Indian Journal of Dental Research

: 2014  |  Volume : 25  |  Issue : 3  |  Page : 364--369

Stress analysis of two methods of ceramic inlay preparation by finite element

Leila Pishevar1, Maryam Ghavam2, Ahmadreza Pishevar3,  
1 Department of Operative Dentistry, Dental School, Islamic Azad University, Khourasgan Branch, Iran
2 Dental School, Tehran University of Medical Science, Isfahan University of Technology, Isfahan, Iran
3 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

Correspondence Address:
Leila Pishevar
Department of Operative Dentistry, Dental School, Islamic Azad University, Khourasgan Branch


Objective: Ceramic inlays are bonded to tooth structure with resin cements. During the resin cement setting, shrinkage stress develops at the interfaces. During tooth preparation, the undercut areas formed due to the different patterns of caries progression can either be blocked out before taking impression with suitable cement such as glass ionomer cement, or before making the final restoration in the laboratory. Then, the relieved space will be filled with luting cement in clinic. The aim of this study was to compare these two methods of undercut filling in term of stress distribution in the ceramic inlay. Materials and Methods: An axisymmetric finite element analysis was performed to study the stress distribution during inlay cementing. The solid model was generated from a longitudinal section of maxillary premolar in which a class I cavity with 60 degree undercut at the preparation wall and 20 degree divergence of the vertical walls was prepared. A thermal model was used to simulate the polymerization shrinkage of the resin cement. Finite element analysis was carried out in ANSYS environment. Results: Filling the undercut by glass ionomer cement decreased the stress concentration at the ceramic/cement interface. The dominant normal stress at the tooth cement interface in absence of glass ionomer cement was tensile with maximum of 30 Mpa. Using glass ionomer, cement developed stresses with different compressive and tensile signs. With increasing the thickness of resin cement (100 µm, 150 µm, 200 µm), the stress increased. Conclusion: Cements with minimum shrinkage and as thin layer as possible should be used. Filling the undercut with glass ionomer cement decreases the stress. Other experimental and clinical studies must follow this research.

How to cite this article:
Pishevar L, Ghavam M, Pishevar A. Stress analysis of two methods of ceramic inlay preparation by finite element.Indian J Dent Res 2014;25:364-369

How to cite this URL:
Pishevar L, Ghavam M, Pishevar A. Stress analysis of two methods of ceramic inlay preparation by finite element. Indian J Dent Res [serial online] 2014 [cited 2022 Sep 30 ];25:364-369
Available from:

Full Text

Ceramic inlays are very popular nowadays because of their esthetic appearance and improvement in physical and mechanical properties. [1] Evolution of new generations of bonding systems has an important role in popularity of these restorations. [2],[3],[4],[5] Ceramic inlays are good alternatives for amalgam. [6],[7] They can be bonded to tooth structure and some restorative materials, to decrease microleakage and strengthen the restored tooth. [8],[9] During polymerization of the resinous matrix, composite cement undergoes shrinkage and deformation as the elastic modulus of the material develops.

Stress formation inside the restoration system depends on the existence of adhesion between the substrate and the restorative material, and on the flow of material occurring at the free (unbounded) surface. [10],[11],[12] Shape of the cavity has an important role in direction and magnitude of stress generated during polymerization. Somehow, ceramic inlays are unique in complexity of stresses generated during their cementation. [10],[13] The luting composite is placed in a tight interfacial gap, and bonded to tooth and etched ceramic surface. Good marginal adaptation of the inlay limits compensation of polymerization stress by the flow of the luting agent. [10],[13] However, polymerization shrinkage can cause some clinical problems such as postoperative sensitivity, fracture of enamel or tooth due to cuspal deflection, and the open margins which may result in microleakage and recurrent caries. [14],[15] The strong adhesion of the set material to the cavity walls also results in internal stress in the composite material. These stresses may lead to formation of microcracks within the restoration and end to fatigue failure. [16] Polymerization shrinkage stress was investigated in many studies and several methods are used to determine the magnitude of stress. These methods include analytical, experimental, and numerical methods (finite element). [17],[18],[19]

During tooth preparation, due to different form of caries progression, the shape of cavity are not regular and undercut areas occur in the cavity walls. In the classic method of cavity preparation for indirect restoration, undercuts are blocked out with proper materials such as glass ionomer cements. Other approaches consider omitting the undercuts on the stone die, and filling it with resin cement during cementation. It is rational that higher stresses develop in the latter method during polymerization process. From a clinical point of view, it is important to investigate the amount of stresses developed at ceramic/tooth interface. If these stresses are not significant, relief of undercut area in tooth before taking impression seems to be unnecessary. The aim of this study was to compare stresses developed in ceramic inlays during two methods of undercut filling (using glass ionomer cement or die blocking out) by finite element analysis.


