Stress distributceramic and rerestorations: a

Pietro Ausielloa,*, San

aDepartment of Cariology, SchPoliclinico Edificio 14, Via PanbUniversity of Amsterdam, AmcU ter Den

Re eceived i

Stress-distributionsimulation;

upper premolar were produced. Model A represented a glassceramic inlay incombination with an adhesive and a high Youngs modulus resin-cement. Model B

conducted.

composite inlays.

Dental Materials (2004) 20, 862872

www.intl.elsevierhealth.com/journals/demaResults: Complex biomechanical behavior of the restored teeth becameapparent, arising from the effects of the axial and lateral components of theconstant occlusal vertical loading. In the ceramic-inlay models, the greatest vonMises stress was observed on the lateral walls, vestibular and lingual, of the cavity.Indirect resin-composite inlays performed better in terms of stress dissipation.Glassceramic inlays transferred stresses to the dental walls and, depending on itsrigidity, to the resin-cement and the adhesive layers. For high cement layermodulus values, the ceramic restorations were not able to redistribute the stressesproperly into the cavity. However, stress-redistribution did occur with the resin-Class II MOD inlayrestorations;

Resin cements

represented the same glassceramic inlay in combination with the same adhesive anda low Youngs modulus resin-cement. Model C represented a heat-cured resin-composite inlay in combination with the same adhesive and the same low Youngsmodulus resin cement. Occlusal vertical loading of 400 N was simulated on the FEmodels of the restored teeth. Ansyse FE software was used to compute the local vonMises stresses for each of the models and to compare the observed maximumintensities and distributions. Experimental validation of the FE models wasniversity of Manches

ceived 4 November 2003; r

KEYWORDSDental materials;3D finite elements

analysis;Occlusal loading;ions in adhesively cementedsin-composite Class II inlay3D-FEA study

dro Rengoa, Carel L. Davidsonb, David C. Wattsc

ool of Dentistry, University of Naples Federico II,sini 5, Naples 80131, Italysterdam, The Netherlandstal School, Manchester, UK

n revised form 13 April 2004; accepted 11 May 2004

Summary Objectives: The purpose of this study was to investigate the effect ofdifferences in the resin-cement elastic modulus on stress-transmission to ceramic orresin-based composite inlay-restored Class II MOD cavities during vertical occlusalloading.

Methods: Three finite-element (FE) models of Class II MOD cavity restorations in an0109-5641/$ - see front matter Q 2004 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: C39-81-7462089; fax: C39-81-7462197.E-mail address: pietausi@unina.it (P. Ausiello).

Significance: Application of low modulus luting and restorative materials domainital

also from mastication. Therefore, marginal andinternal adaptation of composishould also be studied after l[10]. As a variety of mate

cement properties and on its mechanical behavior[14]. Not only the shrinkage-strain, but the shrink-

at 0.33 mm increments by vertical and horizontalscanning. Of these profiles, only 34 were selected,

Ceramic and composite inlay Class II behavior 863te and ceramic inlaysoading and fatiguingrials with diverse

17 vertical and 17 horizontal, at 2 mm increments,for use in the external shape definition of the solid-tooth model. Literature data on the toothto stresses that originate from curing shrinkage, but

dentistry [8]. The cement layer is not only subject For the crown, over 200 profiles were generatedpartially absorb defortransmitted to the remaQ 2004 Academy of Den

Introduction

Resin-composites are limited for direct restorationof the larger stress-bearing posterior Class IIcavities, on account of polymerization shrinkageeffects and some limitations in mechanical proper-ties. Thermally post-cured resin-composite inlays,however, are recommended in preference [1].Thermal post-curing does improve the mechanicalqualities of composites [2,3]. Another advantage ofresin-composite inlays, instead of direct place-ment, is that effects from the bulk curing-shrinkagecan be evaded.

As a further option for restoring large Class IIMOD restorations, strong ceramics are now avail-able that can function properly without metalsupport [4]. For both ceramic and compositematerials, adhesive cementation is imperative toensure reliable coherence of inlay and toothstructure. Moreover, the cementation with (dual-cure) cements has to be accompanied by appli-cation of dentin bonding agents [5]. It is nowcustomary to use resin-based luting cements incombination with dentin bonding agents for com-posite and all-ceramic inlay restorations to enhance(adhesive) retention and survival rates [6,7].

