A comparison of stresses in molar teeth restored with inlays and direct restorations, including polymerization shrinkage of composite resin and tooth loading during mastication


Polymerization shrinkage of composites is one of the main causes of leakage around dental restorations. Despite the large numbers of studies there is no consensus, what kind of teeth reconstruction—direct or indirect composite restorations are the most beneficial and the most durable.


The aim was to compare equivalent stresses and contact adhesive stresses in molar teeth with class II MOD cavities, which were restored with inlays and direct restorations (taking into account polymerization shrinkage of composite resin) during simulated mastication.


The study was conducted using the finite elements method with the application of contact elements. Three 3D models of first molars were created: model A was an intact tooth; model B—a tooth with a composite inlay, and model C—a tooth with a direct composite restoration. Polymerization linear shrinkage 0.7% of a direct composite restoration and resin luting cement was simulated (load 1). A computer simulation of mastication was performed (load 2). In these 2 situations, equivalent stresses according to the modified von Mises criterion (mvM) in the materials of mandibular first molar models with different restorations were calculated and compared. Contact stresses in the luting cement–tooth tissue adhesive interface around the restorations were also assessed and analyzed.


Equivalent stresses in a tooth with a direct composite restoration (the entire volume of which was affected by polymerization shrinkage) were many times higher than in the tooth restored with a composite inlay (where shrinkage was present only in a thin layer of the luting cement). In dentin and enamel the stress values were 8–14 times higher, and were 13 times higher in the direct restoration than in the inlay. Likewise, contact stresses in the adhesive bond around the direct restoration were 6.5–7.7 times higher compared to an extraorally cured restoration. In the masticatory simulation, shear contact stresses in the adhesive bond around the direct composite restoration reached the highest values 32.8 MPa and significantly exceeded the shear strength of the connection between the resin luting cement and the tooth structure.


Equivalent stresses in the tooth structures restored with inlays and in the restoration material itself and contact stresses at the tooth–luting cement adhesive interface are many times lower compared to teeth with direct composite restorations. Teeth with indirect restorations are potentially less susceptible to damage compared to those with direct restorations. Composite inlays also ensure a better seal compared to direct restorations. Polymerization shrinkage determines stress levels in teeth with direct restorations, while its impact on adhesion in indirectly restored teeth is insignificant.


Composite resins have found a variety of applications in modern dentistry, including as a means of restoring tooth cavities and cementing restorations. The advantages of composite resins include the following: aesthetics—these materials have a transparency and colour similar to tooth tissue, mechanical properties comparable to dentin , they attach well to hard tooth tissue with the use of bonding agents, and are easy to work with. Their disadvantages include: considerable polymerization shrinkage (the mean linear polymerization shrinkage of Bis-GMA-based composite resins is 0.3–1.5% , while their volumetric shrinkage is 1.5–3.5% , 2–6 times higher thermal expansion properties than enamel and dentin and high occlusal wear (12–50 μm/year).

The seal and longevity of a composite tooth restoration is determined by its dimensions, shape, location, C-factor and the type of tooth and its load, among other factors. Large class II MOD direct composite restorations in molars appeared to be the least durable due to the high loads exerted in this area and the extensiveness of the restoration . The seal also greatly depends on the chemical composition and properties of the composite material (including composite shrinkage), type of bonding systems used and its bond strength in relation to tooth tissue . If stresses in the adhesive connection exceed the tissue bonding strength, the restoration becomes detached from its base and marginal seal is lost . This results in a gap between the restoration and tooth structures as well as in microleakage . As a consequence, postoperative hypersensitivity may develop, while secondary caries, marginal defects and fracturing of restorations and teeth can occur in the long-term .

Attempts have been made to reduce polymerization shrinkage in composite resins by changing the composition of the material, e.g. by incorporating more filler particles , using alternative resins, e.g. with a high molecular weight, ormocers or siloranes . There have also been clinical attempts to reduce shrinkage by using various cavity filling techniques, e.g. the oblique incremental filling technique . Studies have shown that curing with high-intensity light increases polymerization shrinkage . Hence, “soft start” (delayed curing) or ramped curing techniques are recommended . Unfortunately, neither of these methods have eliminated polymerization shrinkage and its adverse consequences completely.

Another solution is to employ an indirect method instead of direct restorations. Polymerization of composite inlays occurs not only as an effect of light-curing in the oral cavity, but also in a lab oven, where the material is exposed to light, heat and pressure . This leads to significantly higher monomer–polymer conversion rates (in direct restorations the conversion rate is approximately 28–73% . As a result, a composite resin in an inlay has improved mechanical properties: it has a higher Young’s modulus and flexural strength, and is harder and more wear resistant . However, the biggest advantage of the indirect method is that polymerization shrinkage of the composite occurs outside the cavity. Inlays are cemented in the tooth with resin luting cement.