In this research, an axisymmetric finite element model was used to estimate stresses developed by polymerization shrinkage of resin cement in two different clinical methods of ceramic inlay preparation. In this study, an axisymmetric model is used for small and symmetric cavities. Since stresses due to polymerization shrinkage were local and limited to cavity's walls, the precise geometrical details were of little importance and using a three-dimensional model was not convenient for the parametric study and might complicate the interpretation of the results. Axisymmetric models have been also used by other researchers. [20],[21]

The solid model was generated from a digitized picture of longitudinal section of a maxillary first premolar to trace the contour of enamel, dentine, and pulp chamber. Then, a class I inlay with 60º undercut at the preparation bottom line angle and a 20º divergence of the vertical walls was placed in the model considering a thin gap between the inlay and the cavity walls to simulate the resin film behavior. The model is shown in [Figure 1] schematically.

Commercial finite element software (ANSYS) was used in the analysis and the behavior of different materials including enamel, dentin, ceramic, resin cement, and the glass ionomer, which were assumed to be linearly elastic and isotropic. The mechanical properties of materials are given in [Table 1]. The nonlinear behaviors such as the flow of resin cement in pre-gel phase was not considered in this study because the ratio between bonded to unbonded surface (C factor) in cemented inlay is very high and small unbonded surface (the cemented line) has no significant influence on the stress relaxation. [17],[22],[23],[24],[25],[26] The model was meshed with a four nodes linear element, two degree of freedom at each node. Due to the existence of high gradients, at least five elements were placed across the resin film thickness to achieve the required numerical accuracy. It was also tried to use a structured grid in this region by dividing the film thickness into several quadrilateral subdomains. A grid study was performed to show the independence of solution from the mesh. Due to the symmetry, only half of the model was calculated and a symmetry boundary condition was applied on the tooth axis. All displacements were also set to zero at the pulp boundary.{Figure 1}{Table 1}

The cement thickness was considered between 100 to 300µm. The volumetric shrinkage of resin cement was also assumed between 1% to 3%. [22],[26] A thermal model was used to mimic the effect of resin shrinkage. In this model, the coefficient of thermal expansion and the change of temperature from the reference condition were determined in a way that the volume change due to the thermal shrinkage was equaled to the shrinkage of resin during polymerization. In this method, the thermal volume change is obtained from the following formula:


Where [INSIDE:1], is the percent of change in volume, α is the linear coefficient of thermal expansion, and ∆T is the temperature change from the reference condition. Thermal model was also used in other studies to simulate polymerization shrinkage. [17],[23],[24],[27] A distributed compressive force 300N was applied uniformly between the cusp of crown and the axis of symmetry. This force is equal to the biting force at premolar area. [28] Occlusal load was applied as a compressive force on tooth in a circular area with 1.6-mm diameter. [21] Stresses developed in two different methods of inlay preparation was analyzed. In the first method referred to as (A), the undercut area is filled with glass ionomer (before taking the impression, in clinical situations). In the method referred to as (B), the undercut space is filled with resin cement directly (during cementation in clinical situations).

Also, the stress fields at the material interfaces within a given cavity were compared in the two methods of undercut filling, in order to achieve a better understanding of differences in their mechanical behaviors.

In order to show the effect of stresses due to polymerization shrinkage of resin cement, the occlusal load was applied in two different conditions. First, resin cement was undergoing polymerization shrinkage and second, cement was not undergoing polymerization shrinkage.


