1. STRESS ANALYSIS IN
RESTORATIVE DENTISTRY
1

2.  NO OF SLIDES: 118
 NO OF ILLUSTRATIONS: 37
 TIME TAKEN FOR PRESENTATION : 1hr 30 min
2

3. References
1) Craig RG, Powers JM. Restorative dental materials. 11th
ed. St. Louis, Missouri: Mosby, Inc; 2002. p. 110-1.
2) Anusavice KJ. Properties of dental materials. Phillip‘s
Science of Dental Materials. 10th ed. St. Louis Missouri:
W.B Saunders Company;1996.
3) Sturdevant‘s Art and science of operative dentistry
fourth edition
4) Srirekha A, Kusum Bashetty 2010 Infinite to finite: An
overview of finite element analysis Indian J Dent Res,
21(3),425-432
3

4. 5)Desai shrikar, Shinde Harshda2012. Finite element
analysis: basics and its applications in dentistry. Indian
journal of dental sciences 1;4
6) 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 a structure
7) Geramy A, Sharafoddin F. Abfraction: 3D analysis by
means of the finite element method. Quintessence Int
2003;34:526-33.
8) Shihab A. Romeed, RaheelMalik, and Stephen M. Dunne
.Stress Analysis of Occlusal Forces in Canine Teeth and
Their Role in the Development of Non-Carious Cervical
Lesions: Abfraction. International Journal of Dentistry
Volume 2012, Article ID 234845, 7 pages 4

5. 9)Özkan ADIGÜZEL, Sadullah KAYA, Senem YİĞİT ÖZER,
Yalçın DEĞER. Three-dimensional Finite Element Analysis
of Endodontically Treated Tooth Restored with Carbon
and Titanium Posts (Int Dent Res 2011;2:55-59
10)Ivana Kantardžić, Darko Vasiljević, Larisa Blažić,Ognjan
Lužanin 2012Influence of cavity design preparation on
stress values in maxillary premolar:a finite element
analysis. 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 the
stress distribution in maxillary central incisors restored
by means of alumina porcelainveneers: A 3D-finite
element analysis. Dent Mater 2005;21:1178-88 5

6. 12)Aggarwal S, Garg V. Finite element analysis of stress
concentration in three popular brands of fiber posts
systems used for maxillary central incisor teeth. J
Conserv Dent 2011;14:293-6.
13)Magne P, Oganesyan T. Premolar cuspal flexure as a
function of restorative material and occlusal contact
location. Quintessence Int
2009;40:363-70.
6

7. 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

8.  ―Stress analysis is an engineering
discipline that determines the stress in
materials and structures subjected to
static or dynamic forces or loads‖
8

9. What is Stress ???
 When a Force acts on a body to produce deformation, a
resistance develops to this external force, which is called
STRESS
 Definition :It is the Force per Unit Area acting on millions
of 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)
*PHILLIPS
9

10. Types of Stress*
1.) Based on forces acting on the specimen:
 Simple stress: Tensile stress
Compressive stress
Shear stress
 Complex stress: Flexural stress
2.) Based on temperature changes on the specimen:
Thermal stress
*PHILLIPS
10

11. Compressive stress*
 If a body is placed under a load that tends to compress
or shorten it, the internal resistance to such a load is
called a Compressive Stress and it is associated with a
Compressive strain .
 Calculated by dividing the applied force by the cross
sectional area perpendicular to the force direction
*PHILLIPS 12

12. Tensile Stress*
A Tensile Stress is caused by a load that tends to stretch
or elongate a body and it is always accompanied by
Tensile strain .
Tensile stress is generated when structures are flexed
*PHILLIPS 13

13. Shear stress*
 It is produced by a twisting or torsional action on a
material.
 A shear stress tends to resist the sliding on a portion of
a body over another
 Shear stress is calculated by dividing the force by the
area parallel to the force of direction
*PHILLIPS 14

14. 15

15.  During loading, bonds are not compressed as easily as
when they are stretched .*
 Materials resist compression readily and are stronger in
compression than in tension.*
 As loading continues, the structure is ultimately
deformed*
*STURDEVANT‘S
16