Despite the large number of studies there is no consensus, what kind of teeth reconstruction is the most beneficial and the most durable. Some researches prove higher fractures resistance teeth with composite resin inlays in comparison to direct composite restorations . Another one maintains that teeth with indirect restorations are less susceptible to damage and generate higher stresses during curing than those restored with direct filings (particularly along the interface between the cement and the dentin) .

The aim was to compare equivalent stresses and contact adhesive stresses in cement–tooth interface, in molar teeth with class II MOD cavities, which were restored with inlays and direct restorations (taking into account polymerization shrinkage of composite resin) during simulated mastication.

Material and methods

Generation of tooth models for FEA calculations

Upper and lower impressions of a patient with normal occlusion were taken using a polyvinyl siloxane material (Express, 3M/ESPE, St. Paul, MN, USA). Occlusal registrations in the central and lateral positions of the mandible with wax were recorded (Aluwax, Aluwax Dental Product Co, Allendale, MI, USA). Upper and lower casts of class IV stone were prepared (Girostone, Amann Girrbach GmbH, Pforzheim, Germany). A Dental 3D Scanner D250 (3ShapeA/S, Copenhagen, Denmark) was used to scan the surfaces of the two die stone teeth: the lower right first molar and the opposing, upper first molar. These scans were then processed with software (3Shape Dental Designer CAD). Files with PTS extension, containing coordinates of the points on the surfaces of the analyzed teeth, were loaded into FEA software—ANSYS 14 (ANSYS version 14, ANSYS Inc., Canonsburg, PA, USA) . In the preprocessor, selected points on these surfaces were connected with splines on the sagittal planes every 0.1 mm. On this basis the occlusal surfaces of the upper and lower tooth models were reconstructed. A CT scan was made of the lower first molar of the same patient. CT scans provided the base for obtaining the circumferential points of the external tooth structure, along the enamel–dentin–pulp junction in horizontal layers, every 1 mm. These points were used to reconstruct the cross-section of the tooth, including the enamel, dentin and pulp chamber. Connecting the cross-sections and the occlusal surface made it possible to create the tooth model of intact mandibular molar (model A). The tooth model was situated in the coordinate system in such a way that the X -axis indicated the mesial surface of the tooth, the Z -axis the buccal surface, and the Y -axis was oriented upwards. The mandibular molar tooth is anatomically inclined 15 degrees lingually and 8 degrees anteriorly to vertical line ( Fig. 1 a ) . Digital mandibular molar was analogously bended.

Fig. 1
Tooth models subjected to FEA. (a) Model A—mandibular first molar. (b) Model B—mandibular first molar restored with composite resin inlay. (c) Model C—mandibular first molar restored with direct composite resin restoration.

The die stone first molar in the mandibular model was prepared for a composite class II MOD inlay. The prepared tooth was scanned and coordinates of the surface points were loaded into the finite element analysis software (ANSYS). The preparation surface was reconstructed and then used to cut model A. The resulting solids were used to generate a direct restoration and inlay surrounded by a layer of luting cement with 0.1 mm thickness. These structures were added to model A. In this way, tooth model B with an inlay ( Fig. 1 b) and model C with a direct restoration ( Fig. 1 c) were created.

Material data

The direct restorations and inlays were made of a Filtek Z250 composite resin (3M/ESPE, St. Paul, MN, USA). The inlays were bonded to tooth structures using RelyX Unicem resin luting cement (3M/ESPE, St. Paul, MN, USA). The values for Young’s modulus and Poisson’s ratio were entered for the enamel , dentin , periodontal ligament composite resin , and resin luting cement . The data are listed in Table 1 . The test bolus had nut-like properties with a Young’s modulus of 21.57 MPa . The materials used in the models were elastic, homogeneous and isotropic, but had different compressive and tensile strengths ( Table 1 ). The following tensile and compressive strength values were adopted: for enamel 11.5 MPa , 384 MPa ; for dentin 105.5 MPa , 297 MPa ; composite resin 45.1 MPa , 227 MPa , and for cement 51.6 MPa , 145 MPa .

Table 1
Data of materials used in models of molars teeth.
Material Modulus of elasticity [GPa] Poisson ratio Tensile strength [MPa] Compressive strength [MPa]
Enamel 84.1 0.33 11.5 384
Dentin 18.6 0.31 105.5 297
Composite 5.6 0.24 45.1 227
Luting resin cement 5.2 0.24 51.6 145

Model division into finite elements

For calculation purposes, each tooth model was divided into a structural solid with 10-node elements (Solid 187). A total of 57,842 elements joined in 78,698 nodes were used in the models. Pairs of contact elements were used on the surfaces of the studied teeth and boluses. The coefficient of friction between the contact surfaces was assumed to be 0.2 . The pairs of bonded contact elements Targe 170 and Conta 174 were used at the cement–tissue junction around the studied restorations.

