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 Table of Contents  
Year : 2023  |  Volume : 15  |  Issue : 4  |  Page : 391-397

Evaluation of stresses in maxillary first premolar restored with ceramic inlays and onlays by 3D finite element analysis: An in vitro study

Department of Conservative Dentistry and Endodontics, Government Dental College and Hospital, Hyderabad, Telangana, India

Date of Submission02-Dec-2022
Date of Decision26-May-2023
Date of Acceptance30-Jun-2023
Date of Web Publication31-Aug-2023

Correspondence Address:
Vemparala Bhaskara Padma Suryakumari
Department of Conservative Dentistry and Endodontics, Government Dental College and Hospital, Hyderabad 500012, Telangana
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jioh.jioh_255_22

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Aim: The present study evaluated the effect of different cavity configurations on stresses generated in maxillary first premolars restored with ceramic inlays and onlays using a finite element analysis (FEA). Materials and Methods: An extracted maxillary first premolar was used to generate a 3D FEA model from which three FEA models were designed for inlay designated as Group A and two FEA models for onlay designated as Group B. Further, based on the cavity design, they were subdivided into A1—mesio-occlusal, A2—disto-occlusal cavity, A3—mesio-occlusal distal cavity, and B1—conventional onlay preparation, B2—conservative onlay preparation. Leucite and lithium disilicate ceramics were the materials tested. An axial load of 200 N was applied vertically on the Occlusal surface. A static FEA was performed to analyze the stresses generated. Outputs of minimal principal stresses (MPS-compressive) on enamel, maximum von Misses stress values in MPa in dentin, and restoration were recorded and tabulated. Results: MPS recorded in enamel were in the order GrA3 > GrA2 > Gr B1 > GrB2 >GrA1. The von Mises stresses generated in dentin were highest for GrA2 (65.4 MPa), followed by Groups A3, A1, B2, and B1 (24.5MPa). The ceramic materials evaluated did not significantly influence the stresses. Conclusion: None of the cavity designs or the materials tested resulted in deleterious stresses leading to failure. Inlays and onlays prove to be reinforcing restorations in maxillary first premolars, with onlays having an embracing effect on the remaining sound tooth structure.

Keywords: Ceramics, finite element analysis, inlays, onlays, stresses

How to cite this article:
Pallavi Reddy Y, Suryakumari VB, Yadav SS. Evaluation of stresses in maxillary first premolar restored with ceramic inlays and onlays by 3D finite element analysis: An in vitro study. J Int Oral Health 2023;15:391-7

How to cite this URL:
Pallavi Reddy Y, Suryakumari VB, Yadav SS. Evaluation of stresses in maxillary first premolar restored with ceramic inlays and onlays by 3D finite element analysis: An in vitro study. J Int Oral Health [serial online] 2023 [cited 2023 Sep 25];15:391-7. Available from:

  Introduction Top

The biomechanical behavior of tooth restoration complex has consistently been a topic of interest in contemporary restorative dentistry. The enamel dentin complex plays a significant role in the distribution of stresses during function.[1] The restoration of the remaining tooth structure is challenging due to the extensive loss of tooth structure coupled with the deformation of tooth.[2] Inlays and onlays appear to be predictable options for restoring the missing tooth structure. Inlays are conservative intracoronal preparations, while inlays involve occlusal surface preparation to restore one or more cusps in teeth with extensive damage. It has been proven that the susceptibility of vital teeth with conservative restorations to fracture is less compared to restorations involving larger surfaces.[3],[4]

Till date, cast gold alloys, composite resins, and ceramics are the materials used in the fabrication of inlays and onlays. Indirect restorations with ceramic materials have provided predictable long-term success in restoring the lost tooth structure as well as the occlusal vertical dimension.[5],[6] Their excellent esthetics due to increased translucency and light transmission make them the restorative material of choice for inlays and onlays, leucite and lithium disilicate being the most commonly used.[7]

The fracture resistance of the tooth inlay and onlay complexes has always been a debate. Published evidence reports tooth inlay complex to be superior over tooth onlay complex in fracture resistance,[8] while long-term clinical evaluation of the same revealed greater failure rates in inlays.[9] Thus, the stresses generated in both the tooth and restorations need a thorough analysis and evaluation. The fracture resistance of tooth restoration complexes has been evaluated using multifactorial approaches involving occlusal loading in both in vitro and in vivo experimental designs that predicted the failure rate influenced by the design of the preparations. Thus, restoration of posterior teeth necessitates a comprehensive restorative approach as the impact of occlusal loads is borne by molars, and premolars occupy a strategic position in the dental arch—a transition between anterior and posterior segments. The smaller tooth surface makes it further more challenging in restoring the defects or caries in premolars.

