G Model JPOR 470 No. of Pages 7 journal of prosthodontic research xxx (2018) xxx–xxx Contents lists available at ScienceDirect Journal of Prosthodontic Research journal homepage: www.elsevier.com/locate/jpor Original article Effect of preparation design for all-ceramic restoration on maxillary premolar: a 3D finite element study Ebrahim Maghamia , Ehsan Homaeia,b,c , Khalil Farhangdoosta,** , Edmond Ho Nang Powd, Jukka Pekka Matinlinnac , James Kit-Hon Tsoic,* a Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran Toos Dental Lab- Sahebkar, Mashhad, Iran Dental Materials Science, Discipline of Applied Oral Sciences, Faculty of Dentistry, The University of Hong Kong, Hong Kong, China d Oral Rehabilitation, Faculty of Dentistry, The University of Hong Kong, Hong Kong, China b c A R T I C L E I N F O A B S T R A C T Article history: Received 22 June 2017 Received in revised form 18 February 2018 Accepted 9 April 2018 Available online xxx Purpose: The aim of this study was to investigate and quantify the effect of preparation design parameters on a premolar restored with two different CAD/CAM ceramic crowns by three-dimensional finite element analysis (FEA). Methods: A restored human first premolar was digitized by a micro-CT scanner and a 3D model was created by a medical image processing software (Mimics). Following segmentation, dentine and ceramic were extracted by a surface meshing software (3-matic). Models with different preparation designs with three convergence angles (6 , 12 and 20 ) and two preparation heights (3.1 mm and 4.1 mm) were produced. Mesh generation for models was performed in IA-FEMesh software with a lithium disilicate glass ceramic (LD, E = 95.9 GPa) and a polymer-infiltrated ceramic (PIC, E = 30.1 GPa) as the restorative materials. A 5-mm diameter stainless steel hemisphere was employed as an indenter. Twelve models were analyzed numerically in AbaqusTM. Results: The results indicated that preparation height was found to be a major factor affecting stress distribution in different components. In all models, the maximum principal stress of the ceramic crowns was found in contact area against the indenter. This stress was lesser in the longer abutment than the shorter one and it was greater for LD ceramic. Convergence angle had limited effect on stress distribution of ceramic crown in all models. Conclusions: The preparation height appeared to play a more important role in the stress distribution of ceramic crown than the convergence angle. © 2018 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved. Keywords: Tooth preparation design Convergence angle Preparation height All-ceramic crown 3D finite element analysis 1. Introduction Although ceramics have become common restorative materials in modern dentistry [1,2], their mechanical failure in allceramic restorations is still high [3]. In comparison with the conventional fabrication method which may result in structural flaws and imperfections [4], CAD/CAM technology can produce a dental restoration with more homogeneity [5]. Furthermore, * Corresponding author at: Prince Philip Dental Hospital, 34 Hospital Road, Hong Kong, China. ** Corresponding author at: Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad Azadi sq., 9177948944, Mashhad, Iran. E-mail addresses: farhang@um.ac.ir (K. Farhangdoost), jkhtsoi@hku.hk (J.K.-H. Tsoi). CAD/CAM technology allows the reproduction of detailed tooth morphology [6,7]. Apart from the production method, tooth preparation and restoration design also have appreciable effects on fracture resistance of ceramic crowns [8–11]. Various designs for fullcoverage restorations including margin thickness [12–14], degree of convergence angle [15–17], preparation height [16,18], and margin adaptation [16,19] have been studied. While crown thickness is one of the determining factors affecting the stress distribution and thereby survival of a restoration [10], a study suggested a convergence angle below 20 and occlusal-cervical height of 6 mm in order to attain a reasonable internal fit of a ceramic crown for molar teeth [16]. In composite resin crowns, an increase in the occlusal thickness of the crowns and decrease in the total convergence angle led to improvement of the fracture resistance [11]. Although many experimental and numerical https://doi.org/10.1016/j.jpor.2018.04.002 1883-1958/ © 2018 