar and second premolar as retainers and with first molar as pontic, as shown in [Figure 1].
This threedimensional model was designed using the software 3D Studio Max. The basis of the model was simulated as not to scale. This 3D Max File was converted to a Drawing File and exported to Mechanical Desktop. As tooth dimensions differ widely, average values were assigned to the respective teeth according to dimensions specified in a study by Wheeler. ^{[9],[10]} The finite element analysis was done with MSC Nastran software.
The second premolar and the second molar were simulated to be prepared to receive type IV gold alloy fixed prosthesis. Gold crowns play the role of improvised enamel as the stiffness of gold is practically the same as that of enamel. ^{[11],[12]} Hence, gold alloy was considered. The abutments were prepared with 1mm axial reduction, 2mm occlusal reduction, and a 45° cavo surface angle bevel and 0.5mm chamfer margin. ^{[5],[13]} The root of the premolar was surrounded by periodontal membrane of 200 μm width, which was embedded in a normal simulated human cortical bone as seen in [Figure 1].
The standard model was composed of 4299 plate elements, 15 boundary elements, 2 gap elements, and 4607 nodes. Gap elements were used to model the proximal contact point between adjacent teeth. The lower border of the model was considered fixed in all directions to resist for the occlusal load. The elastic modulus, Poisson's ratio of the material, ^{[14]} along with the coordinate and geometry of each node and element were entered into the computer.
Each retainer was modeled with two different cement thicknesses, 20 and 100 μm. 20 μm was selected as it was considered ideal, ^{[15],[16]} and 100μmthick cement layer was selected as it was clinically more realistic. ^{[8],[17]} These two retainers of the 3unit fixed partial prosthesis were created to receive four commonly used luting agents. ^{[7]} This resulted in a total of eight models for computer simulation of clinical situations.
These models were subjected to a range of occlusal forces  20, 30, 40 Mpa. ^{[3]} The simulated occlusal loads were applied in two directions  vertical and 30° to the vertical load. The vertical load simulates the functional masticatory stress and the oblique load simulates the parafunctional stresses. ^{[4]} In this study, models were loaded under controlled conditions at any point, in a downward direction. Models in this study contained 150 elements involving 500 nodes and 500 degrees of freedom.
Finite element analysis revealed stress and deformations at every node in a model. In this study, local stresses were monitored at selected points in 2D plane of 3D model. These points are critical areas for maintaining the integrity of cement layer and for resisting dislodgement of the prosthesis. ^{[18]} Each of these points had different designations at the nodes. Mesial and distal points were represented as a and b, respectively, as shown in [Figure 2]. The areas of stresses at the retainer interface were represented as: margins, 11a and 11b; axiogingival corners, 21a and 21b; axial walls, 31a and 31b; and occlusal region, 41a and 41b.
The same areas were considered with different designations at cement interface: mesial and distal margins, 1a and 1b, respectively; axiogingival corners, 2a and 2b; axial walls, 3a and 3b; and occlusal region, 4a and 4b. The stresses in the pont ic were represented as: 1c, the occlusal region; 2c, the midpoint; 3c, the connector region; and 4c, the gingival point of the pontic [Figure 2].
Results   
Stresses in the components of the fixed prosthesis and cement layer were presented as colorful band as shown in [Figure 3] and [Figure 4]. The colors represent different stress levels in deformed state. The colorcoded scheme portrays stress ranges in increasing order as: 07 = blue; 811 = green; 1215 = orange; and 1620 = dark red.  Figure 3: Visual representations of stresses in prosthesis and cement layer at vertical load
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 Figure 4: Visual representation of stresses in prosthesis and cement layer at 30 degree oblique load
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Though results were generally displayed as stress concentrations for the entire model, the resulting stresses were calculated in the reference points for both prosthesis and cement layer by using the standard formula for each finite element:
where
t = length of the plate element,
w = breadth of the plate element,
K = 2116 (mm ^{2.59} ), which indicates the total value of the plates,
e = load applied, and Sd = stress per unit displacement (MPa).
Sd = stress per unit displacement (MPa).
The stresses were reported as the mean of mesial and distal points and designated for cement layer as 1, 2, 3, and 4, and for prosthesis as 11, 21, 32, and 41. The means were considered as there was only slight asymmetry between the mesial and distal halves of each node.
The equivalent stresses were calculated based on the hypothesis of MaxwellHuberHenckyVon Mises. This determines the total state of stress at a predetermined location. These are mathematic calculations without variance; hence, statistical analysis is not routinely required. However, pooled stresses for reference points 1 through 4 were compared for different conditions of interest. [Table 1] and [Table 2] reveal stresses in the prosthesis for vertical and lateral loading, respectively. Maximum stresses in the prosthesis were recorded at the occlusal surface (at the point of loading), followed by axiogingival corners. The marginal area recorded the least stress, indicative of high tensile stress in that region.  Table 1: Mean stress values in the prosthesis for all the loads at vertical direction of loading (unitMPa)
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 Table 2: Mean stress values in the prosthesis for all the loads at 300 loading (unit MPa)
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The stresses in the prosthesis increased by a factor of 24 in all the reference points, when the direction changed from vertical to 30° loading. Stresses increased gradually with increasing load. The stresses in the pontic were greater than in molar retainer, followed by premolar retainer. The occlusal surface and the connector region of the pontic revealed maximum stresses. The gingival portion revealed minimum stresses, thus suggesting tensile stresses in that region.
