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isotropic- equal physical properties along all axes. Anisotropic- unequal physical properties along different axesA material is orthotropic if its mechanical or thermal properties are unique and independent in three mutually perpendicular directions. Examples of orthotropic materials are wood, many crystals, and rolled metals.
material approach is difficult and the basicof all numerical methods is to simplify theproblem by discretizing (discontinuation) it.In simple words
When the canine tooth was subjected to 100N axial loading,maximum vonMises stresses generated in enamel (108MPa)was higher than the dentine (73MPa) (Figure 2). The changeof the force angulation (45◦ to the long axis) increased thelevel of maximum von Mises stresses drastically, enamelsuffered 3 times greater increase (389MPa) in stress concentrationcompared with dentine
The direction and magnitude of the applied forces on the model, theway in which the model is supported, and the shape of the model must besimilar to the conditions of the actual structure.
con•fron•ta•tion (ˌkɒnfrənˈteɪʃən, -frʌn-) n.1. an act of confronting.2. the state of being confronted.3. a meeting of persons face to face.4. an open conflict of opposing ideas, forces, etc.
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STRESS ANALYSIS INRESTORATIVE DENTISTRY1
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NO OF SLIDES: 118 NO OF ILLUSTRATIONS: 37 TIME TAKEN FOR PRESENTATION : 1hr 30 min2
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References1) Craig RG, Powers JM. Restorative dental materials. 11thed. St. Louis, Missouri: Mosby, Inc; 2002. p. 110-1.2) Anusavice KJ. Properties of dental materials. Phillip‘sScience of Dental Materials. 10th ed. St. Louis Missouri:W.B Saunders Company;1996.3) Sturdevant‘s Art and science of operative dentistryfourth edition4) Srirekha A, Kusum Bashetty 2010 Infinite to finite: Anoverview of finite element analysis Indian J Dent Res,21(3),425-4323
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5)Desai shrikar, Shinde Harshda2012. Finite elementanalysis: basics and its applications in dentistry. Indianjournal of dental sciences 1;46) Wood I, Jawad Z, Paisley C, Brunton P. Noncariouscervical tooth surfaceloss: A literature review. J Dent2008;36:759-66.ents of stress with in a structure7) Geramy A, Sharafoddin F. Abfraction: 3D analysis bymeans of the finite element method. Quintessence Int2003;34:526-33.8) Shihab A. Romeed, RaheelMalik, and Stephen M. Dunne.Stress Analysis of Occlusal Forces in Canine Teeth andTheir Role in the Development of Non-Carious CervicalLesions: Abfraction. International Journal of DentistryVolume 2012, Article ID 234845, 7 pages 4
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9)Özkan ADIGÜZEL, Sadullah KAYA, Senem YİĞİT ÖZER,Yalçın DEĞER. Three-dimensional Finite Element Analysisof Endodontically Treated Tooth Restored with Carbonand Titanium Posts (Int Dent Res 2011;2:55-5910)Ivana Kantardžić, Darko Vasiljević, Larisa Blažić,OgnjanLužanin 2012Influence of cavity design preparation onstress values in maxillary premolar:a finite elementanalysis. Croat Med J. 2012;53:568-76l.11)Zarone F, Apicella D, Sorrentino R, Ferro V, Aversa R,Apicella A.Influence of tooth preparation design on thestress distribution in maxillary central incisors restoredby means of alumina porcelainveneers: A 3D-finiteelement analysis. Dent Mater 2005;21:1178-88 5
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12)Aggarwal S, Garg V. Finite element analysis of stressconcentration in three popular brands of fiber postssystems used for maxillary central incisor teeth. JConserv Dent 2011;14:293-6.13)Magne P, Oganesyan T. Premolar cuspal flexure as afunction of restorative material and occlusal contactlocation. Quintessence Int2009;40:363-70.6
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Contents References Introduction Mechanical properties of dental materials Stress analyses Finite element analysis History Basic theme Steps in processing Advantages Disadvantages Various studies Conclusion 7
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―Stress analysis is an engineeringdiscipline that determines the stress inmaterials and structures subjected tostatic or dynamic forces or loads‖8
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What is Stress ??? When a Force acts on a body to produce deformation, aresistance develops to this external force, which is calledSTRESS Definition :It is the Force per Unit Area acting on millionsof atoms or molecules in a given plane of material Stress = Force / Area Expressed in Units of Load / Area*(Pounds/in2 = PSI or N/mm2 = MPa)*PHILLIPS9
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Types of Stress*1.) Based on forces acting on the specimen: Simple stress: Tensile stressCompressive stressShear stress Complex stress: Flexural stress2.) Based on temperature changes on the specimen:Thermal stress*PHILLIPS10
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Compressive stress* If a body is placed under a load that tends to compressor shorten it, the internal resistance to such a load iscalled a Compressive Stress and it is associated with aCompressive strain . Calculated by dividing the applied force by the crosssectional area perpendicular to the force direction*PHILLIPS 12
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Tensile Stress*A Tensile Stress is caused by a load that tends to stretchor elongate a body and it is always accompanied byTensile strain .Tensile stress is generated when structures are flexed*PHILLIPS 13
