The International Journal of Periodontics & Restoroliue Dentistry 543

Optimization of Resiiience and Stress Distribution in Porceiain Veneers for the Treatment of Crown-Fractured incisors

Pascal Magne. DrMedDent'/William H. Dougias. BDS. MS, PhD" The good overail clinical behav- ior of poroeiain laminate veneers TliQ present study was coriducted to define, wher") restoring extens!ve loss of dentin. ttie oonfigurdfiori of fhe restoration thaf will best reproduce the biome- (PV) in terms of fracture rates, ohanicdi properties of the ihfact origindi toofh in terms ofresiilence and stress dis-microleakaga, debonding, and tribution. The treatment of '¿-crown frdotures and '¿-crown fractures was investigat-soft tissue response is generally ed using different designs of faoiai porceiain veneers with and without underlying weli recognized and attested tc odmposite buiidup. The stress distribution and tcofh compliance were assessed in a numeric mcdei reproducing a 2-dimensionai buocolihgudi cross section cfan by numerous ciinical studies.'"^ As inoisor A 50-N faaai force was dpplied to simuiote an incisai impdot situation. Thea consequence, the indications fociai surface tdngentidi stresses were calculated, and the maximum dispidoe- for PVs have been extended,^-^ menf (harizontdl directian) at the most incisai node of the enamel surface was otsa recorded and used ta caioulate the tooth ccmpiiahce (ie, displacement/ inciuding the treatment of crown- lead ar resiiience) for edch test condition. Tensiie stresses were generated on thefractured incisors'"'^' ond the focidi surface of the porceiain iaminates with a simiiar pattern for dit test condi- rehabilitation of worn down den- tions, the cervicai part of the crown being the most quiescent area Substantiai tition,'^'^ Among these, the differences appeared in the incisai haif cf the crcwn, the lawest stresses being observed for extensively fractured teeth restored without composite buildup treotment of severely damaged (faciai peaks at^ 33 MPd). Fractured teeth restored with minimal veneers and a inoisors oommands speciai atten- 'dentin-iike'composite buiidup shewed stress patterns similar to the intact tooth tion. The use cf PVs is porticuiarly (facialpedks at- 50 MPa). The ndturdi teeth gdve the highest tooth compiionoe ar flexibility. Ali restorative designs fodtured ihcredsed tooth stiffness. However, theinteresting in the presence cf origindi footh oompiionce was aimosf resfored when composite wos used to teeth with short clinical crowns or repldce the missing dentin, with the poroeiain acting only as a facial and incisai insufficient residuai tooth structure enamel substitute. When restoring crown-frdotured incisors, tooth compiionoe to provide adequate stabiiity for and stress distribution can be mcdutated by the combination of composite ond ceramics. Optimized oonñgurafichs can be reached to reproduce the original a conventionai type of fixed pros- biomeohanicai behavior of the intact tooth. Ihe use cf ceramic aione generates thetic restoration (Fig 1). PVs per- low stress ccncentrations, but also less campliant restored teeth. mit above ali the maintenance of (IntJ Periodontics Restorative Dent 1999,19:543-553.) tooth vitality in spite of a severe -Formerly Visiting Associate Professor. Minnesoto Dental Research Center foi breai

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Fig la Ciinicai case of previcusiy frac- Fig ¡b Specific diagnostic approach Fig lc Ceramic aniy was used tP tured incisor. The patient's maxiiiary is used to redeñne tcoth vciume and restore structure and esthetics of anteri- incisors are insufficient in iength and iength. A siiicon index of the corre- or teeth (immediate postoperative have iost their characteristic form. The sponding woxup is used by ihe view, now more than 4 years in service). right central incisor was fractured and ceramist during poroeiain buildup: the (Ceramist: Michei iViagne. dental iabo- previously reconstructed with compos- voiume that wiii be restored by the ratory Crai Design, Montreux. ite resins. Porceioin veneers were future veneer on the left centrai incisor, Switzerland,) Owing to the ceramic pianned to reestabiish anterior taoth which will aiiow both the restoration cf stratification, optimai opticai transition prominence ond esthetics. the faciai aspect and repiacement o' was obtained befween the intact part missing incisai substance, is shawn. ot the right centrai inciser and the buik pt the restoration.

