A comparison of mvM stress of inlays, onlays and endocrowns made from various materials and their bonding with molars in a computer simulation of mastication – FEA



The purpose of the study was to compare the mvM stresses occurring in inlays, onlays and endocrowns made from different materials and their bonding with molars in a computer simulation of mastication.


The study was conducted using the finite elements method with contact elements. Sixteen 3D first molar models were created of a intact tooth – T; a tooth with a ceramic inlay – IN; a tooth with an onlay – ON; and a tooth with an endocrown – EN. The restorations were made of: Comp – resin nanoceramic; Hc – hybrid ceramic; Le – leucite ceramic; Dlit – lithium disilicate; and Zr – zirconia. Computer simulations of mastication were performed. The equivalent stresses according to the modified von Mises criterion (mvM) were calculated in model materials and contact stresses at the interface cement–dental tissue around the examined restorations.


The highest equivalent mvM stresses were concentrated in buccal margins of inlays. The mvM stresses recorded in onlays were 1.6–5 times lower than those found in inlays, while in endocrowns they were 2.3–6.5 times lower. Around the onlays and endocrowns, in tooth structures and luting cement, mvM stresses were significantly lower compared to teeth restored with inlays. The tensile and shear contact stresses between inlays and teeth were several times lower than under another restorations.

The highest stresses (58.5 MPa) occurred in the zirconia inlay. The stresses observed in the enamel of a tooth restored with an INZr inlay were half those noted in INComp, and a third of those observed in cement. Tensile contact stresses at the interface between the INZr inlay and dental tissue were 4.5 times lower than in the INComp, and the shear stresses were more than 7 times lower.


The highest values and unfavorable of stress levels occurred in teeth restored with inlays. Cavities MOD in molars should be reconstructed with cusp-covering restorations. The endocrown in molars should withstand physiological loading.

The higher the modulus of elasticity of the restoration material, the higher the stresses in the restorations, while the lower stresses were observed in the tooth structures, luting cement and at the interface between the restoration and the dental tissue. Ceramic restorations should provide better protection and marginal seal of the reconstructed tooth than composite ones.


One way of restoring extensive MOD cavities in teeth is through indirect composite and ceramic restorations made with CAD/CAM technology . Depending on the shape and size of the defect, they can be classified into inlays, onlays and endocrowns . An inlay reproduces the missing structures of the clinical crown in a tooth in which parts of its occlusal surface are still maintained. An onlay provides additional coverage for the entire occlusal surface including the cusps. Endocrowns are used to restore the significantly damaged crowns of posterior teeth, and, besides adhesion, their retention is based on their macro-mechanical attachment and adhesion in the tooth chamber . Research does not clearly show what shape of a restoration can have a positive impact on the fracture resistance of teeth. Some authors believe that restoring MOD defects in molars with restorations that cover the dental cusps provides greater fracture resistance than less invasive inlays . Other studies showed no differences in tooth strength between inlays and various types of onlays . On the other hand, a meta-analysis revealed that the fracture resistance of teeth decreases with the increasing size of the restoration: in teeth restored with inlays resistance was 1923 N, in the case of onlays – 1644 N, and in the case of overlays – 1383.6 N . This is confirmed by 4-year clinical observations, which shown that classic inlays and onlays placed on molars functioned effectively in 94.6% of cases, while extensive restorations in teeth with reduced tissue had a success rate of 92.1%, and endocrowns – 87.1%. However, other studies show that inlays had a 5-year survival rate of 90.89%, and onlays – 93.5% . The main reasons for failure were chipping or fracturing of the ceramic or tooth structure, and leakage around restorations resulting in caries or endodontic complications.