16. Strain*
 Strain is defined as change in length per unit
initial length .
 Strain (ε) is deformation (▲L) per unit of length
(L).
 Expressed as inch/inch or cm./cm
* PHILLIPS
17

17. The Stress-Strain Curve*
*CRAIG
18
With a constant increase in
loading, the structure is
ultimately deformed.
At first, the deformation (Strain)
is reversible – Elastic Strain.
With increased loading, there is
some irreversible strain which
results in permanent
deformation – Plastic Strain
*Craig

18. 19

19.  Elastic Strain – the deformation that is recovered upon
removal of an externally applied force or pressure .
 Plastic Strain – the deformation that is not recoverable
when an externally applied force is removed
 STURDEVANTS
20

20.  The point of onset of plastic strain is called the
Elastic Limit (Proportional Limit, Yield Point) *.
 It is indicated on the stress – strain curve as the point at
which the straight line starts to become curved.
 Continuing the plastic strain leads to Fracture .
 The highest stress before fracture is the Ultimate
Strength
*STURDEVANTS
21

21. 22

22.  Elastic limit of a material is defined as the greatest
stress to which a material can be subjected to, such that
it returns to its original dimensions when force is
released .*
 Materials that undergo extensive plastic deformation
before fracture are called Ductile (in Tension) and
Malleable (in compression) .**
 Materials that undergo very little plastic deformation are
called Brittle**
**STURDEVANTS
*PHILLIPS
23

23.  Elastic Modulus (E) : *
 Elastic Modulus (E) Also called Young‘s Modulus or
Modulus of Elasticity .
 It describes the relative stiffness or rigidity of a
material, which is measured by the slope of the elastic
region of the stress – strain graph .
 It represents the amount of strain produced in response
to each amount of stress.
Eg. Ceramics have a higher ‗E‘ than polymers, which
means ceramics are stiffer
* Sturdevants 24

24.  Elastic modulus has a constant value that does not
change and it describes the relative stiffness of a
material .*
 The Elastic modulus of Enamel is higher than that of
Dentin
*Phillips
25

25.  Enamel is stiffer and more brittle than dentin.
 Dentin is more flexible and tougher and is capable of
sustaining significant plastic deformation under
compressive loading before it fractures
 Clinical Significance :
When a load is applied to a tooth, it is transmitted through
the material giving rise to stresses and strains. If these
exceed the maximum value the material can
withstand, a Fracture results*
* CRAIG
26

26. The most useful properties of a restorative material are
Modulus of elasticity (E) and Elastic limit.
A restorative material should be very stiff so that under
load, its elastic deformation is minimal.
An exception to this is in Class V cavities, where Microfill
Composites are used – They should be less stiff to
accommodate for tooth flexure*
* STURDEVANTS 27

27.  When selecting a restorative material, the clinician must
bear in mind the stress level during function.
 This should not exceed the Elastic Limit .
 If the stress level is beyond the elastic limit, a resulting
deformation is likely to occur which may cause failure at
some point of time
28

28.  Poisson‘s Ratio: Strain in the lateral direction to that in
the axial direction when an object is subjected to tensile
loading*
 Yield strength: The stress at which a test specimen
exhibits a specific amount of plastic strain.*
 Ultimate tensile strength: Tensile stress at the point of
fracture*
 * PHILLIPS 29

29. STRESS ANALYSES
30

30. Stresses in dental structures have been studied by
various techniques, such as
 brittle coating analysis,
 strain gauges,
 holography,
 2-dimensional (2D) 3-dimensional (3D) photo
elasticity
 finite element analysis (FEA),
 digital moiré interferometric investigation
Srirekha A, Bashetty K. Infinite to finite: An overview of finite
element analysis. Indian J Dent Res 2010;21:425-32
31

31. FINITE ELEMENT ANALYSIS
 More recent method of stress analysis, generally
developed in 1956 in the aircraft industry was the finite
element method (FEM).
 Introduced by Richard courant
 Initially, this technique was used widely only in
aerospace engineering, but slowly due to the
flexibility of the method to model any complex
geometries and provide instant results, it made its
presence felt in dentistry.
It was first used in dentistry in the 1970‘s to
replace photo elasticity tests. 32