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: E. Maghami, et al., Effect of preparation design for all-ceramic restoration on maxillary premolar: a 3D finite element study, J Prosthodont Res (2018), https://doi.org/10.1016/j.jpor.2018.04.002 G Model JPOR 470 No. of Pages 7 2 E. Maghami et al. / journal of prosthodontic research xxx (2018) xxx–xxx studies have been carried out to determine the effective parameters in preparation design, important questions remained unanswered about which, if any parameters, have the greatest influence [13]. Numerical models have been known as a powerful way to predict the behavior of mechanical structures due to its low cost and risk compared to in vitro and in vivo investigations [14,20]. Due to the intricate geometry and several components of a restored tooth, finite element method (FEM) is a non-destructive technique to study the stress and strain distributions in three-dimensional (3D) model [21–23]. To achieve a 3D model with high precision and resolution, micro-CT images are often utilized, especially when small-scale subjects such as tooth, dental implants, and crowns are being studied [24–27]. Finite element analysis (FEA) has been employed in many studies to assess the deformation of each component of restored teeth [13,14,17,20,24–27]. A study investigated the influence of three different taper abutment angles on premolars and it was found that a smaller angle resulted in lower maximum tensile stress [17]. However, the finite element (FE) model was in two dimensions which does not simulate the real conditions accurately. Furthermore, Li et al. [28] carried out a FE study to estimate reliability of all-ceramic crowns, but their model did not include remaining enamel at the margin of the restoration. In the literature, there are limited 3D numerical studies to determine the effect of preparation design parameters on a restored tooth with anatomic design for all-ceramic crowns. In addition, most FE simulations of design parameters have not considered the nonlinear behavior of tooth-to-tooth or indenter-to-tooth contact [29–31]. These studies used a concentrated force to apply load on their models and that does not mimic the real situation. The objective of the present study was to investigate the effect of convergence angle and preparation height on the stress distribution of a restored premolar using FEM. The null hypothesis was that change in convergence angle and preparation height of the abutment would have no appreciable effects on the stress distribution in the ceramic crown. 2. Materials and methods In the present study, a human first maxillary premolar restored with all-ceramic crown was selected for the numerical analysis. Two parameters including three convergence angles (6 , 12 and 20 ) and two preparation heights (3.1 mm and 4.1 mm) were investigated. The whole workflow of obtaining the 3D-FE model is shown in Fig. 1. Additionally, two CAD/CAM ceramics were considered as the restorative materials for the crown, a lithium disilicate glass ceramic (LD, IPS e.max1 CAD, Ivoclar Vivadent, Schaan, Liechtenstein) and a polymer-infiltrated ceramic (PIC, Enamic1, VITA Zahnfabrik, Bad Säckingen, Germany). RelyXTM Ultimate (3M ESPE, St. Paul, MN, USA) was utilized as the adhesive resin cement layer. The mechanical properties of each material are presented in Table 1. 2.1. Micro-CT scanning A 1.3 megapixel camera was used for digitizing the restored tooth using a micro computed tomography (micro-CT) scanner (SkyScan 1172, Kontich, Belgium). The beam accelerating voltage and current were 80 kV and 100 mA, respectively. The frames were taken for 180 of the sample with rotation step of 0.4 and the exposure time of 4.477 s for each frame with an Al + Cu filter. The TIFF-format images taken from the micro-CT scanner were reconstructed using NRecon1 software (SkyScan) for reaching the final bitmap (BMP) files. Fig. 1. The general work-flow for creating FE models. The BMP slices were imported to an interactive medical image processing software (Mimics 14; Materialise, Leuven, Belgium) where different tissues (pulp, enamel, dentin, and ceramic) were identified. Using the segmentation function which was based on the density thresholds, one mask was assigned to each hard tissue. In order to construct a more precise threshold, the slices were edited manually. After constructing the pulp, enamel, dentin, and ceramic, the adhesive mask was created by applying the Boolean operation function which could reduce the working time with accurate boundaries between the masks. After completion of all the 2D masks, their 3D shapes were generated and the stereolithography (STL) file of each mask was extracted. 