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Year : 2019  |  Volume : 10  |  Issue : 2  |  Page : 202-208  

Stress analysis in endodontically treated primary molar with and without stainless steel crown: A comparative finite element model study

Department of Pedodontics and Preventive Dentistry, Yenepoya Dental College, Mangalore, Karnataka, India

Date of Web Publication18-Jul-2019

Correspondence Address:
Reshma M Suvarna
Department of Pedodontics and Preventive Dentistry, Yenepoya Dental College and Hospital, Mangalore - 575 018, Karnataka
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jnsbm.JNSBM_7_19

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Background: Children at high risk exhibiting anterior tooth decay and/or molar caries may benefit by treatment with stainless steel crowns (SSCs) to protect the remaining at-risk tooth surfaces. The nonlinear finite element analysis (FEA) has become an increasingly powerful approach to predict stress and strain within structures in a realistic situation that cannot be solved by conventional linear static models. There are very few studies that have measured the stress in endodontically treated primary teeth, especially when restored with crowns. Hence, this study is done to analyze stress in endodontically treated primary molar without and with SSC using FEA. Methodology: A three-dimensional (3D) FEA model was generated using an intact normally extracted human maxillary deciduous second molar. The tooth was subjected to a computerized tomography (CT) scan, and a cross-section of the tooth was obtained at an equal interval of 0.5 mm, in Digital Imaging and Communication in Medicine (DICOM) format. The 3D geometrical model of the tooth was converted from CT DICOM as a 3D model. Two models were created: Model 1 – without SSC; Model 2 – with SSC. They were then subjected to an occlusal load (354 N, 179 N, 42 N, and 8 N) both vertically and horizontally. Results: With increased load, there is an increase in Von Mises stress and strain. The displacement patterns are well within the safe range for Model 2 as compared to Model 1. Conclusion: Endodontically treated tooth when not suitably restored with a SSC results in fracture of the underlying tooth structure. Finite element model can not only be used to evaluate stress but can also be used as a tool to educate patients regarding the importance of postendodontic restorations.

Keywords: Deciduous molar, finite element model, Poisson's ratio, stainless steel crown, stress analysis, Von Mises stress

How to cite this article:
Hegde K S, Suvarna RM, Bhat SS. Stress analysis in endodontically treated primary molar with and without stainless steel crown: A comparative finite element model study. J Nat Sc Biol Med 2019;10:202-8

How to cite this URL:
Hegde K S, Suvarna RM, Bhat SS. Stress analysis in endodontically treated primary molar with and without stainless steel crown: A comparative finite element model study. J Nat Sc Biol Med [serial online] 2019 [cited 2021 Jul 29];10:202-8. Available from:

   Introduction Top

The human tooth is a marvel of nature. However, tooth has only a limited capacity for regeneration. This necessitates the replacement of tooth structure lost because of caries, trauma, or other reasons, with a suitable restorative material.[1] The primary teeth are a temporary dentition with known life expectancies. By matching the “right” restoration with the expected life span of the tooth, the dental practitioner can succeed in providing a “permanent” restoration that will never have to be replaced. The most commonly used restorative materials available are amalgams, stainless steel crowns (SSCs), and resin composites.[2] in an exhaustive literature review of studies [3],[4],[5],[6],[7] comparing SSCs with intracoronal restorations in primary teeth, reported that these studies agreed that SSCs are superior to Class II amalgam restorations for multisurface cavities in primary molars. Children at high risk exhibiting anterior tooth decay and/or molar caries may benefit by treatment with SSCs to protect the remaining at-risk tooth surfaces.[2]

Finite element analysis (FEA) is a computer-based numerical technique for calculating the strength and behavior of structures. It can be used to analyze either small- or large-scale deflection under loading or applied displacement.[8] The basic concept of this technique is the visualization of actual structure as an assemblage of a finite number of elements. FEA divides the problem domain into a collection of smaller parts (elements). An overall approximated solution to the original problem is determined.[1]

The nonlinear FEA has become an increasingly powerful approach to predict stress and strain within structures in a realistic situation that cannot be solved by conventional linear static models. FEA has proved to be the most adaptable, accurate, easy, and less time-consuming process as compared to the other experimental analysis.[9] Furthermore, there are very few studies which have analyzed the stress in endodontically treated deciduous teeth. To add to the paucity of information regarding finite element model (FEM), there are still fewer studies which compare the stress in endodontically treated deciduous teeth with those restored with SSC. Hence, this study was done to check the authenticity of FEM as reliable stress analyzing method and also to evaluate the efficacy of SSCs as the permanent restoration in the primary teeth.