Unfortunately, luting also induces a significantadverse effect. Luting creates a long and narrowrestoration, analogous to a Class I, made inmaterials that are principally inferior to the usualresin-composite restorative materials. This meansthat a weaker and higher shrinking material isinescapably present, that will set, moreover, in amost unfavorable configuration (high C-value)within the restored tooth [9]. Yet, with respect towall-to-wall adaptation, adhesively luted resin-composite inlays score slightly better than directcomposite restorations, whilst ceramic-inlays per-form as well as cast-gold inlays [4].

Notwithstanding their widespread application,marginal integrity of tooth-colored direct or indir-ect restorations remains a major problem in todaysage-stress magnitude and kinetics [15], the Youngsmodulus and the thickness of the cement determinethe totality of the developing stresses [16].

Ausiello et al. [17] showed, by means of a 3Dfinite element analysis (FEA) model analysis, theinfluence of occlusal loading and polymerizationshrinkage-strain on the stress-distribution in anadhesive Class II MOD direct restoration for resin-composites of different elastic modulus. Also theinfluence of the adhesive-layer thickness on stress-distribution was illustrated by 3D FEA [18].

The aim of the present study was to analyze by3D FEA the stress-distribution in all materialsinvolved in adhesively luted Class II MOD inlayrestorations, of both ceramic and resin-compositetypes.

Materials and methods

Finite element models

A 3D model of a human upper premolar, as used in aprevious study [18] was reused for this study. It wasrealized by digitizing a plaster human upper-premolar model on the scale of one to five with alaser scanner (Cyber-ware). Crown and roots wereconstructed in two different phases and sub-sequently assembled.tions under loading and limit the stress intensity,ng tooth structures.Materials. Published by Elsevier Ltd. All rights reserved.

mechanical properties are involved in inlay designand placement, analysis of the wall-to-wall integ-rity of inlay-restored teeth requires that attentionbe given to the elastic properties of the variousmaterials at the interfaces. For instance, it hasbeen demonstrated that incorporation of someelasticity (lining) to the restoration may decreaseor even prevent interfacial separation [1113].However, particularly the fragile ceramic-inlaysstill require rigid support. In indirect adhesive ClassII inlays, leakage often depends on the resin-

morphology for the definition of the dentine andenamel volumes [20] were used. The model datawere assembled in a 3D wire-frame structure bymeans of a 3D CAD (Autocad 12, Autodesk, Inc.,Neuchatel, Switzerland, 1992). The 3D curves wereexported into Pro-Engineer 16.0 (Parametric Tech-nology Co., Waltham, MA, USA, 1994), where a solidmodel was generated by fitting the horizontal andvertical profiles. The model was cut in the cervicalarea to obtain the final crown.

The roots were modeled by their mesial-distaland buccal-lingual representations taken fromliterature. The two representations were scannedand eight vertical profiles were generated imitatingthe scanned images. The roots were constructed byfitting the vertical profiles. The pulp region wasobtained in an analogous way and subtracted fromthe roots. The crown and the roots, with the pulpchamber, were assembled in the final model.

A parametric cutting plane was chosen togenerate different cavities and MOD preparations.

Different material properties were now assignedto the elements, according to the volume defi-nition. In particular, in the previous study, theadhesive layer was modeled in the FEM programusing spring elements connecting the nodes fromthe cavity wall of the natural tooth with those ofthe composite restoration [18]. In the presentstudy, technical enhancements in the finiteelement model generation were used to increasethe structural relevance of the model itself.

The modeling of the adhesive area in the Class IIMOD preparation was differently realized. In thiscase, where an indirect Class II MOD restoration-type was simulated, one part of the adhesive areawas modeled to be the adhesive layer, contactingthe dental walls. The other part was modeled to bethe resin luting cement, contacting from one sidethis adhesive layer and from the other side the

P. Ausiello et al.864In Fig. 1, the Class II MOD is shown (3.5 mm occlusalwidth). The cavity design was characterized by flatfloor and sharp internal line angles. No bevel wasconsidered at the proximal and occlusal margins.The preparation derived was flat from proximal toproximal surface.