Stress field was calculated for the two methods of undercut filling: with and without glass ionomer cement. A post-processor program was developed to report traction stresses at the interfaces in term of distance from the tooth axis S. The distance parameter S was shown for critical points in [Figure 2]. The parameters of this study are the cement thickness that varies from 100 to 300µm and the volumetric shrinkage which was limited to 1% to 3%. Numerical results predicted a maximum normal stress of 30 Mpa in undercut area at tooth/cement interface for 1% volumetric shrinkage and 100µm cement thickness when the glass ionomer was not used to fill the undercut. This value reduced to 20 Mpa when the cavity was filled with a glass ionomer cement [Figure 3]a]. The maximum tangential stress in the ceramic/cement interface was at the undercut area [Figure 4]a]. Computation also predicted that the maximum normal stress could increase to 60 Mpa as the volumetric shrinkage increase to 3% for the first method [Figure 4]b]. The maximum tangential stress showed similar trend and increased from 20 to 50 Mpa for the same range of variation in volumetric shrinkage [Figure 3]b]. On the other hand, at the ceramic/cement interface, when the glass ionomer was used and the resin thickness is 100 µm, the maximum normal stress was about 8 Mpa, 14 Mpa, and 22 Mpa for 1%, 2%, and 3% volumetric shrinkage, respectively [Figure 5]a]. In this method, the maximum tangential stresses were 4, 7, and 11 Mpa [Figure 5]b].{Figure 2}{Figure 3}{Figure 4}{Figure 5}

By increasing the cement thickness, the maximum normal and tangential stresses at the cement line increased linearly. However, stresses in the undercut region were not influenced by this parameter.

In the next step, the effect of occlusal load was considered. For the clinical method in which the glass ionomer was not used to relief undercuts, a maximum compressive stress of 10 Mpa was developed in the region of undercut when the polymerization shrinkage effects were ignored, but when the shrinkage effects came into account, the stress distribution significantly changed, and tensile stresses appeared with a maximum of 20 Mpa in the region of undercut [Figure 6]a]. However, when the undercut was filled with the glass ionomer, the maximum shrinkage stresses decreased to about 7 Mpa [Figure 6]b].{Figure 6}


Besides functional stresses, bonded ceramic inlays experience other types of stresses resulted from polymerization of resin cement and thermal cycles. The effects of polymerization shrinkage of resin cements are investigated in many experimental studies and are proved to lead to clinical problems due to microleakage and recurrent caries. [10],[ 16] Explaining detailed mechanism of these problems or clarifying the design of polymerization shrinkage process at thin layers of resin cement by experimental methods is very difficult. Finite element analysis provides a very useful method to explore these mechanisms. This is a unique feature of numerical methods that can analyze stress distribution at inaccessible areas of tooth/restoration complex. Moreover, stress distribution due to polymerization shrinkage of resin cements and occlusal loads can be analyzed separately, and therefore, it is possible to assess the effect of each parameter independently.

In this research, an axisymmetric finite element method was used to compare the stresses developed in two different methods of inlay preparation. Also, the stress fields at the material interfaces within a given cavity were compared in the two methods of undercut filling, in order to achieve a better understanding of differences in their mechanical behaviors. In the first method referred to as (A), the undercut area was filled with glass ionomer cement (before taking impression, in clinical situations). In the method referred to as (B), the undercut area was filled with resin cement directly (during cementation in clinical situations).

Stress distribution due to polymerization shrinkage of resin cement at tooth/cement and ceramic/cement interface

[Figure 3] (a, b) shows the normal and tangential stress distribution at the tooth/cement interface for a volumetric shrinkage of 1%. As shown by the figure, for method (B), i.e., when glass ionomer cement is not used as undercut filling material, the maximum normal stress happens at S = 2 mm (undercut area) and is about 30 Mpa. These stresses are often in tensile mode. In method (A), the maximum normal stress decreases significantly and is limited to 20 Mpa. Tangential stress also decreased in this method. However, in method (B), the tangential stress at tooth/cement interface shows an oscillatory behavior [Figure 3]b]. The reason can have stem in the complex distribution of resin within the cavity. As one may notice, in contrast to method (A), the thickness of resin is not uniform in method (B). [Figure 3] (a, b) clearly shows that the more volume of resin in the undercut region, the higher the stress developed due to the volumetric shrinkage. Passed the undercut area (S>2 mm), as expected, the stress is reduced in a way that the stress distribution at the tooth/cement interface for both methods converges to the same value. At the cement line, the average normal stress is about 7 to 8 Mpa for both methods. Meanwhile, in this region, the normal stress is higher than the tangential one. At the cement line, the aspect ratio of the resin film is very high. This implies that resin is actually confined between two unbounded parallel surfaces. Therefore, the angular deformation is negligible compared with the volumetric deformation in this region. In other words, the resin deformation is purely linear in the cement line region during the shrinkage process and the resin film should resist the tensile and compressive stress in the direction of film thickness.