2.2. Extracting surfaces from dentin and ceramic The STL files of pulp, dentin, enamel, and ceramic were imported directly to 3-matic workplace (3-matic 6, Materialise, Leuven, Belgium) where advanced manipulation of the volumetric files and design could be performed. Smoothing operation was used to remove inappropriate and sharp triangles that covered the surfaces of dentin and ceramic. Tessellated surfaces of dentin and ceramic were extracted in Initial Graphics Exchange Specification (IGES) file formats. 2.3. Change in the abutment height and convergence angle The IGES files were imported to SolidWorks 2014 software (Dassault Systèmes, SolidWorks Corp., Waltham, MA, USA) in order to manipulate the models with desired height and convergence angles. As the imported files were in a format of surface, they (dentin and ceramic) were converted to a solid format using the Knit surface tool. By applying extrusion and cutting functions on different surfaces of dentin, different abutment heights and convergence angles were ideally created. Combining function was used, so the intaglio surface of ceramic could fit on the modified dentin with the occlusal surface of ceramic remained unchanged. To mimic the clinical situation, a layer of adhesive with thickness according to the previous studies was also incorporated Please cite this article in press as: E. Maghami, et al., Effect of preparation design for all-ceramic restoration on maxillary premolar: a 3D finite element study, J Prosthodont Res (2018), https://doi.org/10.1016/j.jpor.2018.04.002 G Model JPOR 470 No. of Pages 7 3 E. Maghami et al. / journal of prosthodontic research xxx (2018) xxx–xxx Table 1 Mechanical properties of materials. Material Young’s modulus (MPa) Poisson’s ratio Compressive strength (MPa) Flexural strength (MPa) Shear strength (MPa) LD ceramic PIC ceramic Enamel Dentin Adhesive resin cement Pulp Indenter 95,900 30,100 84,100 18,600 7700 2 207,000 0.23 0.23 0.33 0.31 0.3 0.45 0.3 N/A N/A 95–386 249–315 262 N/A N/A 356.7 135.8 30–35 40–276 98 N/A N/A N/A N/A 60 12–138 40 N/A N/A Fig. 2. The investigated convergence angles and preparation heights in numerical analyses. between the dentin and ceramic [16,19,32]. Dentin, ceramic, and adhesive STL files were then extracted. The resultant 3D models were obtained according to their convergence angle and preparation height (Fig. 2):       T6H1 — 6 convergence angle and 3.1 mm height preparation T12H1 — 12 convergence angle and 3.1 mm height preparation T20H1 — 20 convergence angle and 3.1 mm height preparation T6H2 — 6 convergence angle and 4.1 mm height preparation T12H2 — 12 convergence angle and 4.1 mm height preparation T20H2 — 20 convergence angle and 4.1 mm height preparation Afterwards, by assigning the two restorative materials (LD and PIC) as the crown, twelve models were totally created. 2.4. Volume mesh generation To generate a desired mesh for each part, the IA-FEMesh software (Iowa FE Mesh, The University of Iowa, Lowa, IA, USA) was used for a high quality mesh. By importing the STL files to IAFEMesh and creating blocks, hexahedral elements were generated for each part, according to Grosland et al. instructions [33]. The meshed parts were imported to the AbaqusTM software (AbaqusTM, v. 14, Dassault Systèmes) for FEA. 2.5. Finite element analysis In AbaqusTM, all parts were assembled together and the elements with error were manually edited (Fig. 3). In accordance with the anatomy, pulp elements were separated from the dentin. A stainless steel hemispherical indenter (5 mm diameter) was modeled to load the tooth. It was positioned carefully on the occlusal surface, in a way to make contact with both cusps simultaneously, according to our previous in vitro research [3]. To do that, using an intermediary assembly workplace software (SolidWorks 2014), the indenter was moved towards the cusps until at a moment (a specified location) the indenter had contact with both cusps simultaneously. The position of the restored tooth and indenter was then recorded and imported to Abaqus software. The