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Shear stress* It is produced by a twisting or torsional action on amaterial. A shear stress tends to resist the sliding on a portion ofa body over another Shear stress is calculated by dividing the force by thearea parallel to the force of direction*PHILLIPS 14
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During loading, bonds are not compressed as easily aswhen they are stretched .* Materials resist compression readily and are stronger incompression than in tension.* As loading continues, the structure is ultimatelydeformed**STURDEVANT‘S16
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Strain* Strain is defined as change in length per unitinitial length . Strain (ε) is deformation (▲L) per unit of length(L). Expressed as inch/inch or cm./cm* PHILLIPS17
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The Stress-Strain Curve**CRAIG18With a constant increase inloading, the structure isultimately deformed.At first, the deformation (Strain)is reversible – Elastic Strain.With increased loading, there issome irreversible strain whichresults in permanentdeformation – Plastic Strain*Craig
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Elastic Strain – the deformation that is recovered uponremoval of an externally applied force or pressure . Plastic Strain – the deformation that is not recoverablewhen an externally applied force is removed STURDEVANTS20
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The point of onset of plastic strain is called theElastic Limit (Proportional Limit, Yield Point) *. It is indicated on the stress – strain curve as the point atwhich the straight line starts to become curved. Continuing the plastic strain leads to Fracture . The highest stress before fracture is the UltimateStrength*STURDEVANTS21
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Elastic limit of a material is defined as the greateststress to which a material can be subjected to, such thatit returns to its original dimensions when force isreleased .* Materials that undergo extensive plastic deformationbefore fracture are called Ductile (in Tension) andMalleable (in compression) .** Materials that undergo very little plastic deformation arecalled Brittle****STURDEVANTS*PHILLIPS23
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Elastic Modulus (E) : * Elastic Modulus (E) Also called Young‘s Modulus orModulus of Elasticity . It describes the relative stiffness or rigidity of amaterial, which is measured by the slope of the elasticregion of the stress – strain graph . It represents the amount of strain produced in responseto each amount of stress.Eg. Ceramics have a higher ‗E‘ than polymers, whichmeans ceramics are stiffer* Sturdevants 24
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Elastic modulus has a constant value that does notchange and it describes the relative stiffness of amaterial .* The Elastic modulus of Enamel is higher than that ofDentin*Phillips25
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Enamel is stiffer and more brittle than dentin. Dentin is more flexible and tougher and is capable ofsustaining significant plastic deformation undercompressive loading before it fractures Clinical Significance :When a load is applied to a tooth, it is transmitted throughthe material giving rise to stresses and strains. If theseexceed the maximum value the material canwithstand, a Fracture results** CRAIG26
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The most useful properties of a restorative material areModulus of elasticity (E) and Elastic limit.A restorative material should be very stiff so that underload, its elastic deformation is minimal.An exception to this is in Class V cavities, where MicrofillComposites are used – They should be less stiff toaccommodate for tooth flexure** STURDEVANTS 27
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When selecting a restorative material, the clinician mustbear in mind the stress level during function. This should not exceed the Elastic Limit . If the stress level is beyond the elastic limit, a resultingdeformation is likely to occur which may cause failure atsome point of time28
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Poisson‘s Ratio: Strain in the lateral direction to that inthe axial direction when an object is subjected to tensileloading* Yield strength: The stress at which a test specimenexhibits a specific amount of plastic strain.* Ultimate tensile strength: Tensile stress at the point offracture* * PHILLIPS 29
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Stresses in dental structures have been studied byvarious techniques, such as brittle coating analysis, strain gauges, holography, 2-dimensional (2D) 3-dimensional (3D) photoelasticity finite element analysis (FEA), digital moiré interferometric investigationSrirekha A, Bashetty K. Infinite to finite: An overview of finiteelement analysis. Indian J Dent Res 2010;21:425-3231
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FINITE ELEMENT ANALYSIS More recent method of stress analysis, generallydeveloped in 1956 in the aircraft industry was the finiteelement method (FEM). Introduced by Richard courant Initially, this technique was used widely only inaerospace engineering, but slowly due to theflexibility of the method to model any complexgeometries and provide instant results, it made itspresence felt in dentistry.It was first used in dentistry in the 1970‘s toreplace photo elasticity tests. 32