whether the missing toofh sub- approach (veneer aione) fo the and catastrophic fqiiures at the sfonce should be replaced using resfaration of crown-fractured ievel ofthe roof,The combinafion (1) the veneer alone, (2) a com- incisors could be justified. of bofh composites and ceramics posife buildup diong wifh the However, one may question the seems theoreficaily appropriafe veneer, or C3) the fractured taoth biomechanicai behavior of sin- fo reproduce the original stiffness fragment itself aiong wiih fhe gle feeth restored with extremely of the tooth and modulate fhe veneer. A surprising answer was resistant restorations. Using in vifro foofh-restoration strength. How- given in an assessmenf of sfrength simuiafed impacts. Stokes and ever, no scientific investigations by Andreasen et al," who used Hood'^ cleariy demonstrated have been conducted yet fo de- veneered sheep incisors in a that fhe excessive sfrengfh of fine, when restoring extensive loss load-fo-failure fesf fhaf yielded convenfional prosfhetic restora- of denfin, the opfimai configura- ulfimate strengths at (I) 28.2, (2) tions such as goid and metal tion otthe restoration and related 20,2, and (3) 21,0 MPa, respec- ceramic crowns yieids roof frac- thicknesses of composite and tiveiy. These vaiues are vi/eii above tures fhat wouid be very difficuif ceramic, Oniy a few scienf ific pa- the strength of intact teeth, since to restore. pers"'-" specificaliy addressed the iatfer frqcfured at an aver- The modulation of fhe the problems of internal stress dis- age of 1Ó MPa in a simiiar exper- sfrengfh of fhe toofh-restoration tribution, stress transfer, and foofh iment by Munksgaqrd ef al,''' complex should therefore be sfiffness offer the placement of Therefore, fhe use of a simplified considered to avoid stress transfer PVs.

Th9 Internotionai Journal cf Periodontics a Restorative Dentistry 545

Fig 2 Mesh developed in MËNTATand reiated experimental groups.

An efficient way to access the wos oonducted using the 2- device (UMAX, Umax Data intimóte structure of the tooth- dimensional FE method to define System). The contours of enamel, restoration complex undoubtedly the optimol geometric relation dentin, and pulp chomber were is represented by finite element between oomposite and cero- manually traced using a personal (FE) evaluations. New trends in re- mio moteriols ond reloted thick- computer and grophic softwore search tend to oombine experi- nesses thot should be reproduoed (Freelance Graphics, Lotus). mental approaches and FE evol- to meet the physicomeohanioal Additionol lines were included to uations.'^ In an FE model, a large properties of the naturel tooth. simulate different restorative structure is divided into o number designs, ie, o conventional prepo- of small, simple-shaped elements rotion tor PVs ond 2 grades of trau- for which individual deformation Method and materials matic injury. Point coordinates (strain and stress) can be more were obtained using Scion Imoge eosily calculated thon tor the An extracted maxillary centrol sottwore (Scion). The lines were undivided large structure. By solv- incisor wos embedded in a clear finally transferred to MFNTAT 3,3 ing the deformation of all the epoxy resin (Orthodontic Resin, software (MARC Analysis Res- small elements simultaneously the Caulk/Dentsply) and sectioned earch), ond a single mesh that deformation of the whole struc- longitudinally in the buccolingual inoluded ttie different restorative ture can be reconstructed. plane.The sectioned surface was designs was developed (Fig 2). Accordingly, the present study digitized with a computer scanner The root was modeled to a level 2

Volume 19. Number 6,1999 546

corresponding porcelain Material properties lominate.

Material Elastic modulus (GPaj Poisson ratio • Froctured (FR): FR/i situations correspond to a preparation Composite 20 0.24'a Ceramic 78' 0.28'3 following fracture of the incisai Enamel 50 0.30'8 third of the crown; FR^ situa- Dentin 12 0.2320 tions correspond to a prepa- •Data from manufacturer of Creation Dental Porcelain (Klema]. ration foiiowing the fracture of two-thirds of the crown.