The solid model was transferred into a FEAprogram (ANSYS Rel. 6.0, ANSYS, Inc., Houston,TX, USA, 1994) where a 3D mesh was created. In theprevious work [18], we explained the volumes thatwere redefined and meshed with 8-node-brick and4-node-tetrahedral elements, resulting in 7282elements (3376 hexahedral and 3906 tetrahedralshape elements) and 5236 nodal structures.

Figure 1 Finite element model of Class II MOD indirectrestoration of an upper premolar with particulars relativeto the shell modeling of the adhesive resin bonding and ofthe cement layers.filling material (Fig. 2).The new Class II MOD FE model used a different

element mesh-size (the size of all the elements wasreduced to obtain more detailed analysis results)and a different methodology to simulate the resinbonding and the luting cement layers. To investi-gate the strain-status of the total adhesive areaunder occlusal vertical loading simulation, shellelements (with membrane behavior) wereemployed both for the adhesive layer and for theluting cement layer (Fig. 1), instead of the springelements used previously [18].

The volumes were redefined and meshed with8-node brick and 4-node tetrahedral elements,resulting in a 27,140-element and 18,244-nodestructure, for a total solid elements number of24,818. In particular, 1160 shell membraneelements were used (Fig. 2). In Ansys 6.0 softwarethese elements are called shell 41 and they are 3Dcharacterized for each of the 4 nodes of the single

Figure 2 Finite elements models of the cement andadhesive layers.

element. Because of their low-thickness, they do

loading was to provide both a compressive load to

The simplest approximation to the probable natureof occlusal loading is where forces to the teeth areapplied statically and vertically. In all the FEmodels investigated here, the external rootsnodes were constrained in all the spatial directions.Adhesive mechanical properties are listed in Table 2for all the restored tooth models.

The compression test with a 400 N occlusal loadwas conducted. The loading cylinder was modeled

Table 1 Rigidity comparison of the systems.

ModelG-lC

ModelG-hC

Model C Soundtooth

%RCPA 4.29 5.00 K0.54 0.00%RCPL 8.60 8.60 K2.10 0.00

Ceramic and composite inlay Class II behavior 865the system and also displacement of the cusps.The FE analysis performed was linear and static.

It used the over-position effect principle tonot show flexural deformation. In this way, it waspossible to better simulate the mechanical behaviorof these two different layers.

Experimental model validation

To validate this new Class II MOD FEM model,compression loading measurements were per-formed on sets of differently restored teeth untilfracture of the samples. These were the Class IIMOD designs, corresponding to Models A and C,described below. Ten caries-free human upperpremolars were used for each test group. Class IIMOD cavities were prepared with a diamond bur athigh speed under water coolant. Axial and gingivalwalls were cut non-retentively, at approximately1008 angles. No bevels were prepared at the cavo-surface enamel angles. For the Class II MODrestoration, a heat-cured resin-composite with aYoungs modulus of about 50 MPa (Gradia, GC,Japan) was used. Unifil Bond adhesive (GC, Japan)with a Youngs modulus of 4.5 MPa was applied onthe cavity walls. Unifil Flow (GC, Japan) with aYoungs modulus of 9.6 MPa was used as resin lutingmaterial.

The samples were inserted, as far as thecementumenamel junction, into steel cylindricalrings with the apical root area in contact with thesteel-ring floor. Subsequently, spaces betweenroots and steel walls were filled with rigid resin-composite, so that only material deformationwithin the tooth would be measurable. The test-rings were clamped to the universal testing machineand loading was applied vertically via a 6 mmdiameter steel cylinder, with the axis normal tothe tooth axis. To simulate one major occlusalforce, a 1 mm/min compression rate was used. Thevertical displacement and the axial load wererecorded until each restored tooth fractured. Thisloading situation was also simulated using the FEanalysis, generating closely matched results(Graph 1).

An important parameter to be considered wasthe rigidity of the restored teeth, expressed underthe loading conditions used in this analysis. Twocomponents of rigidity were considered: axial andlateral. Axial rigidity directly measures the resist-ance to compressive forces. Lateral rigiditymeasures cuspal-displacement under flexural load-ing. Thus, the effect of the applied masticatorydetermine the axial rigidity comparative par-ameter (%RCPA) and lateral rigidity comparativeparameter (%RCPL). They represent, in percentage,the perceived rigidity variation of a system withrespect to an other reference rigidity. If they arepositive it means that the test system is more rigidthan reference system. In formulas:

%RCPA Z 1 Kaxial movementperceivedaxial movementreference

!100

%RCPL Z 1Klateralmovementperceivedlateralmovementreference

!10

The sound tooth has been chosen as a referencemodel in numerical calculations [20]. Results areshown in Table 1.