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This method involves a series of computationalprocedures to calculate the stress and strain in eachelement, which performs a model solution. FEM circumvents many of the problems of materialanalysis by allowing one to calculate physicalmeasurements of stress within a structure.**Wood I, Jawad Z, Paisley C, Brunton P. Noncarious cervical tooth surfaceloss:A literature review. J Dent 2008;36:759-66.ents of stress with in astructure.33
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Has the advantage of being applicable to solids ofirregular geometry and heterogenous materialproperties. It is therefore ideally suited to examination of structuralbehaviour of teeth.34
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BASIC CONCEPT OF FEM The FEM is a numerical procedure used for analyzingstructures It consists of a computer model of a material or designthat is stressed and analyzed for specific results. FEM uses a complex system of points(nodes) andelements, which make a grid called as mesh.35
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This mesh is programmed to contain the material andstructural properties (elastic modulus, Poisson‘sratio, and yield strength), which define how thestructure will react to certain loading conditions. The mesh acts like a spiderweb, in that, from each nodethere extends a mesh element to each of the adjacentnodes.37
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The basic theme is to make calculations at only limited(finite) number of points and then interpolate the resultsfor the entire domain (surface or volume). Any continuous object has infinite degree of freedom(dofs) and it is not possible to solve the problem in thisformat. FEM reduces the dofs from infinite to finite with the helpof meshing (nodes and elements) andall the calculations are made at limited number of nodes.Geramy A, Sharafoddin F. Abfraction: 3D analysis by means of the finiteelement method. Quintessence Int 2003;34:526-33.38
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Each element retains the mechanical characteristics oforiginal structure. A numbering system is required to identify the elementsand their connecting points called nodes39
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Finite elements started with triangular elements theseelements being stiffer, resulted in less stress anddisplacement. Later, quadrilateral elements were used for accuracy ofresults. Increasing the number of calculation points(nodes andelements) improves accuracy.41
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For example,increasing the number of lines reduces error margin infinding out the area of a circle . The number of straight lines are equivalent to thenumber of elements in FEM.42
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FEM is performed with material properties that can beisotropic (same properties) or anisotropic (differentproperties) All real-life materials are anisotropic, but it is simplifiedinto isotropic properties or orthotropic properties(different properties along 3 axes, namely- x, y,and z). Elastic modulus, Poisson‘s ratio (strain in the lateral direction to that inthe axial direction when an object is subjected to tensileloading) yield strength for the materials are applied.Anusavice KJ. Properties of dental materials. Phillip‘s Science of DentalMaterials. 10th ed. St. Louis Missouri: W.B Saunders Company;1996. p. 58.43
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The analysis is performed as linear static analysis ornon-linear analysis depending on the allocation ofappropriate physical characteristics to the different partsof the tooth. Linear systems are less complex and effective indetermining elastic deformation. Many of the non-linear systems are capable of testing amaterial all the way to fracture and they do account forplastic deformation**Infinite to finite: An overview of FEM .Indian J Dent 21(3) 2010 44
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Mechanical properties of dentalstructuresMATERIAL ELASTICMODULUS(Mpa)POISSONS RATIOIsotropic enamel 80000 0.3Anisotropic enamel 20,000 0.08Dentin 18,600 0.31Cementum 18,600 0.31Dental pulp 2.07 0.45Periodontal ligament 50 0.49Spongy bone 345 0.3Compact bone 13,800 0.26 45
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COMPARISION OF LINEAR AND NONLINEAR FEMLINEAR PROBLEMS Displacements vary linearlywith applied loads. Thusstiffness is constant. Changesin geometry due todisplacement are assumed tobe small, and hence areignored. Linear up to theproportional/elastic limit.Properties, such as Young‘smodulus are easily available.NON LINEAR PROBLEMS It is non-linear. Thus stiffnessvaries as a function of load It is a non-linear function ofstress-strain and time.These are difficult to obtain andrequire a lot of additionalexperimental material testing.46
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Linear problems The behavior of the structureis fully reversible upon removalof the external nodes. Computational time Small User‘s interaction withthe software is least requiredNonlinear problems The final state after removal ofload is different from the initialstate. Large Requires lot of monitoring asthe software may fail toconverge sometimes47
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The eventual result of any FEM is the normal andshearing stress values of the structure upon loading. The failure criteria is measured by Von-Mises stresses.48Kishen A, Ramamurty U, Asundi A. Experimental studies on thenature of property gradients in human dentine. J Biomed MaterRes 2000;51:650-9.