Fixations and loading of models

Stress analysis was performed on the coronal parts of the tooth models, which were fixed on the cutting surfaces below the cervices. Polymerization shrinkage of the resin luting cement around the inlay (model B) and shrinkage of the direct composite restoration (model C) (load 1) were then modelled. According to Lee et al. and Kwon et al., polymerization shrinkage for Filtek Z250 is 0.70–0.75% . Volumetric shrinkage of this material amounts to 2.26–2.75% . Analogous thermal shrinkage was used in the ANSYS software . The linear thermal expansion coefficient was established at 0.007 , and relative deformation was calculated according to the following formula:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='εshrinkage=εthermal=αΔTwhereα=0.007(1/°C),ΔT=−1°C’>εshrinkage=εthermal=αΔTwhereα=0.007(1/°C),ΔT=1°Cεshrinkage=εthermal=αΔTwhereα=0.007(1/°C),ΔT=−1°C
ε shrinkage = ε thermal = α Δ T where α = 0.007 ( 1 / ° C ) , Δ T = − 1 ° C

In addition, tooth models were loaded with occlusal forces while a bolus was chewed (load 2). The lower and upper tooth models were positioned in the lateral occlusion using reference points from scans of the occlusal record. A 1-mm-thick bolus was inserted between them. A computer simulation was then made of the occlusal phase of mastication. The lower molar was moved vertically upwards and at the same time medially toward the upper tooth until maximum intercuspation was achieved, according to the occlusal record ( Fig. 2 a ) . The displacement of nodes on the lower surface of this tooth was manipulated. The vertical movement was chosen to produce a maximum 100 N reaction force in the Y direction for each model . The buccal cusps of the lower tooth were glided through the boluses along the occlusal surfaces of the upper teeth, thereby grinding the bolus . The highest pressure was exerted on the occlusal surfaces of studied mandibular first molar in the final closing phase of mastication, especially on functional cusps ( Fig. 2 b).

Fig. 2
Model of mandibular first molar and fragment of crown of opposing maxillary first molar during closing phase of mastication cycle. Food morsel is placed between the teeth. (a) Displacement of model (mm). (b) Pressure exerted on occlusal surface (MPa)

Stress calculations were conducted for the following five cases:

  • tooth model A during simulated mastication (load 2)

  • tooth model B1 with a composite inlay and luting cement undergoing polymerization shrinkage (load 1)

  • tooth model C1 with a direct composite restoration undergoing polymerization shrinkage (load 1)

  • tooth model B2 with a composite inlay and luting cement undergoing polymerization shrinkage, additionally loaded with masticatory forces (load 1 and 2)

  • tooth model C2 with a direct composite restoration undergoing polymerization shrinkage, additionally loaded with masticatory forces (load 1 and 2)


FEA contact simulation is a nonlinear analysis that requires the load to be applied in a number of steps. Automatic time stepping was applied in the ANSYS software. The components of stresses were calculated during simulation of polymerization shrinkage (load 1), and later additionally during the closing phase of the masticatory cycle (load 2). The tooth structures and composites are characterized by different tensile and compressive strengths ( Table 1 ). One criterion used to evaluate the strength of materials under compound stress states is the modified von Mises (mvM) failure criterion . According to this criterion, the material will fail when the equivalent mvM stress values exceed the tensile strength of the material. The calculation results are presented in the form of maps of equivalent mvM stresses in enamel, dentin, composite resin and luting cement in the molar tooth models. The maximum stress values in each model were analyzed, compared to one another and to the respective material tensile strength.

Compressive, tensile, and shear contact stresses at the adhesive interface of luting cement–tooth tissue (surrounding the inlays and direct restorations) were also calculated after polymerization shrinkage and during masticatory simulation. They were graphically depicted as maps on the contact surfaces between the restorations and tooth structures in the models. The maximum tensile and shear contact stresses values at the cement–tooth adhesive interface around restorations were compared with the tensile and shear bond strength of luting cement and composite to enamel and dentin. The areas where the contact stresses will be exceed the bond strength of composite resin to hard tooth tissues were exposed to debonding.

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Nov 23, 2017 | Posted by in Dental Materials | Comments Off on A comparison of stresses in molar teeth restored with inlays and direct restorations, including polymerization shrinkage of composite resin and tooth loading during mastication
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