Modern indirect restorations based on CAD/CAM technology can be fabricated from new materials nanoceramic resin composites, hybrid ceramics, leucite ceramic, lithium silicate or disilicate ceramics, zirconia and transparent zirconia. These materials differ from each other in terms of their composition, structure and properties. Nanocomposites (e.g. Lava Ultimate, 3M/ESPE, St. Paul, MN, USA) are composed of 80% ceramic filler (69% SiO 2 , 31% ZrO 2 ) and 20% resins (Bis-GMA, UDMA, Bis-EMA, TEGDMA) . They have a low modulus of elasticity of 12 GPa and a flexural strength of 164 MPa . Hybrid ceramics (polymer infiltrated ceramic network – PICN) (e.g. Vita Enamic, Vita, Zahnfabrik, Bad Säckingen, Germany) consists of 86% ceramic mesh (feldspar and aluminum oxide), the free spaces of which are filled with UDMA and TEGDMA resin. Thanks to this connection, the material is three times more rigid than composites (a modulus of elasticity of 34 GPa) , although it has a comparable flexural strength of 181 MPa . Leucite ceramic (e.g. Empress CAD, Ivoclar, Vivadent AG, Schaan, Liechtenstein) consists of leucite crystals (35–50%) with a grain size of 1–3 μm embedded in amorphous silica. It has a modulus of elasticity of 65–69 GPa , and a fairly low flexural strength (147 GPa) . Lithium disilicate ceramics (e.g. e.max CAD, Ivoclar, Vivadent AG, Schaan, Liechtenstein) are in 60% longitudinal crystals embedded in glass. It has a Young’s modulus of 103 GPa and a flexural strength twice that of previous materials (357 MPa) . Yttria-stabilized zirconia ceramic 3Y-TZP (e.max ZirCAD, Ivoclar, Vivadent, Liechtenstein) consists of densely sintered ZrO 2 crystals approximately 0.5 μm in size. It is the most rigid ceramic (a modulus of elasticity of 205–210 GPa) and has the highest flexural strength, i.e. 887–1286 MPa . It exists in two varieties: 4Y-PSZ and 5Y-PSZ (4 or 5 mol% yttria-partially-stabilized zirconia), which contain a larger amount of optically isotropic cubic phase. The grains are on average the size of 0.95–1.33 μm. These materials are more translucent than 3Y-TZP, but have a lower strength, ranging between 593 MPa (5Y-PSZ) and 749 MPa (4Y-PSZ) . Compared to traditional leucite ceramics, zirconia, lithium disilicate, and new composites they have greater flexural strength and are more resistant to fatigue and aging during cyclic loading .

Teeth with restorations made of rigid lithium disilicate or yttrium-stabilized CAD/CAM zirconia-based ceramic exhibited higher fracture resistance than teeth restored with leucite CAD/CAM ceramic, regardless of the dimensions of the restoration . Some authors claim that ceramic restorations are more effective in stabilizing weakened tooth structures than those made of composites . However, a meta-analysis performed by Amesti-Garaizabal et al. produced opposite results. The fracture resistance of ceramic restorations was 1529.5 N, compared with 1600 N for composite resin, 2478.7 N for resin nanoceramic, and 2108 N for hybrid ceramic. The maximum fracture resistance for inlays was achieved with restorations made from resin nanoceramic; in the case of onlays, maximum fracture resistance was achieved with lithium disilicate ceramic; and in the case of overlays, with leucite-reinforced ceramic . A 10-year clinical observation period showed a 91% survival rate for ceramic inlays and onlays . At the same time, an endocrown fabricated from lithium–disilicate glass had survival and success rates of 99.0%, while the corresponding value for Polymer-Infiltrated Ceramic Network (PICN) was only 89.9% .

The lack of conclusive results prompted us to undertake our own study to answer the following questions: What shape should restorations take in large molar defects to ensure maximum strength and best seal during chewing? Which materials should be used for the fabrication of a crown to ensure it can cope with masticatory forces?

The aim of the study was to compare the equivalent mvM stress of inlays, onlays and endocrowns fabricated from different materials and their bonding with molars in a computer simulation of mastication.