   Materials and Methods Top

In our study, a three-dimensional (3D) FEM model was generated for analysis, using an intact normal extracted human maxillary deciduous second molar.


The first step in FEM analysis is modeling. The quality of the analysis depends on the accuracy of the model. The tooth was subjected to a computerized tomography (CT) scan, and a cross-section of the tooth was obtained at an equal interval of 0.5 mm, in Digital Imaging and Communication in Medicine (DICOM) format. The 3D geometrical model of the tooth was converted from CT DICOM as a 3D model.

Digital Imaging and Communication in Medicine

DICOM is a neutral image format basically for medical imaging purposes such as CT and magnetic resonance imaging (MRI). Using the software Materialise Interactive Medical Image Control System (MIMICS), these cross-sections were converted into a 3D model. MIMICS is an interactive tool for the visualization and segmentation of CT images, as well as MRI images and 3D rendering of objects. Thus, a virtual model of the second deciduous molar was obtained. Analytical and finite element methods were used for the determination of maxillary deciduous teeth loading and stress analysis.

Materialise Interactive Medical Image Control System

MIMICS is an image-processing package that interfaces between 2D image data (CT, MRI, and technical scanner) and 3D engineering applications. Using image segmentation in MIMICS, users can select a specific region of interest from the collected medical data and have the results calculated into an accurate 3D surface model. Furthermore, MIMICS is a part of the MIMICS innovation suite, a software suite that also contains three-matic. Within the suite, MIMICS is used to generate accurate 3D anatomical models after which three-matic is used to do design and meshing operations on those anatomical models. Three-matic significantly extends the possibilities of MIMICS into the field of anatomical engineering.

In the present study, the tooth was modeled with its basic parts: enamel, dentin, and pulp. It was assumed that Young's modulus of ligament and cement closely matches that of dentine. The tooth was modeled by considering the morphological characteristics of the tooth. An endodontically treated tooth filled with zinc oxide eugenol and restored with glass ionomer cement (GIC), GC FUJI 2, Gold Label, GC Corporation, Tokyo, Japan, was modeled initially (Model 1), and then, the same model was restored with the SSC, 3M ESPE, over it (Model 2) [Figure 1] and [Figure 2]. Information on the properties of the material (elastic modulus and Poisson's ratio) is given in [Table 1].
Figure 1: (a) Dentin model, (b) pulp, dentin and enamel model combined, (c) meshing of model 1, (d) final appearance of Model 1 pulp space filled with zinc oxide eugenol, dentin, glass ionomer cement (GC FUJI 9) and enamel

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Figure 2: (a and b) Generation of tooth Model 2 with stainless steel crown and crown isolated, (c) meshing of Model 2, (d) apical view of Model 2 and crown

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Table 1: Physical properties of restorative materials

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Accurate load application was carried out to predict the complex biomechanical behavior of human maxillary tooth under mechanical loading.


FEA uses a complex system of points called nodes which make a grid called mesh. This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading conditions. ANSYS version 12.0: Year 2009, Swanson Analysis System Inc., Canonsburg, Pennsylvania, USA was used here to create the FEM.


Mesh represents a geometric object as a set of finite elements.

In the present study, we have used triangular-shaped mesh element and the number of nodes and elements are as follows [Table 2].
Table 2: Number of elements and nodes in each model

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Loads and constraints

Models 1 and 2 both were subjected to a series of occlusal load both horizontally and vertically. Based on a study by Mountain et al., the following values were taken in this study as the maximum biting force (354 N), the minimum biting force (8 N), and the mean values of biting force (179 N and 42 N) in children of both genders.[14] Not much importance was given to gender as the results were statistically insignificant according to the study.

  • Model 1: Endodontically treated primary second molar without a SSC
  • Forces 354 N, 179 N, 42 N, and 8 N were applied horizontally and vertically.
  • Model 2: Endodontically treated primary second molar with SSC
  • Forces 354 N, 179 N, 42 N, and 8N were applied horizontally and vertically.