The stresses recorded in the cement layer are displayed in Graphs 1 and 2. The stresses in zinc phosphate cement layer were the highest, followed by composites, glass ionomer, and zinc polycarboxylate cement. Increasing the cement thickness from 20 to 100 μm elevated stresses by a factor of 45 times on all the reference points. The stresses for the 30° concentrated load were 5 times greater than for the vertical distributed load.
Discussion   
The stresses induced within a fixed prosthesis and cement layer are an essential feature for the success and longevity of the restoration. The gradual increase in stresses with increase in load indicates a uniform stress distribution. ^{[19]} Greater stresses were in the center of the beam or in the pontic than with premolar and molar retainer, due to threepoint loading of fixed beam supported at both the ends. ^{[4],[20]} These flexural stresses were lesser with vertical loading than with 30° loading, ^{[8],[21],[22]} as the latter load tends to tip the fixed prosthesis away from the abutment, thus resulting in higher stresses.
In the pontic, the occlusal side revealed maximum stresses, followed by the region of rigid connector. ^{[23]} This was in accordance with earlier studies, where the weakest part in the posterior fixed prosthesis was the fixed joint ^{[1]} as it recorded maximum stress. The surface area for load application is more with molar retainer than with premolar retainer, thus resulting in higher stresses. Farah in his study also stated that the distal side of the retainer recorded more stress than the mesial side. ^{[4]}
The maximum compressive stress was observed at the point of loading and these stresses are transmitted to the greater occlusal surface area of the supporting tooth structure. Earlier studies ^{[4],[6]} also concluded that flat occlusal reduction resulted in increased thickness of gold in the occlusal region and reduced the stresses by 40%. The next highest stress was observed in the axiogingival corner of the prosthesis and the cement layer due to inclined plane effect. This region is placed at an angle to the junction of the two different planes, the vertical axial wall, and the nearly horizontal marginal wall. ^{[3]}
The stress in the axial part of the prosthesis was less than in the occlusal and the axiogingival corner, as these stresses were directed parallel to the long axis of the tooth. ^{[5]} The axial wall of the abutment is the major retentive component to prevent the dislodgement of the prosthesis. ^{[4],[24]} With 30° oblique load, the axial region revealed more stresses, suggesting increased tendency for dislodgement. Earlier studies ^{[21],[25]} reveal that rounding of the axial wall reduced the stress concentration up to 50%.
The cervical margin of the prosthesis revealed the least stress, but recorded double the stress level with 30° lateral loading and with increased cement thickness. These factors cause distraction of the margins away from the tooth structure ^{[2]} and also establish the clinical significance of placing finish lines.
Increase in cement thickness (100 μm) revealed 24 times greater stresses in the prosthesis and cement layer. This could be due to the probability of fewer flaws occurring in a thin film. ^{[18]} Thus thinner film thickness favors the success of the prosthesis in withstanding stress as well as in preventing microleakage. Stresses in the cement layer were lesser than the prosthesis due to the difference in the elastic moduli of the cements and the gold alloy. ^{[26]} The higher stress levels of zinc phosphate cement could be attributed to the brittleness of the zinc phosphate cement, ^{[27]} though it had the maximum compressive strength.
To ensure mechanical success, the stress level should be below the endurance limit. In this investigation, the resulting stresses were below 5% of the ultimate compressive strengths ^{[14]} and the overall stress of only 5 MPa was recorded in the prosthesis at 40 MPa load, which makes it only 12.5% of the total applied load. Photini ^{[4]} assumed that during rigorous loading conditions (e.g. 50100 Mpa), the resulting stresses would cause substantial plastic deformation and may be related to cement failure. Thus, these stresses were insufficient to cause cement fracture in single cycles or in fatigue. ^{[27],[28]}
Further studies are required to evaluate the influence of various types of finish line and various structural modifications in the prosthesis on stresses in cement layer, prosthesis, and the periodontium. Instead of gold alloy, base metal alloys can be considered for the same study as increased yield strength and rigidity of the prosthesis material decreases stress concentration. ^{[12]} Finite element analysis is a numerical study based on standard values, so the results should be interpreted on a comparative basis. Further clinical trials can ultimately confirm the predictions made from finite element analysis presented here.
Conclusions   
The following conclusions were drawn from this finite element study:
The lateral loads are more deteriorating on the cement layer and the prostheses. Optimum occlusal reduction is necessary to provide sufficient thickness to the occlusal surface of the prosthesis and the connector region to withstand the stresses. The stresses in the cervical region of the prosthesis establish the clinical significance of placing finish lines. The minimal stresses in the axial margins decrease the fracture potential of the cementing layer, thus preventing dislodgement of the prosthesis.
Smaller cement thickness is more resistant to lateral loading and also emphasizes the significance of closer adaptation of the prosthesis to the margins. Brittle cements like zinc phosphate cement indicate their use only in favorable clinical conditions due to increase in fracture potential.
Acknowledgement   
Special thanks to Mr. Maheswar for helping in finite element modeling and analysis.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2]