interfaces of the parts were coupled together. Deformable contact body definition was designated to the tooth and the indenter. Contact between the indenter and occlusal surface was defined which was automatically detected by AbaqusTM. For boundary conditions, approximately 1 mm below the cemento-enamel junction (CEJ) was constrained with zero displacement and rotation in all directions. A vertical displacement on the top surface of the indenter was applied (along the Z-axis only). The value of this displacement increased from zero to a value which the total calculated load along the Z-axis on the top surface reached to nearly 300 N. This load is the average biting force for premolars [14]. Other nodes of the indenter (except the nodes at the top surface) were free to move in any direction. This is exactly what happened in our previous in vitro study [3] and indeed, the indenter should be free to interact with the occlusal surface when moving down during applying load. All the materials were assumed to be homogeneous, linear elastic, and isotropic. Mechanical properties of dentin, enamel, adhesive, pulp, and the indenter were taken from literature [34–38]. Young’s modulus of LD and PIC were calculated by Homaei et al. [39], while the Poisson’s ratios for materials used have been reported in other studies [40,41]. The mechanical properties of adhesive were obtained from the manufacturer’s document [42]. The mechanical properties of all components are listed in Table 1. All models were solved with the increment of 0.005. To attain a more accurate stress distribution analysis, a convergence test was used to guarantee that Please cite this article in press as: E. Maghami, et al., Effect of preparation design for all-ceramic restoration on maxillary premolar: a 3D finite element study, J Prosthodont Res (2018), https://doi.org/10.1016/j.jpor.2018.04.002 G Model JPOR 470 No. of Pages 7 4 E. Maghami et al. / journal of prosthodontic research xxx (2018) xxx–xxx (FI) was defined as the proportion of a component’s material strength to the maximum generated stress in the component, according to a FE study [43]. Thus, failure happened in a model when FI of one component is lower than 1. For each component in all models, the FI was calculated and presented in Table 6. It can be seen that enamel in all LD crown models and also in four other models (T6H2, T12H1, T12H2 and T20H2) with PIC crowns experienced failure, having FI lower than 1. In addition, adhesive layer in two models (T20H1 and T20H2) with LD crowns had FI lower than 1 (Table 6), while other components survived under occlusal loads (Table 6). The current T12H1 model has been used and verified with the experimental results in a previous study [44]. In addition, the stress distribution pattern of the contact spot on the buccal and lingual cusps was comparable with other previous numerical and experimental studies [26,45]. The compressive and tensile stress found at the contact point and its vicinity (Fig. 5) could lead to cone cracks and that was in agreement with other studies [45–47]. 4. Discussion Fig. 3. An assembled model consisted of different parts: (a) the assembled model, (b) indenter, (c) ceramic crown, (d) adhesive, (e) enamel, (f) dentin, and (g) pulp. no further mesh refinement was required. The number of elements and nodes for each part of all models has been listed in Table 2. 3. Results The effects of convergence angle and tooth preparation height on stress distribution were investigated with the stress value of each component of the restored tooth (ceramic crown, adhesive, dentin, and enamel). Twelve 3D models of the restored premolar were analyzed and their stress distributions of different regions are presented in Tables 3–5. The regions are depicted in Fig. 4, which are named as: R1 (contact area on occlusal surface), R2 (ceramic central fossa), R3 (lingual region of ceramic in interface with adhesive), R4 (buccal region of ceramic in interface with adhesive), R5 (central fossa region of ceramic in interface with adhesive), R6 (adhesive shoulder region), R7 (dentin shoulder region), R8 (whole enamel), and R9 (dentin-enamel interface in dentin). Maximum shear (Tresca) stress of adhesive and maximum principal stress (MPS) for other components were calculated separately in different regions for all models. Fig. 5 demonstrates the stress distribution