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The information needed for calculating thestresses is:(1) total number of nodal points,(2) total number of elements,(3) a numbering system identifying each element.(4) Young‘s modulus and Poisson‘s ratio associated witheach element,5) a numbering system identifying each nodal point,(6) the coordinates of each nodal point,(7) the type of boundary constraints, and(8) the evaluation of the forces at the external nodes.49
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In practice, an FEM usually consists of 3 principle stepsPre-processing: It includes CAD (computer-aideddesigning) data, meshing, and boundary conditions.• Processing or solution: This is the step in which thecomputer software does the job of calculation.Internally, the software carries out matrixformulations, inversion, multiplication, and solution. Post-processing: This step includes viewingresults, verifications, conclusions, and thinking aboutwhat steps would be taken to improve the design.Srirekha A, Kusum Bashetty 2010 Infinite to finite: An overview of finiteelement analysis Indian J Dent Res, 21(3),425-432 50
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Steps in finite element method: (a) 3D-model; (b) meshing;and (c) resultant stresses51
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Steps in the solution procedure usingFEA 1. Discretization of problem 2. Imaging 3. Meshing 4. Boundary conditions 5. Types of solutions52
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Discretization of problem Nodes work like atoms with gap in between filled by anentity called as element. Calculations are made at nodes and results areinterpolated for elements.There are two approaches to solve any problem: 1. Continuous approach (all real life components arecontinuous). 2. Discrete approach ( equivalent mathematicalmodeling).53
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All the numerical methods including finite element followdiscrete approach. Meshing (nodes and elements) is nothing butdiscretization of a continuous system with infinitedegree of freedoms to finite degree of freedoms54
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IMAGINGa) Imaging and three-dimensional Reconstruction: Three dimensional surface reconstructions created fromCT scans are used as templates for three-dimensionalfinite element models. Initial 3D surface reconstructions are quite rough andrequire significant editing before they can be importedinto a FE tool and successfully meshed as a finiteelement model55
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b) Image processing: editing the three dimensional image. The ultimate goal of 3D image processing is togenerate a ―water-tight‖ surface model that can beimported into and successfully manipulated in FEsoftware. The most important aspect of the simplification processof three-dimensional images involves smoothening andremoving details in selected areas of the model. 3Dsurface representations are composed of connectedpolygons and are often referred to as ‗polygon models‘.56
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The more polygons a model contains, the greater is itsfidelity to the object it represents and the larger is itssize.Image processing is the most labor-intensive aspect ofconducting FE analyses of biological structures.57
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MESHING FEM uses a complex system of points(nodes) andelements, which make a grid called as mesh. Basic theme of FEA is to make calculations at onlylimited (finite) number of points and then interpolate theresults for entire domain (surface or volume).58
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Any continuous object has infinite degrees of freedomand it is just not possible to solve the problem in thisformat. FEA reduces degrees of freedom from infinite tofinite with the help of discretization i.e. meshing (nodesand elements)2D MESHING: simpleAllows the analysis to be run on a relatively normalcomputerYields less accurate resultsSHAPES :triangular, quadrilateral61
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3D MESHING: produces more accurate results and canrun only the fastest computers effectively.Boundary conditionsBoundary condition is application of force and constraint.Different ways to apply force and moment are concentrated load (at a point or single node), force on line or edge, distributed load (force varying as equation), bending moments and torque . After fixing the boundary conditions the software is runfor determining stresses &strains using linear staticanalysis & nonlinear analysis62
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Types of solutions The analysis is done to assess the stresses acting uponthe materials during function in the oral cavity byapplying various material properties These stresses are:1. Normal or principal stress: acts perpendicular to thecross section and causes elongation or compression.2. Shear stress: acts parallel to the cross section andcauses distortion (changes in original shape).63
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Maximum principal stress.The maximum principal stress gives the value of stressthat is normal to the plane in which the shear stress iszero. The maximum principal stress helps us understand themaximum tensile stress induced in the part due to theloading conditions64
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Minimum principal stress.The minimum principal stress acts normally to the plane inwhich shear stress is zero. It helps you to understand the maximum compressivestress induced in the part due to loading conditions65
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Von Mises stress. The von Mises criterion is a formula for calculatingwhether the stress combination at a given point willcause failure. The von Mises criterion is a formula for combining threeprincipal stresses into an equivalent stress, which is thencompared to the yield stress of the material .The yieldstress is a known property of the material and is usuallyconsidered for the failure stress.66
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If the ―von Mises stress‖exceeds the yieldstress, then the material is considered to be atthe failure condition. The von Mises theory is used for ductilematerials such as metals and evaluates stressesin both static and dynamic conditions67
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Software used for finiteelement analysis The various software used in FEA areAbaqus Explicit, Ansys, Dytran, Femfat,Hypermesh , Ls - dyna , Madymo ,Magmasoft, MSC Nastran, Pro mechanicaStar-CD, Tosca, Unigraphics,68
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GENERAL APPLICATIONS OF FEM FEA has been applied for the description of formchanges in biological structures (morphometrics),especially in the area of growth and development . The knowledge of physiological values of alveolarstresses is important for the understanding of stressrelated bone remodeling and also provides a guidelinereference for the design of dental implants69