Numerical simulation

Graph 1 Validation data: showing the theoretical plot,determined numerically, and the experimental plot ofaxial load versus displacement.

as a 3D elastic beam (Fig. 3). End rotations were notconstrained. The common end was displaced in thecentral position of the loading cylinder section inthe experimental test. The load was applied on the

cocoMo

the luting cement and the adhesive are positioned

Results

with parpresentewhich weMises sh

utilize ashould bessential

Table 2 Materials properties.

Material Elasticmodulus,E (GPa)

Poissonratio

Thickness,T (mm)

*Enamel 48 0.23Dentine 18 0.2Composite 50Ceramic 90Cement hm 10 70Cement lm 6 70Adhesive 4.5 10

*Verluis, 1996 [20]. Co., data.

P. Ausiello et al.866Thus, all materials were considered elasticthroughout the entire deformation, which is areasonable assumption for brittle materials innon-failure conditions.

Dentin is an elastic and isotropic material. Enamel was treated as mechanically homo-

geneous and isotropic, as in Refs. [19,20].

In Fig. 2, the different thicknesses of the twointerfacial layers is shown. The elements simulatingFigmonitely rigid compared to the tooth. Resin-mposite support was not modeled and it wasnsidered to be as rigid as the loading system.reover, the following assumptions were made:

A static linear numerical analysis was performed.infi

betooth at two points (Fig. 3) through the beamselements on the cusps (red areas). The resultingforce F crossing the central position of the loadingcylinder section was 400 N (Fig. 3, red arrow). The

am elastic properties were treated as beingan octah

compressive or shear stress. However, other types

ure 3 The model structure is blocked avoidingvement in the three directions of the space.of output from most FE programs can provide suchinformation.

Figs. 46 show the varying biomechanics arisingfrom the differing rigidity of the three models: A, Band C. These figures show, respectively, stressescomputed: at the surface of each model (Fig. 4ac),within each model cavity preparation (Fig. 5ac),within each MOD restoration (Fig. 5df) and (inFig. 6) from the interfacial areas (adhesive layerCresin-cement layer) between the inlay restorationdecodedfalse-color non-linear scale for stress. Ite understood that von Mises stress isly an aggregate stress, sometimes termededral stress. As such, it cannot be directlyinto specific contributions from tensile,outcometicular stress behavior. The results ared in terms of von Mises stress maps in MPa,re computed within Ansys using the von

ear-strain-energy failure criterion, as anof the 400 N occlusal loading. The figuresInspection of the results revealed critical zonesIn all the combinations, one resin bonding systemwas considered. Physical properties of the usedmaterials are presented in Table 2.between the tooth and the filling material. Wehypothesize the perfect and absolute bondingbetween the two materials. In the FE analysisdifferent conditions were simulated, modifying thethickness of the cement, not varying the adhesiveresin bonding one, and including different fillingmaterials properties (Fig. 2). Three differentmodels of Class II MOD inlay restorations wereconsidered in order to simulate three differentclinical indirect restorations types.

Model A (G-hC, Glass-core ceramic with highmodulus Cement), in which an highmodulus glassceramic filling materialwas considered in combination with anhigh modulus cement;

Model B (G-lC, Glass-core ceramic with low mod-ulus Cement), in which an high modulusglassceramic filling material was con-sidered in combination with a low moduluscement;

Model C (Composite restoration), in which a heat-cured resin-composite inlay was con-sidered in combination with a low moduluscement.

Ceramic and composite inlay Class II behavior 867and the cavity preparation. In these interfacialareas, the biomechanical differences wereespecially critical.

Experimental and theoretical validation curvesare compared in Graph 1. The two similar stressstrain behaviors gave good support to the validity ofthe model. Even the extreme (high strain) proper-ties could be rather well approximated by thetheoretical curve. The experimental curve shows amild non-linear behavior near to the origin and alinear behavior thereafter. This apparent non-linearity was not due to a real material orgeometrical non-linearity but to the initial systemassessment that included effects due to contact andsliding. These phenomena were unimportant in theFE model validation.