of contact area on the occlusal surface. The Tresca stress in the adhesive was found in the shoulder region (Fig. 6). MPS in the dentin was also found on the shoulder margin (Fig. 7). The effect of convergence angle on the MPS values of ceramic and enamel was negligible. For all the preparation designs, the MPS value of the ceramic crown on the lingual cusp (R3) was higher than on the buccal cusp (R4) (Table 3). Figs. 5–7 are representatives; MPS and Tresca stress locations did not change with different test configurations or materials but, as noted in the tables, the level of MPS and Tresca stress changed. In addition, the concept of failure in the tooth components for each model in the present study was defined as when stress values in any components reached to its ultimate strength. By comparing the MPS of ceramics (Table 3), dentin and enamel (Table 5) with their flexural strength (Table 1), some components failed. Moreover, failure in the adhesive resin cement layer was considered once Tresca stress (Table 4) reached to its shear strength (Table 1). In overall, failure in the restored tooth was assumed to happen once a component in the whole structure failed. In order to show these results quantitatively, a Failure Index FEA is considered to be a good alternative to explore the behavior of all-ceramic crowns [27]. In the present study, the effect of convergence angle and tooth preparation height on the stress pattern of a premolar restored by an all-ceramic crown was investigated by FEM. A considerable effort was performed using a set of software to achieve an accurate FE model. The models contained ceramic crown, dentin, adhesive, enamel and pulp while most studies [17,34,48–50] did not take the remained enamel into account. This simulation was robust because three-dimensional hexahedral elements were used which could produce more accurate results compared to the conventional approach using tetrahedral elements [51]. The FEA results still need validations which are achievable with further experimental work [52]. Following FE validation, the models can be utilized to study on a wide range of purposes, while for the models totally beyond from them, new in-lab studies are required [53]. The models investigated in this study are in the same range and validation of just one model (T12H1) with experimental results might be enough to trust the other models. Regarding the results of the current study, the null hypothesis is partially rejected. It was observed that convergence angle had negligible effects on the MPS values of ceramic, whereas the effects of tooth preparation height on the MPS values of ceramic were appreciable. The static load analysis performed in this study is an acceptable method to assess mechanical behavior of tooth [5]. However, it should be noted that cyclic fatigue leads to failure of dental restorations in clinical conditions which usually happen in subcritical loads [39]. Homaei et al. [39] expressed a fatigue limit which was approximately half of the mean static flexural strength, below which no failure is expected to occur [54]. According to this limit and flexural strengths of two ceramic crowns (Table 1), MPS of PIC ceramic (Table 3) was more close to its half of flexural strength in comparison with LD. However, resistance of PIC against crack propagation is increased considerably in cyclic loadings, in particular when used as a crown [3]. LD glass ceramic is known as a brittle material, whereas the plastic behavior of PIC postpones fatigue failure [39,55]. Therefore, both materials seem to be reliable under cyclic masticatory forces as a crown restoration for premolars. An important factor of the fracture resistance is the margin thickness. Increasing the margin thickness could allow the restoration to withstand a greater axial load before it fractured [13,56]. However, it has a limit and it was recommended that the margin thickness for all-ceramic crowns should range from 0.5 to Please cite this article in press as: E. Maghami, et al., Effect of preparation design for all-ceramic restoration on maxillary premolar: a 3D finite element study, J Prosthodont Res (2018), https://doi.org/10.1016/j.jpor.2018.04.002 G Model JPOR 470 No. of Pages 7 5 E. Maghami et al. / journal of prosthodontic research xxx (2018) xxx–xxx Table 2 Number of elements and nodes in each component of all