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70 FEM is useful with structures containing potentiallycomplicated shapes, such as dental implants andinherent homogenous material.• It is useful for the analysis of stresses produced in thePDL when subjected to orthodontic forces.• It is also useful to study stress distribution in tooth inrelation to different designs.• It is used in the area of optimization of the design ofdental restorations.• It is used for investigation of stress distribution in toothwith cavity preparation
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The type of predictive computer model described maybe used to study the biomechanics of tooth movement,even though accurately assessing the effect of newappliance systems and materials without the need togo to animal or other less representative models.• FEM technique is widely used in structural engineering.• It is also used to predict and estimate the damages inthe electrical fields.• It is also used in optimization of sheet metal blankingprocess.71
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Requirements for doing finiteelement analysis Finite Element Analysis is done principally withcommercially purchased software. These commercial software programs can cost roughly$1,000 to $50,000 or more. Software at the high end of the price scale featuresextensive capabilities -- plastic deformation, andspecialized work such as metal forming or crash andimpact analysis. Finite element packages may include pre-processorsthat can be used to create the geometry of thestructure, or to import it from CAD files generated byother software.72
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The FEA software includes modules to create theelement mesh, to analyze the defined problem, and to review the results of the analysis. Output can be in printed form, and plotted results suchas contour maps of stress, deflection plots, and graphsof output parameters.NISA-II Users Manual; Feb. 1997, Version 7.0; Engineering MechanicsResearch Corporation, Troy, Michigan.. Display-IV Users Manual; Mar. 2001, Version 10.5; EngineeringMechanics Research Corporation, Troy, Michigan.73
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The choice of a computer is based principally on the kindof structure to be analyzed, the detail required of themodel, the type of analysis (e.g. linear versus nonlinear),the economics of the value of timely analysis, and theanalysts salary and overhead. An analysis can takeminutes, hours, or days.74
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Advantages When finite element modeling is compared withlaboratory testing, it offers several advantages. The variables can be changed easily, simulation can beperformed without the need for human material and itoffers maximum standardization. FEM can minimize laboratory testing requirement. FEM provides faster solutions with logical andreasonable accuracy in an era where the industry prefersfaster solutions75
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Limitations The most significant limitation of FEA is that theaccuracy of the obtained solution is usually a function ofthe mesh resolution. Any regions of highly concentrated stress, such asaround loading points and supports, must be carefullyanalyzed with the use of a sufficiently refined mesh. In addition, there are some problems which areinherently singular (the stresses are theoreticallyinfinite).Special efforts must be made to analyze such problems76
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Obtaining solutions with FEA often requires substantialamounts of computer and user time.-- expensive finite element packages have become increasinglyindispensable to mechanical design and analysis.77
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The use of this method in dental structures was startedin 1968 when Ledley and Huang developed a linearmodel of the tooth based on experimental data and onlinear displacement force analysis. The one shortcoming of their study was that theyconsidered the tooth to be homogeneous structure. In reality the human tooth is highly inhomogeneoussince the elastic modulus of the enamel outer surface ofthe tooth is about three times that of the inner dentinmaterial.79
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The major contribution was made by W. Farah (1972), Thresher R.W (1973) and Yettram A.L (1976) whomodeled a tooth and studied the stresses in a toothstructure using a finite element method. -80
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Stress distribution around implant81Three-dimensional finite element analysis of the stress distribution around theimplant and tooth in tooth implant-supported fixed prosthesis designs.Journalof dental implants Year : 2011 | Volume : 1 | Issue : 2 | Page : 75-79
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After removing third molar82Finite Element Analysis of the Human Mandible to Assess the Effect ofRemoving an Impacted Third Molar J Can Dent Assoc 2010;76:a72
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Finite element analysis of stress concentration inthree popular brands of fiber posts systems usedfor maxillary central incisor teeth Computer aided designing was used to create a 2-Dmodel of an upper central incisor. Post systems analyzed were theDTLight Post (RDT, Bisco),Luscent Anchor (Dentatus) &RelyX (3M-ESPE).The entire design assembly was subjected to analysis byANSYS for oblique loading forces of 25N, 80N & 125 N83
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When a fiber-reinforced post is bonded within the rootcanal, it dissipates functional and parafunctionalforces, reducing the stress on the root. Acute consequences of such forces in the assembly arenot anticipated, but there will be a gradual build-up ofdestructive stresses that finally cause the failure of theassembly. When a catastrophic force is placed on the crown of thetooth, the crown will fracture instead of thepost, transmitting the energy of force down the rootand creating a vertical root fracture.84
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Consequently, a post system should be able to dissipatethe function of energy and even overcome moderatetrauma. Fiber-reinforced posts have demonstrated the ability tofracture at the coronal portion of a tooth restoration withthe presence of catastrophic forces without root fracture,permitting scope of retreatment of the remaining rootstructure.85
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ResultsMaterials Modulus of elasticity (Gpa)DT LIGHT POST 13LUSCENT ANCHOR 20RELYX 37.588Group C showed maximum stress distribution in theentire structure and least forces generated (stressconcentration at apical third of the tooth model, whichwas significantly different from other two groups.Aggarwal S, Garg V. Finite element analysis of stress concentrationin three popular brands of fiber posts systems used for maxillarycentral incisor teeth. J Conserv Dent 2011;14:293-6.