The glassceramic-restored teeth, respectivelycemented with a high (10 GPa) and low (6 GPa)

Figure 4 (a) von Mises stress-distribution of Model A (G-hC).Mises stress-distribution of Model C.modulus cement material (Models A and B; Fig. 4aand b) may be compared with the behavior shownin Fig. 4c of the composite-restored tooth (ModelC), luted with the low modulus cement. Thehighest stress values of about 400500 MPa for allthree models were concentrated on the cuspalloading points. At the center of the occlusalsurface, for Models A and B, a stress value of100500 MPa was computed while for Model C itwas generally much lower, ranging from 40 to100 MPa. All the tooth models were low-stressedmesial-distally, with values of only 1015 MPa. Onthe vestibular and lingual sides, depending on thedisplacement of cusps, stresses appeared higher,about 2040 MPa.

In Fig. 5ac, analysis was conducted within thecavity preparation, while the filling material wasextracted from the cavity itself. This was possible

(b) von Mises stress-distribution of Model B (G-lC). (c) von

because of the CAD/FE model configuration. Stres-ses were particularly intense in Models A and B(1040 MPa) compared with Model C (15 MPa),specifically localized on the vestibular and lingualcavity walls of Models A and B (Fig. 5a and b).In Model C, a lower modulus (50 GPa) heat-curedcomposite resin was simulated.

In Fig. 5df is displayed the stress behavior withinthe core of the restoration of Models AC. Slightdifferences are evident between the ceramicrestorations of Models A and B, where von Misesstress values appear elevated but similar, irrespec-tive of the modulus of the cement material used inthe two simulations. Stress is concentrated in thecore of the restoration, extending to the vestibularand lingual sides of the restoration itself and totallytransmitted to the cavity walls, as already shown inFig. 5a and b.

In Fig. 5f, by contrast, where lower modulus(50 GPa) resin-composite was used for restoration,stress gradients from the internal area to the cavitywalls were lower, matching the distribution seen inFig. 5c.

In Fig. 6 are shown for the three models the stress-distributions, as successive pairs, for the adhesiveand the resin-cement. The change of stress scale(010 MPa) should be noted.

For the adhesive layer, no differences are evidentbetween ceramic Models A and B (Fig. 6a-1 and b-1).For the cement layer, higher stress was apparentwith the higher modulus cement (Fig. 6a-2) com-pared with the lower modulus lute (Fig. 6b-2).Fig. 6c-1 and c-2 illustrates the interfacial stressesfor the adhesive and cement layers within compositeModel C. The lowest stress values were recorded forthis condition.

-hCisesatio

P. Ausiello et al.868Figure 5 (a) von Mises stress-distribution within Model A (G(c) von Mises stress-distribution within Model C. (d) von M(G-hC). (e) von Mises stress-distribution within the restorwithin the restoration of the Model C.). (b) von Mises stress-distribution within Model B (G-lC).stress-distribution within the restoration of the Model An of the Model B (G-lC). (f) von Mises stress-distribution

Ceramic and composite inlay Class II behavior 869In Graph 1, a linear analysis on Model A and Cis represented in which it can be seen thatwith increasing the loading from 400 to 800 N,the stresses proportionally increase, leading toa critical stress concentration in Model A, particu-larly on the lingual cusp.

Discussion

Teeth in posterior regions are subject to functionaland para-functional forces of varying magnitudesand directions. In vitro mechanical tests on Class IIadhesive posterior restorations revealed the differ-ent aspects related to the stress-distributionregarding the marginal and internal adaptationof adhesive Class II restoration [21]. The role of

Figure 5 (Cothe filling material, of the adhesive resin and of theresin cement was clearly demonstrated and resultsindicated various important points to observe toobtain high performance of the restoration itself.The rigidity or elastic modulus of dental restorativematerials was considered extremely important atthe adhesive tooth-restoration interface.

In the present work, the FEA method was used toinvestigate the stress-distribution resulting fromocclusal loading within the restoration and incorrespondence to that of the interfacial layers(adhesive and cement) between the cavity wallsand the inlay materials.