Two treatment modalities oould be assessed tor each situ- ation of the fractured incisai edge (Fig 2): f'Jthe replacement cf enamel and dentin using the ceramic veneer alone (FR'/^C, PR'AC [C = ceramic)) cr (2) the enamei replacement by the veneer, the lost dentin being replaced by a composite buildup CFRÄCR FR%CP1, FR^/3CP2 (CP = composite)). The restoration of the most extensive fracture (FR'/j) was explored either with a lorge mm beiow the cementoenamei veneer.The stress distribution was composite buildup (FRVJCPI) or a junction. It is assumed that the solved using the MARC Anaiysis reduced composite buildup overall stress distribution on solver (MARC K7.3, MARC Anaiysis (FR'^CP2). A totai of seven condi- impact is constrained to the ooro- Research).The simulation was per- tions was tested (Fig 2), including nai restoration. Fixed zero dis- formed with plane-strain eiements the natural tooth. piacement in botin horizontal and (linear, 4-node, isoparametric, The iuting composite thick- verticai direotions was therefore arbitrary quadrilateral). ness averaged 200 pm at the applied at the cut plane of the axiai and Incisai ievel, whereas root. Functional stress transfer into 50-|jm thicknesses were pro- the Jaw would have required Resforafive designs duced tor both buccal and meshing the entire root and the palatal margins and 100-|jm periodontai iigament, which was The intact originai tooth and 3 thicknesses were used at the not the purpose of this investiga- different preparation designs ievei ct the palatal chamfer. tion. A facial load of 50 N was were reproduced, generating Three extra layers of elements applied to the incisai edge of the the foiiowing situations (Fig 2): (approximately 400 pm) were veneer (Fig 2) to simulate the meshed to accentuate the facial equilibrium response ot a tooth In • Natural tooth (NAT): intact contour of the natural tooth.This an impact case.This situation was original tooth. feature ccrresponds to reievant also chosen to generate tensile Veneer (VEN): troditionai ciinicai conditions because stresses at the facial surface of the veneer preparation with its the desirobie preservation of

The Internationai Journai of Periodantics & RGstorative Dentistry 547

Faciai surface tangential stress (MPa

FR,«:P 00 1 1 1 / r 50 i 1 I 0 - a 1Í f •

; (MPa) Hill 0 25 SO 75 100

Fig 3 Surface tangential stresses (upper port) and modified Von Mises stresses (iower par!) for eacti expérimentai design The gray line on ttie piofs corresponds to the sur- foce tangentiai stress distribution of the intact tooth. ' = moximum vaiues (Fig a)

enamel during tooth preparation distribution of modified Von Mises often leads to the overcon- stresses (mVM) aoross the section touring of the finoi restoration,^^ ot the restored tooth (Fig 3). Ttie Two mechanical material prop- where f) is the angle between original Vcn Mises stress is an inte- erties were required far this FE the X axis and the surface of the gral vclue that incarparates both simulation: the Poisson ratia and element, The maximum horizon- tensile and campressive compo- elasticity modulus are listed in tal displacement (x displace- nents within ane number, making Table 1. Both of these properties ment) at the most inoisal node of it easier for the observer to appre- for the luting agent and the com- the enamel surfaoe was also ciate the totai stress distribution in posite buildup materials were recorded and used to calculate most materials. However, such a assumed tc be the same. The the tocth compliance (ie, dis- criterion predicts that the yield FE calculations generated the placement/load cr resilience) for stresses measured in uniaxial ten- values af stress in the x and y each test condition. sion and compression wiii be directions (o-^ and o-^ and the equal. Beth dentai hard tissues xy shear stress (T^^^). The surface and restorative materials are brit- tangential stress u, for each Results tie materials that present a higher nade located at the facial sur- strength in compression thon in face cf the tooth was calculated The surface tangential analysis af tension. Accordingly, a specific using the following fransforma- stress was plotted for each exper- faiiure criterion for brittle types of imental design, alang with the materials must be used, ie, the