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CUSPAL FLEXURE Magne and Oganesyan conducted one study to measurecuspal flexure of intact and restored maxillary premolarswith different restorative materials: (mesio-occlusal-distal porcelain, and composite-inlayrestorations) and occlusal contacts (in enamel, atrestoration margin, or in restorative material). They concluded that a relatively small cuspaldeformation was observed in all the models. There is an increased cusp-stabilizing effect of ceramicinlays compared with composite ones.Magne P, Oganesyan T. Premolar cuspal flexure as a function ofrestorative material and occlusal contact location. Quintessence Int2009;40:363-70.89
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Tooth preparation design Zarone et al., evaluated the influence of toothpreparation design on the stress distribution andlocalization of critical sites in maxillary central incisorrestored by means of alumina porcelain veneers underfunctional loading. They concluded that when restoring a tooth by means ofporcelain veneers, the chamfer with palatal overlappreparation better restores the natural stressdistribution under load than the window technique.Zarone F, Apicella D, Sorrentino R, Ferro V, Aversa R, Apicella A.Influence oftooth preparation design on the stress distribution inmaxillary centralincisors restored by means of alumina porcelainveneers: A 3D-finiteelement analysis. Dent Mater 2005;21:1178-88.90
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Influence of cavity design preparation onstress values in maxillary premolar:a finite element analysis To analyze the influence of cavity design preparation onstress values in three-dimensional (3D) solid model ofmaxillary premolar restored with resin composite. 3D solid model of maxillary second premolar wasdesigned using computed-tomography (CT) data. Based on a factorial experiment, 9 different mesio-occlusal- distal (MOD) cavity designs weresimulated, with three cavity wall thicknesses (1.5mm, 2.25 mm, 3.0 mm),91
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Three cusp reduction procedures without cusp reduction, 2.0 mm palatal cusp reduction, 2.0 mm palatal and buccal cusp reduction). All MOD cavities were simulated with direct resincomposite restoration (Gradia DirectPosterior,GC, Japan). Finite element analysis (FEA) was used to calculatevon Mises stress values92
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The von Mises stresses in Enamel- 79.3-233.6 MPa dentin, - 26.0-32.9 MPa resin composite -180.2-252.2 MPa, respectively.Considering the influence of cavity designparameters, cuspal reduction (92.97%) and cavity wallthickness (3.06%) significantly (P < 0.05) determinedthe magnitude of stress values in enamel.94
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The influence of cavity design parameters on stress valuesin dentin and resin composite was not significant. When stresses for enamel, dentine, and resin compositewere considered all together, palatal cusp coverage wasrevealed as an optimal option. Cavity wall thickness did not show a significant effect onstress values.Conclusion a palatal cusp reduction could be suggested forrevealing lower stress values in dental tissues andrestorative material.Ivana Kantardžić, Darko Vasiljević, Larisa Blažić,Ognjan Lužanin2012Influence of cavity designpreparation on stress valuesinmaxillary premolar:a finite element analysis.Croat Med J. 2012;53:568-76l. 95
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Stress analysis on non cariouscervical lesions An extracted human upper canine tooth was scanned byμCT machine (Skyscan,Belgium). These μCT scans were segmented, reconstructed, andmeshed using ScanIP (Simpleware, Exeter, UK) to createa three dimensional finite element model. A 100N load was applied axially at the incisal edge andlaterally at 45◦ midpalatally to the long axis of the caninetooth. Separately, 200N axial and non-axial loads were appliedsimultaneously to the tooth.96
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It was found that stresses were concentrated at theCEJ in all scenarios. Lateral loading produced maximum stresses greaterthan axial loading,and pulptissues, however, experienced minimum levels ofstresses. This study has contributed towards the understandingof the aetiology of non-carious cervical lesions which is akey in their clinical management.97
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Micro-CT imaging, modelling, anddeveloping FE model of caninetooth98
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Enamel has suffered much higher stresses than dentineespecially at the cervical buccal CEJ region under lateralloading The enamel tooth tissue is known to be thin, having avery weak prismatic structure and low ultimate tensilestrength at the CEJ. In addition, the CEJ is usually subject to erosion andabrasion, caused by acidic exposure and toothbrushing, respectively, which further weaken andunderminethe structure of cervical enamel and dentine Therefore, tensile stresses, along with other contributingfactors, concentrated at the CEJ seem to be most105
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Conclusions of this study(1) maximum stresses and crown displacement generatedby lateral loading were generally higher than the verticalloading;(2) peak stresses were concentrated at the CEJ in allloading scenarios;(3) the greatest levels of stress generated within enameland dentine were located at the CEJ when axial andnon-axial loadings were applied simultaneously;106
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(4) pulp tissues sustained the minimum level ofstress under all loading conditionsShihab A. Romeed, RaheelMalik, and Stephen M. Dunne .StressAnalysis of Occlusal Forces in Canine Teeth and Their Role in theDevelopment of Non-Carious Cervical Lesions: Abfraction.International Journal of Dentistry Volume 2012, Article ID 234845, 7pages107
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The stress values on the dentin and luting cement forthe endocrown restoration were lower than those for thecrown configuration. Weibull analysis revealed that the individual failureprobability in the endocrown dentin and luting cementdiminished more than those for the crown restoration.112
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While the overall failure probabilities for the endocrownand the classical crown were similar, fatigue fracturetesting revealed that the endocrown restoration hadhigher fracture resistance than the classical crownconfiguration (1,446 vs. 1,163 MPa)Finite element and Weibull analyses to estimate failure risks in theceramic endocrown and classical crown for endodontically treatedmaxillary premolar Eur J Oral Sci 2010; 118: 87–93 .113