An arbitrary load of 400 N was applied in thistest, which is probably lower than can be applied bythe teeth in vivo. Different data are reported onthis aspect. Tortopidis [22] found that 580 N was

ntinued)

P. Ausiello et al.870the maximum bite force of healthy people inposterior areas. Other investigations [23] suggestedthat these values differ between males (522 N) andfemales (441 N).

Figure 6 (a-1) von Mises stress on Model G-hC, adhesive. (a-2stress on Model G-lC, adhesive. (b-2) von Mises stress on Model(c-2) von Mises stress on Model C, cement.Under laboratory conditions, varied loading ratescan be applied to the samples to investigatebiomechanics of natural and restored teeth. Inparticular, fracture resistance of Class II

) von Mises stress on Model G-hC, cement. (b-1) von MisesG-lC, cement. (c-1) von Mises stress on Model C, adhesive.

restorations in upper premolars submitted to By contrast, in Model C, a 50 GPa resin-compo-

tested were able to completely prevent interfacialgaps developing when inlays were cemented with a

cement layer thickness and minimal modulus to stillsufficiently support the ceramic inlay are in

Ceramic and composite inlay Class II behavior 871vertical loading has been experimentally investi-gated [24]. It ranged for resin-composites incombination with dentin bonding systems between700 and 800 N. These data were also confirmedrecently [25], where the use of resin-composite andceromers as restorative materials was considered.However, it was not the objective of this study todetermine the absolute numerical stress levelscreated within the restoration but to examinetheir distribution and localization. The softwareused in this study was not programmed for evaluat-ing the model to failure and therefore higher orlower loads would only change the magnitude of thestresses in the distribution pattern.

In the ceramic Models A and B, where a ceramicinlay of high modulus (90 GPa) was used incombination with 70 mm thick resin-cements oftwo different Youngs moduli, no major differenceswere found in terms of stress-distribution withinthe restoration. However, when the inlay moduluswas reduced to 50 GPa, still in combination with thesame parameters for the cement layer, the stress-distribution significantly changed. ComparingFig. 5d and e with Fig. 5f (respectively, Model Aand B, with Model C) the stress-distribution wasmore intensive where the 90 GPa modulus inlay wasused and these stresses are almost totally trans-ferred to the cavity walls, as shown in Fig. 5a and b;whilst for the 50 GPa inlay (Fig. 5f), the stresses arepartially absorbed and partially transfered to thecavity walls.

From the load-strain values as represented inFig. 3, it can be derived that a 400 N loading inhorizontal direction, when flexural deflections willtake place in the prepared brittle tooth structure,destructive damage will occur earlier than withvertical, occlusal loading.

Recently, Abu-Hassan et al. [26], used 3D-FEA toinvestigate stress-distributions associated withloaded ceramic onlay restorations with differentdesigns of marginal preparation. It was possible toestablish how vertical and horizontal forces actdifferently in correspondence with the total mar-gins of the restoration. Hence interesting con-clusions could be drawn regarding the optimummorphology of the butt-joint onlay preparation.

In our investigation, the 400 N axial simulationsshowed that ceramic Models A and B transmittedhigher stress to the cavity walls than compositeModel C.

Fig. 4a and b shows that Class II MOD prep-arations, restored by a 90 GPa ceramic inlay withthe same 4.5 GPa adhesive but with either a 10 or6 GPa resin-cement, do not show a substantiallydifferent stress-distribution after axial loading.progress.

Conclusions

From this FE analysis on stress-distribution in inlay-restored Class II MOD cavities under axial load, it isevident that both optimum stress magnitude anddistribution are best served with low modulusrestorative materials. FEA enabled investigation ofoptimal conditions, material selection and theirinteraction when adhesively restoring teeth. Class IIMOD restorations by glass core inlay materialscreated higher stress levels at the cusp and at theinternal sides. Thermally post-cured resin-compo-site Class II restorations presented elastic biome-chanics similar to that of the sound tooth.

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Stress distributions in adhesively cemented ceramic and resin-composite Class II inlay restorations: a 3D-FEA studyIntroductionMaterials and methodsFinite element modelsExperimental model validationNumerical simulation

ResultsDiscussionConclusionsReferences