The biomechanical evaluation and analysis of the stresses generated leading to failure could be better explained by a noninvasive, biomimetic methodology like finite element analysis (FEA).[2],[10],[11]

As the available data on stresses generated in maxillary first premolar was limited, the present study aimed at analyzing the biomechanical performance of leucite and lithium disilicate inlays and onlays in maxillary first premolars. The effect of different cavity configurations like mesio-occlusal (MO), disto-occlusal (DO), and mesio-occlusal distal (MOD) for inlays and conventional and conservative designs for onlays were evaluated using an FEA for the stresses generated.

  Materials and Methods Top

Generation of maxillary first premolar CAD model

An intact, caries-free maxillary first premolar was used as a reference to obtain a CBCT (CS 8200 Carestream Dental 3625 Cumberland, Atlanta GA 30339, US) Dental scan. A 3D CAD model of maxillary first premolar was generated from the CBCT scan using FEA soft (Ansys 19.2, ANSYS INC, Pittsburg, Pennsylvania) [Figure 1]. The anatomical references containing enamel, dentin, and cementum were created in the model.
Figure 1: A 3D CAD model of maxillary first premolar

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Generation of CAD models for different cavity configurations

Five experimental models, one each for the specific study designs—three for inlay and two for onlay were generated from a 3D CAD model. They were grouped as Group A for inlay and Group B for onlay. Further, based on the cavity designs, the models were divided into subgroups as follows:

Group A—inlay cavity model

  • A1—MO cavity

  • A2—DO cavity

  • A3—MOD cavity

  • Group B—onlay cavity model

  • B1—conventional preparation

  • B2—conservative preparation

  • The cavity for inlay model extended to the full length of occlusal groove, including the mesial pit for DO cavity, distal pit for MO cavity. The occlusal cavity was designed with a depth of 3 mm and width of 2 mm between the buccal and lingual cusp tips, while that of proximal box was 2 mm deep and 2 mm wide. For MOD model, both mesial and distal pits were included with proximal box extending on both sides with the same dimensions as mentioned.

    The model for onlay had an intracoronal part similar to MOD inlay with an additional cuspal coverage. Based on the intracoronal box and the extent of cuspal coverage, the models were designated as conventional and conservative. Conventional model was designed with an internal box and cuspal coverage of 4 mm, while conservative model with 2 mm cuspal coverage only without any internal box.

    It was ensured that the prepared models had pulpal and axial walls with dentin thickness over the pulp for at least 1.0 mm, while cervical walls of proximal boxes were located at least 1.0 mm above the cementoenamel junction. All the experimental models were restored with two types of ceramic materials—leucite and lithium disilicate.

    Specifications for finite element analysis

    The mechanical properties of the hard tissues and materials used were represented by Young’s modulus of elasticity and Poisson’s ratio extracted from the literature [Table 1].[3],[12] All materials were assumed to be linear, elastic, homogeneous, and isotropic. Boundary conditions were defined by the restriction of the movements applied at the external lateral outline and cylindrical specimen support base. Based on the model inlay or onlay, the elements and nodes for the models were created. The nodes and elements for inlay ranged from 145,193 to 254,899 and 210,782 to 370,274, while those for onlay were from 224,682 to 241,322. To prevent the rigid body displacement for all models, XYZ directions were assigned to the nodes at the bottom of the tooth.
    Table 1: Material properties of dental tissues and restorative material

    Click here to view

    Testing conditions and finite element analysis

    Intraoral biting forces were simulated by an axial load of 200 N[13] applied vertically as 40 N each at five specific points on the occlusal surface—palatal cusp tip, buccal cusp tip, central fossa, mesial and distal marginal ridges[14] [Flow Chart 1]. A static FEA was performed to predict stress concentration produced by occlusal loading. Outputs of minimal principal stresses (MPS-compressive) on enamel, maximum von Mises stress values in MPa in the dentin, and restoration were evaluated separately.
    Flow Chart 1: Study design with the experimental models

    Click here to view

      Results Top

    The results of the present study evaluated the magnitude and distribution of stresses in each component of the hard tissues and restoration separately when an intraoral axial biting load of 200 N was applied onto the occlusal surface of the maxillary first premolar. The stress distribution patterns in all the models evaluated were similar though the magnitude was different.

    Outcome of the loads was analyzed in terms of von Mises stress values in MPa for all the components tested. Since enamel is a brittle structure, the Minimal principal stresses in MPa were considered to be applicable for evaluation.