32.  This method involves a series of computational
procedures to calculate the stress and strain in each
element, which performs a model solution.
 FEM circumvents many of the problems of material
analysis by allowing one to calculate physical
measurements 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 a
structure.
33

33.  Has the advantage of being applicable to solids of
irregular geometry and heterogenous material
properties.
 It is therefore ideally suited to examination of structural
behaviour of teeth.
34

34. BASIC CONCEPT OF FEM
 The FEM is a numerical procedure used for analyzing
structures
 It consists of a computer model of a material or design
that is stressed and analyzed for specific results.
 FEM uses a complex system of points(nodes) and
elements, which make a grid called as mesh.
35

35. 36

36.  This mesh is programmed to contain the material and
structural properties (elastic modulus, Poisson‘s
ratio, and yield strength), which define how the
structure will react to certain loading conditions.
 The mesh acts like a spiderweb, in that, from each node
there extends a mesh element to each of the adjacent
nodes.
37

37.  The basic theme is to make calculations at only limited
(finite) number of points and then interpolate the results
for 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 this
format.
 FEM reduces the dofs from infinite to finite with the help
of meshing (nodes and elements) and
all the calculations are made at limited number of nodes.
Geramy A, Sharafoddin F. Abfraction: 3D analysis by means of the finite
element method. Quintessence Int 2003;34:526-33.
38

38.  Each element retains the mechanical characteristics of
original structure.
 A numbering system is required to identify the elements
and their connecting points called nodes
39

39. 40

40.  Finite elements started with triangular elements these
elements being stiffer, resulted in less stress and
displacement.
 Later, quadrilateral elements were used for accuracy of
results.
 Increasing the number of calculation points(nodes and
elements) improves accuracy.
41

41.  For example,
increasing the number of lines reduces error margin in
finding out the area of a circle .
 The number of straight lines are equivalent to the
number of elements in FEM.
42

42. FEM is performed with material properties that can be
isotropic (same properties) or anisotropic (different
properties)
 All real-life materials are anisotropic, but it is simplified
into 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 in
the axial direction when an object is subjected to tensile
loading)
 yield strength for the materials are applied.
Anusavice KJ. Properties of dental materials. Phillip‘s Science of Dental
Materials. 10th ed. St. Louis Missouri: W.B Saunders Company;1996. p. 58.
43

43.  The analysis is performed as linear static analysis or
non-linear analysis depending on the allocation of
appropriate physical characteristics to the different parts
of the tooth.
 Linear systems are less complex and effective in
determining elastic deformation.
 Many of the non-linear systems are capable of testing a
material all the way to fracture and they do account for
plastic deformation*
*Infinite to finite: An overview of FEM .Indian J Dent 21(3) 2010 44

44. Mechanical properties of dental
structures
MATERIAL ELASTIC
MODULUS(Mpa)
POISSONS RATIO
Isotropic enamel 80000 0.3
Anisotropic enamel 20,000 0.08
Dentin 18,600 0.31
Cementum 18,600 0.31
Dental pulp 2.07 0.45
Periodontal ligament 50 0.49
Spongy bone 345 0.3
Compact bone 13,800 0.26 45

45. COMPARISION OF LINEAR AND NON
LINEAR FEM
LINEAR PROBLEMS
 Displacements vary linearly
with applied loads. Thus
stiffness is constant. Changes
in geometry due to
displacement are assumed to
be small, and hence are
ignored.
 Linear up to the
proportional/elastic limit.
Properties, such as Young‘s
modulus are easily available.
NON LINEAR PROBLEMS
 It is non-linear. Thus stiffness
varies as a function of load
 It is a non-linear function of
stress-strain and time.
These are difficult to obtain and
require a lot of additional
experimental material testing.
46

46. Linear problems
 The behavior of the structure
is fully reversible upon removal
of the external nodes.
 Computational time Small
 User‘s interaction with
the software is least required
Nonlinear problems
 The final state after removal of
load is different from the initial
state.
 Large
 Requires lot of monitoring as
the software may fail to
converge sometimes
47

47.  The eventual result of any FEM is the normal and
shearing stress values of the structure upon loading.
 The failure criteria is measured by Von-Mises stresses.
48
Kishen A, Ramamurty U, Asundi A. Experimental studies on the
nature of property gradients in human dentine. J Biomed Mater
Res 2000;51:650-9.