Volume 19, Number ó, 1999 548

—

90-

n ane e (% ) 40- 1—1 • 1 •

e stres s (MPa ) e 1 1 ao- 20- mien s 1 1 70- 11 B 1 1 1 n M E LJ N CL 1 • m • 1 60- 1M M K NAT I CL u o à: FR',iCP 2 ^M

Fig 4 Maximum tensile stresses found in the incisai hait of the Fig 5 fíeiative tooth compliance or flexibility (as a percent- orown facial surface for each experimental design. age of the compliance of the intact tooth, NAT) calculated from fhe maximum horizontoi dispiacement (x displacement) at the most incisai node of the enamei surface.

mVM criterion^^: it incorporates The most cervicoi part of the (Fig 3).This value is reported in the sc-calied strength differential tooth, especiaiiy the denti- Fig 4 for eoch restorative effect, namely the ratio between noenamel junction, exhibited design, it is mainly this part of compressive strength and tensile high levéis of stress. the tooth that exhibited major strength. For all test conditions very The cervicai half of the crown differences between test con- iow mVM stresses were detected wos aiways the most quies- ditions.The maximum stresses in the poiotal hoit of the tooth cent area, with stresses on all ot the surtace of the ceramic (mainiy subjected tc compressive restored teeth being substan- were here generally iower forces), whereas significant mVM tiaily iower than the intact when compared tc the sur- stress concentrations were found enamel. This can be ex- face ot intact enamel (49 on fhe facial side (moinly sub- plained by the cervical over- MPa), except for FRKCP (54 jected to tensile forces). contour cf the veneer, the MPa) and FR^,iCPl (59 MPa). The pattern ot surface tan- ceramic iayer at this levei Test condition VEN showed a gentiai stresses was similar for all being actuaily thicker than pattern of stresses similar to test conditions: voiues were al- the preexisting enamel. The the intact tooth (Fig 3), as did ways positive except in the area reasons for this design were fractured teeth restored with of the load point where, as ex- justified above, minimal veneers and a pected, it was highly negative. in the incisol half of the crown, dentin-like composite buildup The tcoth can be analyzed in 3 another maximum of tensile (FRléCPandFR%CPl),The low- portians: stresses wos always present est stresses were observed for

The Internationai Journal of Pariodontics & Restorative Dentistry 549

fracfured feeth restored wifh- are fherefore commendable demonstrated by the mVM stres- cuf composite buildup (FR'AC because of fheir improved per- ses (Fig 3), the simuiation of a fa- formance in ferms of element cial impact was chosen because The reiafive footh compli- and simulafion quality. In the pre- it generates harmful fensile ances (rated as a percentage ot senf study the assumption was sfresses af the surface of fhe fhe compliance af the intact fhaf force causing traumatic veneer, A palafai load or a verti- fooffi, NAT) are presented in Fig 5. impact fravels in the 2-D sagiffal cal load on fhe incisai edge All expérimentai designs showed plane. vi^ouid have produced compres- a loss of resilience when com- sive stresses on most of fhe pared to the intact taaf h (100%), restoration, thereby reducing fhe FR-^C being fhe stitfest, with a rel- Relevance of selected ability of fhe present analysis fo otive compliance of 87%. Com- boundary conditions discriminate between differenf pliances close fo fhe original resforafive designs. foofh were found for FR',éCP and Fixed displacement. Generally FR=¿CP1 (relative values of 99,0% speaking, when local sfress disfri- and 99,9%, respecfiveiy), corre- butions in a crown qre studied, sponding again to fractured fixation ot the modei is pre- feeth resfored with minimal scribed along the cross section veneers and a composite build- of fhe root. Because fhe model is up that substituted for fhe ioss of fixed at the cut piane of the roof, dentin. a stress is generafed in fhis area. Normally fhis sfress would be dif- fused throughout fhe perlodon- Discussion fal membrane and, as here, not influence caranal evenfs, in addi- Reievance of 2-D FE model fion, fhe enamel surfdce at fhe crown-roof junction shows a dis- When if comes fo fhe analysis ot tincf sfress peak. This can be fhe tooth crown portion, fhe explained by the thin enamei as accuracy of 2-D plane-strain FE well as the change of maferiai analyses considered in a bucco- properties (enamel-dentin tran- lingual cross section was sition), Suoh subtle detaiis would demonstrated on several occa- require a mare precise model sions and validated by experi- definition and further study. mental strain measurement.^""^* Owing fo fhe abovementioned Three-dimensianal models, reasons, no conclusions can be although more realistic, present drawn from the high ieveis of fen- coarser meshes fhat wouid not siie stresses encountered in the aiiow fhe fihe represenfafion of roof portion of fhe crown. thin layers such as fhe lufing composite or preparation Load application. The setup of detaiis such as marginai cham- the present study corresponds to fers,^'Two-dimensional FE mod- a chailenging situafion for a els wifh plane-sfrain condificns veneered maxillary incisor. As