The null hypothesis assumes that the mvM stress and bonding of restorations in teeth are not affected by the shape or material of the restoration.

Material and method

Creating a tooth model for FEA calculations

FEA was performed using a model of a first mandibular molar constructed beforehand . Maxillary and mandibular impressions (Polyvinylsiloxane Express– 3M/ESPE, St. Paul, MN, USA) were taken of a patient with normal occlusion. Segmented models were cast from Class 4 plaster (Girostone, Amann Girrbach GmbH, Pforzheim, Germany). Surface scans of the plaster model of the first right lower molar and the opposing first upper molar were performed with a Dental 3D Scanner D250 laser scanner (3ShapeA/S, Copenhagen, Denmark). Sets of point coordinates on the surfaces of the examined teeth were then entered in the finite element method (FEA) ANSYS 14 program (ANSYS version 14; ANSYS Inc, Canonsburg, USA). In the program pre-processor, selected points of these molar surfaces were connected together by means of curves on the frontal planes, at a distance of every 0.1 mm. These lines provided the basis for constructing models of an intact mandibular molar (model T) ( Fig. 1 a) .

Fig. 1
Models of the first mandibular molars with various restorations. (a) Tooth model, (b) tooth model with inlay, (c) tooth model with onlay, (d) tooth model with endocrown.

In addition, three segmented hard plaster models were cast from an impression of the lower arch. The plaster first molars were prepared for an inlay and then for an onlay. The prepared surfaces of these teeth were then scanned. The point coordinates on the surfaces of these teeth were entered into the ANSYS program. The surfaces of the prepared teeth were then reproduced, and these were subsequently used to dissect a model of the mandibular molar. To produce an endocrown, the model was cross-sected with a plane 1 mm above the CEJ and a 4 × 4 × 3 mm box was added. The solids cut out from the model were used to construct an inlay, onlay and endocrown surrounded by a 0.1 mm layer of cement. These structures were added to the models of prepared teeth. In this way we constructed an IN model for a tooth with an inlay ( Fig. 1 b); an ON model with an onlay ( Fig. 1 c); and an EN model with an endocrown ( Fig. 1 d). The scanned surface of the first maxillary molar were used for modeling a fragment of its crown ( Fig. 2 ).

Fig. 2
Simulation of mastication. (a) The initial phase of the masticatory cycle: first right molar of the mandible and a fragment of the crown of the opposing tooth in a lateral position, with a morsel between the teeth. (b) The closing phase of the masticatory cycle: first right molar of the mandible and a fragment of the crown of the opposing tooth in a central occlusion with a morsel between the teeth.

Material data

The tested restorations were fabricated from the following materials: resin nanoceramic – Comp., hybrid ceramic – Hc, leucite ceramic – Le, lithium disilicate ceramic – Dlit, and zirconia – Zr. All the restorations were bonded with tooth structures using resin luting cement. The modulus of elasticity values and Poisson’s coefficients were entered for enamel , dentin , composite , hybrid ceramic , leucite ceramic , lithium disilicate ceramic , 3Y-TZP ceramic , and composite cement . The bolus had the properties of a nut with a modulus of 21.57 MPa . It was assumed that the materials used in the model were elastic, homogeneous, and isotropic, but differed from one another in terms of their compressive and tensile strengths. Tensile and compressive strength values were determined for enamel , dentin , resin nanoceramic , hybrid ceramic , leucite ceramic , lithium disilicate ceramic , 3Y-TZP ceramic , and cement . The material data are presented in Table 1 .