48.  The information needed for calculating the
stresses 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 with
each 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

49. In practice, an FEM usually consists of 3 principle steps
Pre-processing: It includes CAD (computer-aided
designing) data, meshing, and boundary conditions.
• Processing or solution: This is the step in which the
computer software does the job of calculation.
Internally, the software carries out matrix
formulations, inversion, multiplication, and solution.
 Post-processing: This step includes viewing
results, verifications, conclusions, and thinking about
what steps would be taken to improve the design.
Srirekha A, Kusum Bashetty 2010 Infinite to finite: An overview of finite
element analysis Indian J Dent Res, 21(3),425-432 50

50. Steps in finite element method: (a) 3D-
model; (b) meshing;
and (c) resultant stresses
51

51.  Steps in the solution procedure using
FEA
 1. Discretization of problem
 2. Imaging
 3. Meshing
 4. Boundary conditions
 5. Types of solutions
52

52. Discretization of problem
 Nodes work like atoms with gap in between filled by an
entity called as element.
 Calculations are made at nodes and results are
interpolated for elements.
There are two approaches to solve any problem:
 1. Continuous approach (all real life components are
continuous).
 2. Discrete approach ( equivalent mathematical
modeling).
53

53.  All the numerical methods including finite element follow
discrete approach.
 Meshing (nodes and elements) is nothing but
discretization of a continuous system with infinite
degree of freedoms to finite degree of freedoms
54

54. IMAGING
a) Imaging and three-dimensional Reconstruction:
 Three dimensional surface reconstructions created from
CT scans are used as templates for three-dimensional
finite element models.
 Initial 3D surface reconstructions are quite rough and
require significant editing before they can be imported
into a FE tool and successfully meshed as a finite
element model
55

55. b) Image processing: editing the three dimensional image.
 The ultimate goal of 3D image processing is to
generate a ―water-tight‖ surface model that can be
imported into and successfully manipulated in FE
software.
 The most important aspect of the simplification process
of three-dimensional images involves smoothening and
removing details in selected areas of the model.
 3Dsurface representations are composed of connected
polygons and are often referred to as ‗polygon models‘.
56

56. The more polygons a model contains, the greater is its
fidelity to the object it represents and the larger is its
size.
Image processing is the most labor-intensive aspect of
conducting FE analyses of biological structures.
57

57. MESHING
 FEM uses a complex system of points(nodes) and
elements, which make a grid called as mesh.
 Basic theme of FEA is to make calculations at only
limited (finite) number of points and then interpolate the
results for entire domain (surface or volume).
58

58. 59

59. 60

60.  Any continuous object has infinite degrees of freedom
and it is just not possible to solve the problem in this
format.
 FEA reduces degrees of freedom from infinite to
finite with the help of discretization i.e. meshing (nodes
and elements)
2D MESHING: simple
Allows the analysis to be run on a relatively normal
computer
Yields less accurate results
SHAPES :triangular, quadrilateral
61

61.  3D MESHING: produces more accurate results and can
run only the fastest computers effectively.
Boundary conditions
Boundary 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 run
for determining stresses &strains using linear static
analysis & nonlinear analysis
62

62.  Types of solutions
 The analysis is done to assess the stresses acting upon
the materials during function in the oral cavity by
applying various material properties
 These stresses are:
1. Normal or principal stress: acts perpendicular to the
cross section and causes elongation or compression.
2. Shear stress: acts parallel to the cross section and
causes distortion (changes in original shape).
63

63.  Maximum principal stress.
The maximum principal stress gives the value of stress
that is normal to the plane in which the shear stress is
zero.
 The maximum principal stress helps us understand the
maximum tensile stress induced in the part due to the
loading conditions
64

64.  Minimum principal stress.
The minimum principal stress acts normally to the plane in
which shear stress is zero.
 It helps you to understand the maximum compressive
stress induced in the part due to loading conditions
65