At the ceramic/cement interface, the normal stress near the undercut region was a combination of tensile and compressive states for method B. However, for method A, the normal stress was often in the tensile state.

At the predefined conditions of this study, blocking out of undercut area with glass ionomer cement before taking impression is reasonable. It helps to decrease the shrinkage stresses due to the polymerization and confines them to the cement line region. A small amount of cement volume for filling the undercut area can produce significant amount of stresses. Despite compensating mechanisms (such as resin flow at pre-gel phase, water absorption and hygroscopic expansion of resin), some of these stresses can remain at the ceramic/cement and tooth/cement interfaces. [29] It is important to note that blocking out of undercut area can be accomplished by any suitable material other than glass ionomer cement such as resin composite or flowable composite. In any method, the blocking out material must have little shrinkage during setting or the stress must be released during bonding procedure of ceramic restoration. Therefore, the type of blocking out material only depends on clinician's preference and mechanical properties needed for special situations.

Increasing the cement thickness from 100 to 300 µm leads to an increase in the stress magnitude. This well agrees with the previous finite element study about stress generated by luting resin during cementation of ceramic and composite inlays. [17],[18],[4],[29]

The incremental technique in direct composite restorations helps to decrease polymerization shrinkage stress, but obviously cannot be applied in indirect techniques. Therefore, minimum volumetric shrinkage is an important factor in resin cement selection. This factor is more important when blocking out of undercut area on the stone die by technician because the volume of resin used for cementing is more than the other technique. In this method, the shrinkage stress can affect ceramic and tooth destructively and lead to problems such as postoperative sensitivity, enamel and tooth fracture due to cuspal deflection, marginal opening of restoration, microleakage, and recurrent caries.

Stress distribution during application of occlusal load

In order to show the significance of polymerization shrinkage stress of resin cement, occlusal load was applied in two different ways: in the first case, resin was undergoing polymerization shrinkage, and in the second case, it was not [Figure 6]a,b]. The results showed that the shrinkage stresses have the same order of occlusal loads. When resin cement was undergoing polymerization shrinkage, the maximum amount of normal stress at s = 0.38 mm were 20 Mpa. At this area, the ceramic inlay was diverged occlusally. These stresses were predominantly tensile [Figure 6]a].

When occlusal load was applied in non-polymerization mode, tensile stresses were omitted considerably at gingival floor and ceramic inlay was more affected by compressive stress [Figure 6]b]. When the undercut was blocked out with glass ionomer, the interaction of polymerization shrinkage stress and occlusal load was observed only at s >0.38 mm and in other areas, the amount of stresses were similar [Figure 6]b].

Blocking out with glass ionomer omits the tensile stresses and reverses them to compression stress. In clinical point of view, this is very important because dental ceramics are very brittle and their tensile strength is lower than compressive strength; [8] thus, blocking out with proper material is an important clinical procedure in tooth preparation for ceramic restorations.


Results of the present study showed that stresses generated due to polymerization shrinkage of resin cement are noticeable. Thus, minimum volume of cement must be used during bonding procedure.

Blocking out of tooth with glass ionomer can replace the resin cement which lacks good mechanical properties to substitute dentin. This method also reduces polymerization shrinkage stresses.

Volumetric shrinkage is an important property which must be considered in resin cement selection.

It should be noted that only short-term aspects are covered by the experimental and numerical analysis in this study. If the concept is considered to be used clinically, additional laboratory case studies may be useful.