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Carbon post The analysis of the vonMises stress values forcarbon post model showedthat maximum stressconcentrations werenoted on the coronalthird and the cervicalarea of the root in therange of 353.149 and13.878 MPa114Özkan ADIGÜZEL, Sadullah KAYA, Senem YİĞİT ÖZER, Yalçın DEĞER.Three-dimensional Finite Element Analysis of Endodontically Treated ToothRestored with Carbon and Titanium Posts (Int Dent Res 2011;2:55-59)
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Titanium post Titanium post modelshowed that maximumstress concentrationswere noted on thecoronal third and thecervical area of the rootin the range of 540.736and 22.777 MPa.115
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This study shows that titanium postsyields larger stresses than carbon post.Özkan ADIGÜZEL, Sadullah KAYA, Senem YİĞİT ÖZER, YalçınDEĞER.Three-dimensional Finite Element Analysis ofEndodontically Treated Tooth Restored with Carbon andTitanium Posts (Int Dent Res 2011;2:55-59116
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Conclusion Finite element analysis has proved to be the mostadaptable, accurate, easy and less time consumingprocess as compared to the other experimental analysis.It has provided clinicians with useful information toachieve higher degree of success and satisfaction to thepatients117
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Strain guageA strain gauge is a device used to measuredeformation (strain) of an object Invented by Edward E. Simmons and Arthur C.Ruge in 1938 The most common type of strain gauge consistsof an insulating flexible backing which supportsa metallic foil pattern . The gauge is attached to the object by asuitable adhesive 123
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A strain gauge is a long length of conductorarranged in a zigzag pattern on a membrane. When it is stretched, its resistance increases.124
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They use the principle that when a certain electricalresistance is subjected to an object, it produces strain . Tension produces an increase in resistance; compressioncauses a decrease in resistance . Therefore, if such a strain gauge were bonded to thesurface of a structure under a load, monitoring theresistance changes would yield knowledge of the straincharacteristics at that point126
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Photoelasticity is a nondestructive, whole-field, graphicstress-analysis technique based on an optomechanicalproperty called birefringence, possessed by manytransparent polymers. Noonan was the first to apply photoelasticityto restorative dentistry128TAM 326—Experimental Stress AnalysisJames W. Phillips
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Based on the property of some transparent materials toexhibit colorful patterns when viewed with polarizedlight. These patterns occur as the result of alteration of thepolarized light by internal stresses into two waves thattravel at different velocities The pattern that develops is consequently related to thedistribution of the internal stresses and is calledPhotoelastic effect129TAM 326—Experimental Stress AnalysisJames W. Phillips
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To use this special characteristic, a model of thestructure of interest must be fabricated in the rightdimensions and proportions . The model should be made from a transparent materialcapable of exhibiting a photoelastic response . The stresses that develop in the model as the result ofthe applied loads can then be visualized by examiningthe model with polarizing filters131
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The general procedure for photoelastic analysis involvesbonding a special plastic coating onto thestructure, shining polarized light onto the plastic, andthen analyzing the resultant images.132
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The polarizer has the property of passing only thosecomponents of the incident light waves which areparallel to the polarizing axis. Consequently, plane polarized light is produced whichimpinges upon the stressed model made of a materialexhibiting temporary double refraction under stress.134
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Selecting the material.Many polymers exhibit sufficient birefringence to be usedas photoelastic specimen material.However, such common polymers aspolymethylmethacrylate (PMMA) and polycarbonate maybe either too brittle or too intolerant of localizedstraining. Homalite®-100 (araldite) has long been a populargeneral purpose material, available in variousthicknesses in large sheets of optical quality.137
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PSM-1® is a more recently introduced material that hasexcellent qualities, both for machining and for fringesensitivity. Another good material is epoxy, which may be castbetween plates of glass, but this procedure is seldomfollowed for two-dimensional work138
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Advantages anddisadvantagesAdvantages.—Photoelasticity, as used for two dimensionalplane problems,• provides reliable full-field values of the differencebetween the principal normal stresses in the plane of themodel• provides uniquely the value of the nonvanishingprincipal normal stress along the perimeter(s) of themodel, where stresses are generally the largest139
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furnishes full-field values of the principal stressdirections (sometimes called stress trajectories) is adaptable to both static and dynamic Investigations . requires only a modest investment in equipment andmaterials for ordinary work is fairly simple to use140
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Disadvantages.—On the other hand, photoelasticity requires that a model ofthe actual part be made (unless photoelastic coatingsare used)• requires rather tedious calculations in order to separatethe values of principal stresses at a general interior point• can require expensive equipment for precise analysis oflarge components• is very tedious and time-consuming for three-dimensionalwork141
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Two-dimensional Photoelastic StressAnalysis ofTraumatized Incisor Two homogeneous two-dimensional central incisormodels were prepared from Araldite B (Ciba-Geigy S.A.,Bale, Switzerland), a birefringent plastic material with amodulus of elasticity within the range of human dentin.142Braz Dent J (2001) 12(2): 81-84 Two-dimensional PhotoelasticStress Analysis of Traumatized Incisor
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Each specimen was 5 mm thick. Alveolar bone was alsoprepared from Araldite B. The models were loaded witha constant force of 1 kg. Loads were applied to the labial side of incisal edge(point A) and middle third of the crown (point B) at 45°(F1 and F3 forces) and 90° (F2 and F4forces) .143