Table 1
Data of materials used in models of molars with ceramic inlays, onlays and endocrown made of various materials.
Material Modulus of elasticity [GPa] Poisson ratio Ultimate tensile strength [MPa] Ultimate compressive strength [MPa]
Enamel 84.1 0.33 11.5 384
Dentin 18.6 0.31 105.5 297
Resin nanoceramic 12.1 0.35 100 516
Hybrid ceramic 34.5 0.24 100 370
Leucite ceramic 65.5 0.19 48.8 162.9
Lithium disilicate ceramic 103 0.25 173 448
Zirconia ceramic 210 0.24 745 904
Resin cement 8.3 0.35 45 178

Division of the models into finite elements

For calculation purposes, each tooth model was divided into 10-node structural solid elements. Pairs of contact elements were applied to the occlusal surfaces of the examined teeth and to the bolus. The friction coefficient on the contact surfaces was assumed to be 0.2 . Pairs of connected contact elements were applied at the cement-tissue interface around the ceramic restorations. In tooth model A, a total of 16,421 solid elements connected together in nearly 24,522 nodes were used, in model B – 57,842 elements connected together in 78,698 nodes, and in model C – 71,315 elements connected together in 96,744 nodes, in model D – 80,036 elements connected together in 107,814 nodes.

Fixation of models and loads

Models of antagonist teeth were spatially positioned in occlusion using reference points obtained from a lateral scan. They were moved away from each other vertically by 3 mm and shifted horizontally in a buccal direction by 1 mm and in a protrusive direction by 0.2 mm. A 1 mm thick bolus was inserted between the opposing teeth. In this way, 3D models of opposing molars were created during the initial closing phase of the chewing cycle ( Fig. 2 a).

The models were fixed in nodes on the upper surface of the fragment of maxillary tooth crown. The degrees of freedom were also taken away in the nodes on the lower surface of the mandibular tooth model. The closing phase of the chewing cycle was simulated. The mandibular molar was displaced vertically upwards and at the same time shifted medially and distally toward the maxillary tooth until maximum intercuspation was achieved ( Fig. 2 b) . The displacement of nodes on the lower surface of the lower tooth model was controlled. Vertical displacements were chosen so that the maximum reaction force in a vertical direction was 100 N for each model . The buccal cusps of the lower tooth slid down on the bolus along the occlusal surfaces of the upper teeth, thereby crushing the bolus.


The pressure on the occlusal surface of the first mandibular molar was investigated. Equivalent stress (mvM) of the modified von Mises failure criterion in the materials of tooth models was calculated during a simulation of mastication . This criterion takes into account the different tensile and compressive strengths of materials. The maximum values of mvM stresses for enamel, dentin, composites, ceramics and cement in the models during the clenching phase of the chewing cycle are summarized in Table 2 , and their distributions are presented in the maps. Compressive, tensile and shear contact stresses around restorations, between cement and the surrounding tissue were calculated. They are presented in Table 3 and graphically depicted as maps on the bonding surfaces.

Table 2
Maximal modified von Mises stresses (mvM) in teeth models with inlay, onlay, endocrowns made of various materials (MPa).
Model Materials Comosite Hybrid ceramic Leucite ceramic Litium disilicate ceramic Zirconia
Molar with inlay – IN Inlay 51.9 38.0 38.6 43.1 58.5
Enamel 9.8 6.7 5.7 5.3 4.8
Dentin 3.0 3.0 3.0 3.0 3.0
Cement 14.9 6.2 3.5 3.2 4.4
Molar with onlay – ON Onlay 9.7 17.7 22.9 25.9 28.7
Enamel 6.8 5.4 4.6 4.1 3.6
Dentin 3.5 3.3 3.1 3.0 2.9
Cement 8.1 4.8 3.5 2.7 2.4
Molar with endocrown –EN Endocrown 8.0 13.2 14.5 18.7 38.6
Enamel 7.4 5.7 5.2 5.0 4.9
Dentin 3.3 3.5 3.7 3.8 3.9
Cement 2.5 2.3 2.7 2.5 1.7
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Aug 9, 2020 | Posted by in Dental Materials | Comments Off on A comparison of mvM stress of inlays, onlays and endocrowns made from various materials and their bonding with molars in a computer simulation of mastication – FEA
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