Volumel9, Number 0,1999 550

The biomimefíc principie strongest restorotion, but rather o most elevated stresses. Res- restoration that is oompotible with torative designs demonstrating The modest results ot the present the mechanical and biologic a stress pottern similar to the study may constitute a supple- properties cf underlying dental tooth aiso happened to have mentary link between restorative tissues—the biomimetic principle. almost the same compliance dentistry and a newly emerging The dramatic consequences of (FR'ACP FR'/,CP2). The latter con- interdisciplinary materiel soience the "biomechonicol mismatch" stitutes an essentiel quolity in any called "biomimetics."^^ This mod- between tooth ond restoration structure; otherwise it would be ern concept involves investi- can be found in the literoture. A unable to absorb the energy of gation of both structures and simuloted impact study by Stokes a traumatic blow. In other words, physical functions of biologic ond iHood^^ showed the prob- a compliant restoration will cush- "composites" and the designing lemotic root tracture pattern gen- ion a sudden blow by bending of new and improved substitutes. erated with stiff restorations (gold elastically under the load. Up to In restorotive dentistry biomimet- crowns, metal oeromics), whereos a point, the more resilient o struc- ics starts with the understanding teeth veneered with bonded ture the better.-" In our model of hard fissue arrangement and porcelain performed similar to the natural tooth gave the high- relafed stress distribution within intact feeth. Certain types of est compliance. In this context it the intact tooth.^'' Enamel ond veneers, however, can be very is interesting to note the findings dentin form a composite struc- sturdy: Andreosenetol'^ showed of Stokes and Hood.^^ who ture that provides a tooth with the excessive resistance of showed thot in an impoct situa- unique ohorocteristics^^: on one bonded porcelain veneers when tion the intact tooth absorbs the hond, the hordness of enomel it comes to the restoration of highest energy of fracture when protects the soft underlying den- crown-froctured incisors. compared to teeth restored tin, yet the crack-orresting effect with veneers or different types ot dentin and cf the thick colla- of crowns. The complionoe of gen fibers at the dentinoenomel Optimization of restorative the intact tooth was therefore junction™ compensate tor the design: i.oiv stress versus high taken as the biomimetic refer- inherently brittle nature of ena- compiionce ence tor the oaiculotion of the mel. This struotural ond physical relotive compliance ot our interrelationship between on The present study comes as a experimental models. extremely hard tissue and a more voluable complement to the pliable softer tissue provides the previous works of Andreasen natural tooth with its unique abil- and coworkers^°'^^ and Stokes High-compliance designs ity to withstand masticatory and ond Hood. '' ^ It shows, using stress thermai loads during a litetime. distribution and resilience os Among modern dental materi- Because of the improvement of indicators, how optimal inter- als, ceramics best feature the adhesive procedures and the mediate performance can be physiccmechanicoi characteris- development of restorative mate- obtained by modulating the tics of enamel in terms ot eiostic rials, the behovicr of the enamel- restorative design. In the present modulus, fracture strength, hard- dentin complex can be partially work, a correlation logically ness, and thermal expansion. mimicked. In this context it seems emerges between the maxi- Stiffness and hordness of dentin reasonable to conclude that mum stresses and the tooth are much lower and more likely new restorative approaches compliance, with the most to be simulated by composite should not aim to create the strained structures showing the resin materiols. Because of their