1Thordrup M, Isidor F, Horsted-Bindslev P. A prospective clinical study of indirect and direct composite and ceramic inlays: Ten year results. Quintessence Int 2006;37:139-44.
2Santos MJ, Bezerra RB. Fracture resistance of maxillary premolars restored with direct and indirect techniques. J Can Dent Assoc 2005;71:585.
3Fabianelli A, Goracci C, Bertelli E, Monticelli F, Grandini S, Ferrari M. In vitro evaluation of wall-to-wall adaptation of aself-adhesive resin cement ued for luting gold and ceramic inlays. J Adhes Dent 2005;7:33- 40.
4Donova TE, Chee WW. Conservative indirect restorations for posterior teeth, cast versus bonded ceramics. Dent Clinic North Am 1993;37:433- 43.
5Banks RG. Conservative posterior ceramic restorations: A literature review. J Prosthet Dent 1990;63:619-26.
6Blatz MB. Long term clinical success of all ceramic posterior restorations. Quintessence Int 2002;33:415-26.
7Sandowsky SJ. An overview of treatment consideration for esthetic restoration: a review of the literature. J Prosthet Dent 2006;96:433-42.
8Davidson CL, de Gee AJ, Feilzer AJ. The competition between the composite-dentin bond strength and the polymerization contraction stress. J Dent Res 1984;63:1396-9.
9Kleverlaan CJ, Feilzer AJ. Polymerization shrinkage and contraction stress of dental resin composites. Dent Mater 2005;21:1150-7.
10Feilzer AJ, De Gee AJ, Davidson CL. Setting stress in composite resin in relation to configuration factor. J Dent Res 1987;66:1636-9.
11CHOI KK, Ryu GJ, Choi SM, Lee MJ, Park SJ, Ferracane JL. Effect of cavity configuration on composite restorations. Oper Dent 2004;29:462-9.
12Nikolaenko SA, Lohbauer U, Roggendorf M, Petschelt A, Dasch W, Frankenberger R. Influence of c factor and layering technique on microtensile bond strength to dentin. Dent Mater 2004;20:579-85.
13Feilzer AJ, De Gee AJ, Davidson CL. Increase wall to wall curing contraction in thin layers. J Dent Res 1989;66:50-8.
14Eick JD, Welch FH. Polymerization shrinkage of a posterior composite resins and its possible influence post operative sensitivity. Quint Int 1986;17:103-11.
15Kemp-Scholte CM, Davidson CL. Marginal sealing of curing contraction gaps in class V composite resin restoration. J Dent Res 1988;67:841-5.
16Martin N, Jedinakiewick NM, Williams DF. Cuspal deflection during polymerization of composite lutes. J Dent 1999;27:29-36.
17Rees JS, Jacobson PH. Stress generated by lutting resins during cementation of composite and ceramic inlays. J Oral Rehabil 1992;19:115-22.
18Watts DC. Composite inlay system, materal properties and designs. J Dent 1990;18:69.
19Mahler DB. Letter to editore. J Dent Res 1990;69:913.
20Hubsch PF, Middelton J, Knoz JA. Finit element analysis of the stress at the restoration tooth interface, comparing inlay and bulk filling. Biomaterial 2000;21:1015-9.
21Proos KA, Swain MW, Ironside J. Finite element analysis studies of an all ceramic crown on a first premolar. Int J Prosthodont 2002;15:404-12.
22Rees JS, O'Dougherty D, Pullin R. The stress reducing capacity of unfilled resin in a class V cavity. J Oral Rehabil 1999;26:422-7.
23Mange P, Versluis A, Douglas W. Effect of lutting composite shrinkage and thermal loads on stress distribution in porcelain laminate veneer. J Prosthet Dent 1999;81:335-44.
24Mange P, Douglas W. Interdental design of porcelain veneers in the presence of composite filling. Finite element analysis of composite shrinkage and thermal stresses. Int J Prosthodont 2000;13:117-24.
25Enssaf H, O'Dohery DM, Jacobson PH. The influence of the restoration -tooth interface in light cured composite restoration: a finite element analysis. Biomaterial 2001;22:3097-103.
26Ausiello P, Apicella A, Davidson CL. Effect of adhesive layer properties on stress distribution in composite restoration. Dental Mater 2002;18:295-303.
27Winkler MM, Katona RY, Paydar NH. Finit elementstress analysis of three filling techniques for class V light cured composite restoration. J Dent Res 1996;75:1477-83.
28Craig R, Powers J. Restorative dental material 11 th ed. USA: Mosby; 2002.
29Alster D, Feilzer AJ, De Gee AJ, Davidson CL. Polymerization contraction stress in thin resin composite layers as a function of layer thickness. Dent Mater 1997;13:146-59.