models. Preparation design models T6H1, T12H1, T20H1 Elements Nodes Elements Nodes T6H2, T12H2, T20H2 Adhesive Ceramic Dentin Enamel Pulp Indenter 4900 9653 4612 9369 40,824 46,269 40,824 46,269 35,537 40,596 35,824 40,525 840 1960 840 1960 2463 3634 2463 3634 7600 8574 7600 8574 Table 3 The maximum principal stress values of ceramic crown in the preparation designs for five different regions with regard to the crown materials. Region Crown material Preparation design models T6H1 T6H2 T12H1 T12H2 T20H1 T20H2 R1 PIC LD PIC LD PIC LD PIC LD PIC LD 58.5 64.8 48.5 51.7 30.3 32.4 7.3 7.9 8.1 9.2 51.1 47.1 41.2 44 47.2 45.2 13.3 9.2 11.1 12.8 58.4 64.8 49 53.3 30.7 33.5 6.8 7.2 8.5 9.4 51.2 49.8 40.6 44.6 46.7 44.4 13.5 9.3 11.8 12.8 59.3 64.8 49 53.2 29.7 31.7 8.6 6.2 8.3 9.5 50 45.5 40.5 44.6 47.3 45.7 16.7 10.9 11 11 R2 R3 R4 R5 Table 4 The maximum shear stress of the preparation designs for adhesive (R6) with regard to the crown materials. Crown material Preparation design models T6H1 T6H2 T12H1 T12H2 T20H1 T20H2 PIC LD 22 31.8 26 34 18.8 36.3 22 37 30 42.2 32 43.2 Fig. 4. The different regions of the restored premolar for the stress distribution analyses. Table 5 The maximum principal stress of the preparation designs for dentin shoulder (R7), enamel (R8) and dentin in interface with enamel (R9) with regard to the crown materials. Region Crown material Preparation design models T6H1 T6H2 T12H1 T12H2 T20H1 T20H2 R7 PIC LD PIC LD PIC LD 24.9 21.7 33.6 49.5 10.4 14.1 4.8 9.7 37.8 52 9.7 13 21.8 23.1 35.8 51 6.3 9 4.1 9.5 38.2 54 8.9 11.8 17 22.2 32.4 52 7.9 11.3 5.1 8.9 39.2 53.6 7.8 10.4 R8 R9 1.0 mm [13] and that has been adopted in the present simulated model. Regarding the importance of convergence angle in the laboratory experiments, it is claimed that a high convergence angle could avoid tooth fracture [56,57]. In addition, increase in the preparation angle enhances the marginal fit [58]. Moreover, it was estimated in another study that a minimum convergence angle of 12 is needed to avoid undercut in the preparation [59]. Nevertheless, by increasing the angle of convergence, the retention of preparation decreases [60,61]. In the present study, the 12 design was found to be the best convergence angle for both ceramic materials with lower stresses compared to other angles, particularly on the adhesive layer. Also variations in the convergence angle displayed no appreciable difference in stress values in the ceramic crowns. In models with the same convergence angle, the MPS of dentin in the 4.1 mm group was lower than the 3.1 mm one. This might be Fig. 5. The stress distribution pattern of ceramic crown in contact area with indenter. due to the greater surface area of preparation which resulted in greater retention [61,62]. The MPS of enamel component in the LD group was greater than that in the PIC group. Since LD ceramic has a greater elastic modulus, higher stresses are created and that could be transferred to the enamel at the margin which is considered to be a supporter of the crown [11]. Furthermore, FI values of enamel in preparation design models with LD crowns were considerably lower than 1 (Table 6), while these FI values for enamel in models with PIC crowns were greater than or near to 1 (Table 6). This might be related to the fact that a stiffer crown like LD caused greater stresses values to be generated in enamel. Indeed, the considerable difference between flexural strengths of LD crown (356.7 MPa) and enamel (30–35 MPa) might lead to a more unbalanced stress distribution between both the LD crown and enamel where a stronger material (LD crown) was placed on a weaker material (the remained enamel at the margin of the restoration). Additionally, adhesive layer in two models (T20H1 and T20H2) with LD crowns had the FI lower than 1 (Table 6). Please cite this article in press as: E. Maghami, et al., Effect of preparation design for all-ceramic restoration on maxillary premolar: a 3D finite element study, J Prosthodont Res (2018), https://doi.org/10.1016/j.jpor.2018.04.002 G Model JPOR 470 No. of Pages 7 6 E. Maghami et al. / journal of prosthodontic research xxx (2018) xxx–xxx Table 6 FI values for each component in all twelve models. Component Crown material Preparation design models Ceramic crown Adhesive PIC LD PIC LD PIC LD PIC LD 2.32 5.5 1.81 1.25 1.04 0.7 11 12.7 T6H1 T6H2 T12H1 T12H2 T20H1 T20H2 Enamel Dentin Fig. 6. Tresca stress distribution pattern of adhesive in T12H1 model of PIC crown. 