The International Journal of Periodontics & Restorative Dentistry 551

elastic modulus, composites straightfcrward and features alone are not abie to restore the optimal esthetic results (Fig 1). loss of stiffness toliowing tooth The dentai technician can use preparation and the related loss specific porceiainsto accurately of enamel,"' It is therefore logi- reproduce the anatomy and cal that there should be similari- optical characteristics of dentin, ties in the stress pattern and com- ie, opaque dentin for adequate pliance cf intact teeth and translucence and fluorescent restored teeth incorporat- stains for an adequate iumines- ing ceramic and composite cence. Mcst composite resins do as enamel and dentin substi- not allow such precise charac- tutes, respectively (FR/CP and terization. FR-:iCP2),The ccnfguration of the it seems cbvious that a iow veneer oould stiii be optimized to surface stress might be preferred fit exactly the stress distribution of in a restoration since this might the tooth by increasing ceramic reduce the risk ot locaiized frac- thickness at the incisai level and ture. However, with regard to bio- removing the cervical overccn- mimetics, ceramic-oniy designs tour. Even though the combina- (FR'-'C and FR/C) may present an tion of composite and ceramic excessive strength. In the case of seems best to reproduce the recurrent trauma this could gen- behavior of the intact tooth, one erate a tatal root fracture or at may stili criticize the high thermai least the loss ot an additional por- expansion of certain composite tion of the tooth. These assump- resins.The latter proved tc have a tions now require experimental significant influence in the devel- validation using the latest gener- opment of ceramic postbcnding ation of dentin adhesives, as the flews, even when used oniy as a dentin bond proves to be an thick iuting agent.^^-^ essentioi determinant in the trac- ture pattern and fracture mech- anics of the tooth.^^ Low-stress designs

From Figs 4 and 5 it can be con- oiuded that the maximum tensiie stress reached its lowest vaiue in the restorative designs showing the lowest relative compliance (FR'^C, FR%C. and FR^¿CP2). These restored teeth had extensive ceramic thickness taking the place ot preexisting dentin. This simplified design is often pre- terred by oiinicians because it is

Voiume 19, Number 6,1999 552

Conclusions When restoring crown-frac- References tured incisors, the use ot ceramic The treatment af crown-fraotured aione generates iow stress con- 1. Caiomia JR, Ciinical evaluation of incisors was investigated using dif- centrations but also less compli- etctied porcelain veneers. Am J Dent 1989:2:9-15. ferent designs of faciai porcelain ant restored teeth. Tooth resili- 2. Caiamia JR, The current status of veneers with and withcut under- ence and stress distribution can etohed porcelain veneer restorations, lying composite buiidup, A 2-D FE be moduiated by the combina- J indionaDentAssoc 1993:72:10-15, model simulating an inoisal tion of composite resins and 3. Rucker LM, Richter W, MacEntee M, impaot situation was used to cai- ceramics. Optimized configura- Riohardson A, Porceiain and resin ouiate the stress distributions and tions can be reaohed to repro- veneers clinicoily evaiuated: 2-year resuits J Am Dent Assoc 1990:121: tooth resiiience. duce the originai biomechanical 594-59Ó, behavior ot the intact tooth. 4. Kourtkouto S, Walsh TT, Davis LG, The • Tensiie stresses were gener- effect of porceiain iominate veneers ated on the facial surface of on gingivai heaith and bdcteriai the porceiain iaminates with Acknowledgments plaque characteristics. J Ciin Periodontoi 199421:ó3B-ó40, a simiiar pattern for aii test conditions, the cervical port Ttie authors wish to express ttieir gratitude 5. Peumons M, Van Meerbeel< B. Lambrechts fi Vuyistei