    In the present study, the stress distribution patterns were found to be maximum on the lingual cusps, the maximum von Mises stresses on the tooth surface were concentrated at the cusp tips corresponding with the regions of force application, with a gradual descent toward the cement-enamel junction (CEJ). [Figure 2] and [Figure 3] represent the stresses in enamel, dentin, and restoration for Groups A and B.
    Figure 2: Stresses in enamel (E), dentin (D), and restoration (R) for Group A

    Click here to view
    Figure 3: Stresses in enamel (E), dentin (D), and restoration (R) for Group B

    Click here to view

    [Table 2] depicts the MPS (compressive) in enamel for inlay varied with designs and ceramic materials. The observed values were 283–450.6 MPa. For onlay model, the values were 286–310 MPa. MPS recorded in enamel for both the experimental models were in the order MOD > DO > onlay conventional > onlay conservative > MO. The ceramic materials evaluated did not significantly influence the stresses.
    Table 2: Tabularized values of stresses in enamel, dentin, and restoration

    Click here to view

    Whereas for dentin and ceramic materials, von Mises stresses in MPa were evaluated. The minimum von Mises stresses recorded was 24.5 MPa, while the maximum was 65.4 MPa. Similarly, the von Mises stresses in the ceramic material had a minimum value of 19.2 MPa and a maximum of 70.6 MPa.

      Discussion Top

    The stomatognathic equilibrium is maintained by a synchrony between anterior and posterior teeth. While anterior teeth play an important role in phonetics and aesthetics, posteriors are vital for mastication, thus being subjected to heavy masticatory loads. The consequences of these heavy loads can be complete or incomplete vertical root fractures (VRFs) determined by multiple factors like gender, tooth type and location, age, radiographic and clinical findings, bruxism, and pulpal status. It was proven that VRFs are statistically more prevalent in mandibular molars and maxillary premolars.[15] Thus in the present study, maxillary first premolars were chosen for analysis as they are the transition between anterior and posterior segments of dental arch with a significant predilection for fractures.

    The congregation of stresses can lead to tooth fracture, failure of cement-restoration interface, or fracture of restorations perse, resulting in clinical failures.[16],[17] Also, the impact of stresses and fracture resistance of a restored tooth is greatly influenced by the cavity preparation design, more so with extensive MOD cavities in maxillary premolars.[18],[19],[20] In the present study, the conventional onlay preparation design depicts the clinical scenario where in an extensive loss of tooth structure necessitates an internal box preparation with an added cuspal coverage for retention and reinforcement of the tooth structure. The design tested had a cuspal coverage of 2 and 4 mm, signifying mild-to-moderate loss of tooth structure due to caries. In comparison to the conventional model, a less invasive conservative preparation with onlays was also selected in the study.

    Though cast gold restoration is the standard care for indirect restorations, ceramics and composites have been proven to reinforce teeth and provide a comparable fatigue resistance against fracture in cuspal restorations.[21] Thus in the present study, leucite and lithium disilicate ceramics were evaluated distinctly in inlay and onlay cavity configurations. Reinforcing the remaining tooth structure is as important as the conservation of sound tooth structure. At times this may necessitate the removal of additional tooth structure to reinforce the tooth, as seen in MOD and onlays. The involvement of marginal ridges coupled with increased width and depth of cavities may contribute to fracture susceptibility in maxillary first premolars, which can be compensated by partial coverage indirect adhesive restorations proven to be favorable on vital teeth.[22]

    FEA has proven to be an extremely powerful tool in analyzing the biomechanical behavior of materials and tooth tissues with structural and material complexity, which otherwise are difficult to be addressed by conventional methods. The calculation of stress and strain in the tooth and the restorations, which otherwise could not be determined in vivo, are predictably analyzed by FEA.[23]

    Hence, the primary objective of this study was to evaluate the stresses generated in maxillary first premolars restored with ceramic inlays and onlays when subjected to occlusal loads of 200 N in total applied on five specific points on the Occlusal surface as a divided load of 40 N each using an FEA. It is evident from the previous studies that the maximum stress concentration in a maxillary first premolar is the functional cusps (palatal cusp), central fossa, marginal ridges, and the least at the nonfunctional cusps. Hence, to simulate the contacts with the antagonistic teeth under masticatory and parafunctional loads, these points were selected for evaluation.[14]

    As enamel is a brittle material the MPS were evaluated. A generalized observation of the results of the present FEA revealed that irrespective of the tooth tissue—enamel (450.5 MPa), dentin (61.5 MPa), or the restoration (21.3 MPa), higher stresses were recorded for Gr A3 (MOD) compared to other groups which were in accordance with a study by Georges et al.[24]

    The MPS in enamel recorded were the least for GrA1 (283 MPa). The ascending order of stresses was as follows: GrA1 < B1 < B2 < A2 < A3. The stresses recorded for all the groups in enamel (maximum recorded being 450.5 MPa) were more than the yield stress of 232 MPa, indicating the stresses are not allowable. This could be predicted to act as a hot spot indicating a future region of failure when the loads exceed further. Regarding the location of the stresses, the greatest stresses were concentrated at the CEJ region on the palatal side. There was no effect of the load tested on the cementum.