2.65 7.5 1.53 1.17 0.92 0.67 28 21.2 2.32 5.5 2.12 1.1 0.97 0.68 12.6 11.9 2.65 7.1 1.81 1.08 0.91 0.64 31 23.3 2.29 5.5 1.33 0.94 1.08 0.67 16.2 12.4 2.71 7.8 1.25 0.92 0.89 0.65 35.3 26.5 It is believed that tooth dentin and enamel consist of heterogeneous and anisotropic components [45,64]. Nevertheless, all tooth components and restorative materials in the present research were assumed to be isotropic, homogenous, and linearly elastic, following most of the FE studies [45,64,65]. It should also be noted that there are many other factors such as wet condition, luting procedure and cyclic loading that could affect the stress distribution. This said, extrapolating the results of the present study directly to clinical situations are difficult without considering these factors and further studies are needed. 5. Conclusion Within the limitations of this current study, the following conclusions could be drawn: Fig. 7. The principal stress distribution pattern of dentin in T12H1 model of PIC crown. Perhaps, a steeper preparation design (greater convergence angle) resulted in greater Tresca stress values. For the same reason, regarding models with PIC crowns, the FI values of adhesive in T20H1 and T20H2 were lower than that of the other models (Table 6), but not still failed. In realistic situation of tooth-to-tooth or food bolus-to-tooth contact, nonlinear analysis is considered to be a promising method to evaluate the stress and strain state within the tooth structure [25,26]. In this research, a hemispherical indenter was used to apply the load as an alternative to concentrated forces in order to avoid any undesirable stress distribution on the occlusal surface. Because concentrated forces often impose excessive stress around the loading point which is far from the real condition of tooth-totooth contact [26]. An increase in tooth preparation height accompanied a decrease in ceramic MPS value (and increase in compressive stress) on the occlusal surface, while MPS values increased in ceramic regions in interface with adhesive. These results are similar to behavior of a 3-point bending beam, where applying load on a thinner beam creates greater MPS in comparison with a thicker beam [63]. In addition, increasing MPS values in the ceramic at the adhesive interface increases the ceramic’s vulnerability to radial cracks developing. Furthermore, in the models with larger abutment and indeed thinner ceramic thickness, an appropriate ceramic material is expected to withstand more tensile stress (here LD). The maximum principal stress of ceramic at the adhesive interface under the lingual cusp was higher than the one under the buccal cusp. The ceramic volume under the buccal cusp is greater compared to the region under the lingual cusp. It could absorb more energy and consequently, minimize the stress at the adhesive interface.  The methodology used in the present study could be a good alternative when a restored tooth was being studied by FEM.  Tooth preparation height had a more appreciable effect on stress values than the convergence angle. The maximum principal stress on occlusal surface of the shorter preparation was greater than on the longer one.  Remained enamel was an important component to support the ceramic crown and that should not be neglected during FE modeling.  Convergence angle showed no appreciable effect on stress values of the ceramic crowns.  For the materials studied, clinicians should minimize occlusal reduction of the tooth to the extent possible within the choice of materials which in turn, reduces the maximum principal stress in occlusal surface of ceramic restoration. However, it should be noticed that in such cases, the maximum principal stress of the ceramic restoration in interface with adhesive increases, and therefore, a ceramic with higher flexural strength could be a more conservative choice. Acknowledgement The authors acknowledge a part of this study has been presented in FDI 2017 congress in Spain. References [1] Leung B.T.W., Tsoi JKH, Matinlinna JP, Pow EHN. Comparison of mechanical properties of three machinable ceramics with an experimental fluorophlogopite glass ceramic. J Prosthet Dent 2015;114:440–6. [2] Homaei E, Farhangdoost K, Akbari M. 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