   Results Top

After applying the above-specified loads (both vertically and horizontally) on Models 1 and 2 ranging from 354 N to 8 N, the stress patterns were analyzed. The resultant Von Mises strain and displacement for the given stress are tabulated in [Table 3], and the Von Mises stress distributions and displacements are represented in [Figure 3], [Figure 4], [Figure 5], [Figure 6]. The measurement of stress is given on a color scale present beneath the tooth in each figure. The areas of red represent the areas of highest Von Mises stress and the areas of blue represent areas of least Von Mises stress.
Table 3: When forces were applied on Models 1 and 2, the above values were observed

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Figure 3: Von Mises stress observed when different loads were applied on Model 1. (a) 354 N, (b) 179 N, (c) 42 N, and (d) 8 N

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Figure 4: Displacement observed when different loads were applied on Model 1. (a) 349 N, (b) 179 N, (c) 42 N and (d) 8 N

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Figure 5: Von Mises stress observed when different loads were applied on Model 2. (a) 354 N, (b) 179 N, (c) 42 N, and (d) 8 N

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Figure 6: Displacement observed when different loads were applied on Model 2. (a) 354 N, (b) 179 N, (c) 42 N, and (d) 8 N

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   Discussion Top

Normal mastication with its varying magnitude and direction generates considerable reactionary stresses in teeth and their supporting tissues. The finite element method, a modern technique of numerical stress analysis, has great advantage of being applicable to solids of irregular geometry and heterogeneous material properties.[15] For functional reasons, the external (i.e., the topography of the enamel cap) and internal architecture (i.e., enamel thickness and its microstructural organization) of a tooth must distribute the high stresses produced during masticatory loadings both in the teeth and their supporting structures. To evaluate the stress and strain distribution in teeth under loading conditions, several methods have been applied: electrical wire resistance gauge, photoelasticity, and ultimately FEA.[16]

Fracture resistance tests cannot evaluate fatigue in other dental tissues according to masticator forces. Thus, stress analysis methods are currently considered to be superior to fracture resistance tests because they provide comparative information about dental tissues, restoration fatigue, and deformation over time with the use of different restorative techniques.[17]

Pulpless teeth have less humidity in dental tissue and less plasticity and deformability, showing a significant decrease of hardness, increase of brittleness, and higher tendency to fractures.[18] Hickel et al. compiled a survey of the longevity and reasons for failure of SSCs, amalgam, glass ionomer, composite, and compomer in stress-bearing cavities of primary molars and concluded that SSCs are still a valid restorative procedure for heavily destroyed primary molars.[19]

There are very meager-reported data regarding stress analysis on endodontically treated deciduous teeth and SSCs or FEM studies in pediatric dentistry. In our study, we have analyzed the stress under two conditions; first one is an endodontically treated deciduous second molar restored with GIC but without an SSC as seen in Model 1 and second is endodontically treated teeth restored with GIC with SSC as seen in Model 2. Generally, in case of a vital tooth (with healthy gingiva) with irreversible pulpitis, pulpectomy is performed and SSC may be given immediately or after a span of a week or two. Although literature says that pulpectomy should be followed by SSC,[20] the exact time is not specified. The exact time to place SSC could be decided by the practitioner depending on the level of infection before treatment and patient convenience. Sometimes, this could result in a situation where the patient may fail to return for SSC, leading to fracture and failure of endodontic therapy. In this regard, this study attains importance as we can use FEM as a method to analyze stress in endodontically treated deciduous second molar with and without SSC. The results of this study could be used as a tool to educate and motivate patients in clinical practice.

Several stress concentration studies [15],[16],[17],[18] have been carried out in permanent tooth but not many in deciduous teeth. In a study done on first permanent molar by Musani and Prabhakar, it was found that when the tooth was loaded at mesial cusp tip, comparatively higher magnitudes of both tensile and compressive stresses were seen in the cervical third of the crown, thus producing a potentially damaging environment for the remaining tooth structure, which would lead ultimately to fracture.[15] Similar observations were seen in a study by Narayanaswamy et al. where stresses generated in Class V lesions unrestored and restored with various restorative materials were evaluated. It was found that when the loading angle and the restorations' size were kept fixed, increasing the load was found to increase the Von Mises stress in the immediate vicinity of the restored area and was found to be inversely proportional to Young's modulus value of the restorative material.[1] Another study by Rees and Hammadeh, it was concluded that undermining of buccal cervical amelodentinal junction causes increased cervical stress profile which causes crack initiation in enamel leading to bulk loss.[21]

In our study, when forces 354 N were applied on Model 1 in both horizontal and vertical direction, areas of moderate stress or stress above the intermediate zone were seen at the tooth–restoration interface which indicates that any tooth which is endodontically treated and restored with GIC and not covered by SSC is bound to accumulate stress and fracture eventually as represented in [Figure 3] and [Figure 4].