    The von Mises stresses generated in dentin were highest for GrA3 (65.4 MPa), followed by Groups A2, A1, B2, and B1 (24.5 MPa). The stresses generated were less than the yield value of dentin (68 MPa), thus indicating that at the load tested, the stresses are allowable and do not cause failure in dentin. The maximum von Mises stresses were observed in Gr A compared to Gr B, which were in unison with earlier studies wherein the wedging effect of small restorations causing horizontal stresses on cavity walls has been proven.[25]

    The locations of stresses in dentin were more concentrated at the cusp tip region on the palatal side, similar to the pattern observed in enamel [Figure 2]. None of the stresses in the different groups tested had an impact on the cementum, indicating that there was no significant effect of the load on the root surface that could lead to root fractures. In both enamel and dentin, neither leucite nor lithium disilicate ceramic material had any significant effect on the stresses generated in contrary to the previous study by Vianna et al.[26] wherein the lithium disilicate ceramic group showed significantly higher fracture resistance than the leucite ceramic group, irrespective of the cavity design. The von Mises stresses in the ceramic material were least for Gr A1 and highest for Gr B2. When both Gr A and Gr B were evaluated, the von Mises stresses were significantly higher for Gr B2 (70.6 and 67.5 MPa for lithium disilicate and leucite, respectively) [Figure 3]. Lithium disilicate exhibited greater stress compared to leucite in all groups. This could be attributed to its greater modulus of elasticity, high stiffness of material rendering it to absorb more stresses, thereby transferring less to the tooth structure, indicating a better clinical performance of the material.[27]

    Inlays fabricated from ceramic material exhibited uniform stress distribution in the dentin around restoration, which contributes for the integrity of restorations and lesser predilection to failure, as in accordance with the present study.[28] Inlays and conservative onlay designs have been proven to provide better resistance for ceramic restorations and thus can be safely advocated in terms of fracture resistance.[29]

    In a prepared cavity, both enamel and dentin showed significant differences in the stresses generated on the MO and DO cavity designs which may be attributed to the variation in the anatomy of tooth structure. Relatively on a restoration, there were no significant differences in the stresses generated on MO and DO cavity designs, indicating even distribution of forces, thereby reinforcing the tooth against greater loads. This FEA thus throws some light on the fact that inlays and onlays prove to be reinforcing restorations for extensively damaged tooth. Onlays have been found to have a more embracing effect on the remaining sound tooth structure, suggesting a superior clinical performance of leucite and lithium disilicate onlays.

    This study analyses anisotropic tissues, such as periodontal ligament, hard tissues of tooth, and the restorative materials, which are considered isotropic initially. The load applied was static rather than the dynamic load encountered during function, which happens to be a limitation. The effect of moisture and thermal changes, which can affect the material properties and thereby the stress distributions in vivo have not been simulated in the present study, which happens to be scope for further analysis in future. FEA depends on mathematical calculations to analyze the biomechanical behavior, but living tissues cannot be contained within set parameters and values since biology does not exist in the same way as set parameters. Further studies for extrapolation in simulated oral environments, when complemented with FEA, provide an accurate analysis.

      Conclusion Top

    It was observed that at a tested load of 200 N, when Max I PM was evaluated for stresses in inlay and onlay models, neither the cavity configuration nor the ceramic material evaluated exhibited critical stresses leading to failure. Inlays and onlays prove to be reinforcing restorations for extensively damaged tooth. Onlays have been found to have a more embracing effect on the remaining sound tooth structure, suggesting a superior clinical performance of leucite and lithium disilicate onlays. However, the effect of intraoral clinical environment on the biomechanical behavior of the analyzed materials needs to be evaluated in further studies.


    The authors would like to acknowledge simulation engineers Mr. Sunil G and Mr. Sravan of CS TECH Solutions for the valuable support in designing and analysis of the FEA model.

    Financial support and sponsorship


    Conflict of interest


    Author contributions

    Dr. Y. Pallavi Reddy: concept, design, experimental studies, data acquisition, data analysis, manuscript review. Dr. V.B.P. Surya Kumari: concept, design, definition of intellectual content, literature search, clinical studies. Manuscript preparation, manuscript review. Dr. Sarjeev Singh Yadav: statistical analysis, manuscript editing, and manuscript review.

    Ethical policy and institutional review board statement

    Not applicable.

    Patient declaration of consent

    Not applicable.

    Data availability statement

    Not applicable.

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

      [Table 1], [Table 2]


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