The internationai Journal of Periodantics & Restorative Dentistry 553

12. Walls AW. The use af adhesively 23 De Groot R, Peters MCRB, De Hoon 34, Mogne R Versluis A, Douglos WH. retained all-porcelair) veneers during YM, Dop GJ, Piossohaeri AJM. Eoilure Effeot ot luting composite shrinkoge the management of tractured and stress oriterio tor composite resin. J ond thermai loads on the stress distri- worn anterior teeth: Port 1. Ciinical Dent Res 1987:66'1,748-1,752. bution in porceloin iaminate veneers, technique.Br Dent J 1995:178:333-330. J Prosthet Dent 1999:81.335-344. 24 Morin DL Cross M, Voiier VR, Dougias 13. Wails AW. Ttie use of adhesively WH, DeLong R. Biophysicai stress onaiy- 35, Versluis A, Tontbirojn D, Dougias WH. retoined all-porcelain veneers dur- sis of restored teeth. Modeling ond Why do shear bond tests puli out ing the manogement ot troctured anaiysis. Dent Mater 1988:4:77-64. dentin? J Deht Res 1997:76: and worn onterior teeth' Part 2. 1,298-1,307. 25. Morin DL Cross M, Voller VR, Douglas Ciinicai results after 5 years ot toliow- WiH, DeLong R. Biophysical stress analy- up.BrDentJ 1995;178:337-34O. sis ot restored teeth: Experimental 14. MunksgaardECHajtvedLJargensen Strain measurement. Dent Mater EH, Andreasen JO, Andreasen FM. 1988:4:41-48. Enamel-dentin orown troctures bond- 26 Magne P Versluis A. Douglas WH. ed with various bonding ogents. Rationoiiiotion ot incisor shope: Endod DentTraumdtoi 1991:7:73-77. Experimentol-numericai onoiysis J 15. Stokes AAN, Hood JAA. impaot frac- Prosthet Dent 1999:81:345-355. ture characteristics ot intoct and 27. Korloth TWRVersluis A. Modeiing the crowned human centrai incisors J mechanioai behavior ot the jows Oral Rehabil 1993:20:89-95. and their reioted structures by finite 1Ó. Reeh ES, Ross GK. Tooth stiffness with element (FE) onolysis. Crit Rev Orai composite veneers. A strain gauge BioiMed 1997:8:90-104. and tinite eiement evaiuation. Dent 28 Sarikaya M. An introduction to bio- Mater 1994:10:247-252. mimetios: A structurai viewpoint. 17. Hightan R, Caputo AA Matyas J. A Microsc Res Tech 1994:27:300-375. photoelastic study ot stress on porce- 29. Kraus BS, Jordan RE, Abrams L. loin lominate preparations. J Prosthet Histoiogy ot the teeth and their invest- Dent 1987;58:157-1Ó1. ing struotures. In: Kraus BS, Jordan RE, 18. Craig RG. Restorative Dental Matetiols, Abrams L(eds), Dental Anatomy and ed Ó, St Louis: Mosby, 1980:76 Occiusion. Baitimore: Wiiiiams a Wilkins, 1969:135. 19. Anuscivice KJ, Hojjatie B. Influence ot inoisal iength at ceramic and loading 30. Lin CR Dougias WH. Struoture-prop- orientatian on stress distribution in erty reiatiohs and crack resistance at oeramic crowns, J Dent Res 1988;67: the bovine dentin-enamel junction. J 1,371-1.375. Dent Res 1994:73:1,072-1,078. 20. Watts DC El fvlowatV OM, Gront AA. 31. Gordon JE, Stroin energy and mod- Température-dépendance ot com- ern fracture mechanics. In: Gordon pressive properties of human dentin. J JE (ed). Structures: Or Why Things Dent Res 1987;ó6:29-32. Don't Fail Down. New York: DaCapo, 1978:70-109. 21. Sorensen JA, Avera SRMaterdomini D Marginai fidelity ond microleokage ot 32. Barghi N, Berry TG Post-bonding porcelain veneers made by two tech- crack formation in porceiain venee's. niques. J Prosthet Dent l992;ó7:1ó-22. JEsthetDent 1997;9:51-54.

22. Gere JM, Timoshenko SP Anaiysis of 33. Magne R Kwon KR, Beiser U. Hodges stress and strain, in: Gere JM, JS, Douglas WH, Crack propensity of Timoshenko SP (eds). Meohanics ot porcelain laminate veneers' A simu- Materials, ed 3. Boston: PWS, lated operotory evaluation. J Prosthet 1990:378-460. Dent 1999:81:327-334.

Volume 19, Number 6,1999