In a study by Hickel et al., it was concluded that GIC had the highest annual fracture rate as compared to other restorative materials in the primary teeth.[19] The findings in a FEM study by Bratosin et al. (2014) also showed concurrent results where GIC showed greater stress concentration as compared to composite material in deciduous tooth.[22] This could be attributed to the fact that GIC has a smaller value of Young's modulus as compared to composite or other restorative materials which have the same property nearly equal to that of the tooth. Similar findings were seen when forces of 179 N were applied on the tooth where areas of high stresses were found at the restoration–tooth interface indicating failure of restoration in due course of time.

In the present study, when endodontically treated primary second molar restored with SSC (Model 2) were subjected to 354 N both in horizontal and vertical direction, the stress and strain values were well within the safe levels [as indicated in [Figure 5] and [Figure 6] on the occlusal surface as compared to without SSC (Model 1). In a study by Braff, it was concluded that SSCs were significantly superior to multisurface amalgams in the restoration of primary molars and were more economical.[3] Studies by Einwag and Dünninger [7] and Randall et al.[23] also exhibited similar results in their studies. The efficacy of SSC could be explained since it has a greater Young's modulus than that of the natural tooth and much larger than that of any restorative material used in pediatric patients. Similar findings were seen in the present study where loads of 179 N were also applied on endodontically treated tooth restored with SSC, i.e. Model 2.

Areas of extreme stress and displacement were observed on the occlusal surface of endodontically treated deciduous second molar without SSC when a load of 354 N was applied. Hickel et al. in their study also recommended the use of SSC for severely affected primary molars; however, in smaller cavities, they recommended composite and compomers when the child is cooperative.[19] When the same forces were applied on the occlusal surface of Model 2, the areas of stress and the stress exerted were also much smaller. The stress exerted was within the yielding limit of the SSC.

In a study done to compare the stress analysis of a homogeneous and a nonhomogeneous human tooth using FEM by Thresher and Saito et al., it was concluded that the enamel portion of the tooth carries the major portion of the load and the load is transferred into surrounding bone structure remarkably high on the tooth root.[24] In our study also, similar findings were found where areas of high stress were found in the apical region of the roots when forces were applied on deciduous second molars without SSC as seen on Model 1. When the same forces were applied on Model 2, the amount of stress observed was well within the permissible range, thus indicating that SSCs provide excellent protection and are the material of choice to restore teeth following endodontic therapy.

There is not much difference in the stress and strain patterns when loads of 42 N and 8 N were applied on the tooth. With both the loads, the prototypes of stress and strain were well within the safe range. Moreover, displacement patterns were alike when we compared all the four different forces ranging from 354 N to 8 N in the case of the tooth restored with SSC. However, in the case of a tooth not restored with SSC, even the least force applied in this study, i.e., 8 N, showed areas of significant stresses. This indicates that unprotected tooth following endodontic therapy restored with GIC is always a precursor for breakdown of the restoration after pulp therapy.

In recent years, lot of interest has been shown toward stress analysis methods like FEA as the results were found to be close to accurate from the various studies done in the past. However, more studies have to be done in this regard to substantiate it.

   Conclusion Top

When comparing the patterns of stress on the second deciduous molars when different loads were applied, it was found that the patterns of stress and strain were almost similar. Conversely, the displacement patterns did not mimic the stress and strain patterns. Thus, we can conclude the study deducing that at higher forces, the tooth and restorative materials such as glass ionomer are bound to fracture under masticatory stress. This actuality holds truer especially when the tooth is endodontically treated and not suitably covered by an SSC.

However, this study comes with some limitations; wherein first, the luting cement and periodontal ligament were not taken into consideration in this study. Second, the fact that not many studies have been done on deciduous teeth also adds to the dearth of literature in this study. Further studies must be done to compare SSCs with other modes of so-called permanent restorations such as resin-modified glass ionomer, composite restorations, or newer materials with higher strength.


  1. We thank the Yenepoya University for the Research Grant bestowed on us which enabled us to conduct the study meticulously
  2. We thank Prof. (Dr.) Vidya Bhat for her useful suggestions during the study and timely advice
  3. We thank Prof. (Dr.) RekhaPD, deputy director, Yenepoya Research Center for her help during this study
  4. Finally, we acknowledge the scholarly help of Prof. (Dr.) Rohan Mascarenhas for his practical counsel during the study.

Financial support and sponsorship

Yenepoya Research Center, Yenepoya University, supported the study.

Conflicts of interest

There are no conflicts of interest.

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  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]

  [Table 1], [Table 2], [Table 3]


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