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When photoelastic material is subjected to force, opticalproperties change in direct proportion to the stressesdeveloped. The material becomes ―birefringent‖ and a colorfulinterference pattern is observed when polarized lightpassing through the stressed material splits into twobeams. A fringe is defined as a line separating the red and greencolor bands144
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A fringe order will consist of a sequence of colorbands, including fringe line. The zero fringe order is black and indicates no stress.Stress can be quantified and localized by counting thenumber of fringes and density. The closer thefringes, the steeper the stress gradient, indicating anarea of stress concentration145
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This case shows that the normal forces applied to teethon the apical area cause more stress than those appliedat an angle. It has been observed that the highest stress value isobtained under F2 loading. This fact clearly shows that pulp dies when the effectedforce is transferred to the apical third of the tooth thathas not been fractured after trauma.When crown fracture occurs, the force affecting the toothdivides into its components and causes less damage tothe pulp.146
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A fracture occurs if the effecting force exceeds theresistance against the sliding force of hard tissue. Otherwise the resistance depending on the strength anddirection of the force may cause pathological damages Finally, the forces exerted horizontally to the labial sideof the tooth caused more stress on the tooth andalveolar bone than inclined forces147
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Comparison between FEM andPEMFEM All stress components arecalculated. Changes of relavantparameters and loads canbe easily incorporatedinto calculation program . Allowance can be madefor any homogeneity andanisotropy in materialphotoelasticity All stress components arenot calculated. Only fringe patternsrepresent stress values. Model should mimicactual structure148
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FEM Super computers andhighly expensivesoftwares are needed. Based on meshing andimaging of nodes andelementsPHOTOELASTICITY It uses a polariscope,andphotoelastic polymersonly for evaluation ofstress patterns Based on wave theory oflight and polarizationprinciple.149
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Holography Holographic interferometry, a non-destructive full-field technique thatmeasures small static or dynamicdeformations occurring in an object, isbased upon standard holographicprinciples150
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Holography was previously used to investigate variousdeformations of dentures or dental implants Holography is a method for recording three-dimensionalinformation on a two-dimensional recording medium(photographic emulsion, thermoplastics, etc) Unlike a photograph, the hologram contains all theinformation about the surface of the object .T. Puškar, et al., Holographic interferometry as a methodfor measuring strain caused... Contemporary Materials,I–1 (2010) 151
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Holography follows a different principle fromconventional photography. A laser is needed to produce a coherent, monochromaticlight beam. The difference in phase between a reference ray and theobject ray (to be analyzed) produces an interferencepattern that is recorded on a high-resolutionphotographic plate (hologram). When developed and suitably exposed to laser light, thishologram reconstructs a three-dimensional image of theobject. Resolution is that of the order of the laser wavelengthor that of a photographic film152
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The hologram is an interference pattern ofcoherent wave fronts scattered from the objectand recorded by the medium . The basic principles of holography underly thetechnique in double-exposure holographicinterferometry .154
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Because tension moves perpendicularly to the fringes, itis possible to evaluate tension distribution within thebody of the mandible quantitatively . The higher the number of fringes, the greater thetension transmitted. Qualitative evaluation is achieved by observing theaspect and direction of the fringes157
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Real-time holography is a dynamic methodthrough which the deformations can bemonitored during the entire experiment .Detection and recording of the interferencepattern can be done with CCD camera andcomputer .158
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BRITTLE COATING ANALYSIS Brittle Lacquer stress analysis makes use of abrittle coating also known as brittle lacqueror StressKote. The brittle coating will fracture in response tothe surface strain beneath it. The coating indicates the direction andmagnitude of stress within the elastic limit of thebase material.159
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Stresscoat coatings provide a graphic picture ofthe distribution, direction, location, sequenceand magnitude of tensile strains. The coating cracks at a predetermined value. This value is determined by a simple calibrationmethod.160
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161Craig and Peyton Measurement ofStresses in Fixed-Bridge RestorationsUsing a Brittle Coating Technique.J. dent. Res. July-A list 1965
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The bridges were cleaned with carbon disulfide andsprayed with the desired brittle lacquer. The selection of the lacquer dependson the humidity, temperature, and sensitivity. The lacquer is sprayed so that a uniform coating of0.005- 0.006 inches is applied to the bridge. An air pressure of 20-psi gauge was adequate, and3-4 passes of the lacquer spray at a distanceof 2.5 inches produced the proper coatings162
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The stress may be calculated by multiplying thesensitivity of the lacquer by the modulus of elasticity ofthe material which is coated. For example, if a crack is observed in the lacquer coatingon one of the gold-alloy bridges during loading, thestrain at this position is 800 micro inches/inch and thestress is 0.0008 X 14 X10-6 = 11,200 lb /sq inch. In this instance 14 X 10-6 is the value of the modulus ofelasticity of the alloy.163
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ConclusionStress analysis techniques are invaluable for clinicians andmanufacturers of dental materials as they help inevaluating critical stress levels of various materials .Theyhelp in evaluating the mechanical properties of dentalmaterials under laboratory conditions and also give athree dimensional view .Their accuracy has been a pointof confrontation for many years164
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