65.  Von Mises stress.
 The von Mises criterion is a formula for calculating
whether the stress combination at a given point will
cause failure.
 The von Mises criterion is a formula for combining three
principal stresses into an equivalent stress, which is then
compared to the yield stress of the material .The yield
stress is a known property of the material and is usually
considered for the failure stress.
66

66.  If the ―von Mises stress‖exceeds the yield
stress, then the material is considered to be at
the failure condition.
 The von Mises theory is used for ductile
materials such as metals and evaluates stresses
in both static and dynamic conditions
67

67. Software used for finite
element analysis
 The various software used in FEA are
Abaqus Explicit, Ansys, Dytran, Femfat,
Hypermesh , Ls - dyna , Madymo ,
Magmasoft, MSC Nastran, Pro mechanicaStar-
CD, Tosca, Unigraphics,
68

68. GENERAL APPLICATIONS OF FEM
 FEA has been applied for the description of form
changes in biological structures (morphometrics),
especially in the area of growth and development .
 The knowledge of physiological values of alveolar
stresses is important for the understanding of stress
related bone remodeling and also provides a guideline
reference for the design of dental implants
69

69. 70
 FEM is useful with structures containing potentially
complicated shapes, such as dental implants and
inherent homogenous material.
• It is useful for the analysis of stresses produced in the
PDL when subjected to orthodontic forces.
• It is also useful to study stress distribution in tooth in
relation to different designs.
• It is used in the area of optimization of the design of
dental restorations.
• It is used for investigation of stress distribution in tooth
with cavity preparation

70.  The type of predictive computer model described may
be used to study the biomechanics of tooth movement,
even though accurately assessing the effect of new
appliance systems and materials without the need to
go 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 in
the electrical fields.
• It is also used in optimization of sheet metal blanking
process.
71

71. Requirements for doing finite
element analysis
 Finite Element Analysis is done principally with
commercially 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 features
extensive capabilities -- plastic deformation, and
specialized work such as metal forming or crash and
impact analysis.
 Finite element packages may include pre-processors
that can be used to create the geometry of the
structure, or to import it from CAD files generated by
other software.
72

72.  The FEA software includes modules to create the
element mesh,
 to analyze the defined problem,
 and to review the results of the analysis.
 Output can be in printed form, and plotted results such
as contour maps of stress, deflection plots, and graphs
of output parameters.
NISA-II User's Manual; Feb. 1997, Version 7.0; Engineering Mechanics
Research Corporation, Troy, Michigan.
. Display-IV User's Manual; Mar. 2001, Version 10.5; Engineering
Mechanics Research Corporation, Troy, Michigan.
73

73.  The choice of a computer is based principally on the kind
of structure to be analyzed, the detail required of the
model, the type of analysis (e.g. linear versus nonlinear),
the economics of the value of timely analysis, and the
analyst's salary and overhead. An analysis can take
minutes, hours, or days.
74

74. Advantages
 When finite element modeling is compared with
laboratory testing, it offers several advantages.
 The variables can be changed easily, simulation can be
performed without the need for human material and it
offers maximum standardization.
 FEM can minimize laboratory testing requirement.
 FEM provides faster solutions with logical and
reasonable accuracy in an era where the industry prefers
faster solutions
75

75. Limitations
 The most significant limitation of FEA is that the
accuracy of the obtained solution is usually a function of
the mesh resolution.
 Any regions of highly concentrated stress, such as
around loading points and supports, must be carefully
analyzed with the use of a sufficiently refined mesh.
 In addition, there are some problems which are
inherently singular (the stresses are theoretically
infinite).
Special efforts must be made to analyze such problems
76

76.  Obtaining solutions with FEA often requires substantial
amounts of computer and user time.-- expensive
 finite element packages have become increasingly
indispensable to mechanical design and analysis.
77

77. Studies
78

78.  The use of this method in dental structures was started
in 1968 when Ledley and Huang developed a linear
model of the tooth based on experimental data and on
linear displacement force analysis.
 The one shortcoming of their study was that they
considered the tooth to be homogeneous structure.
 In reality the human tooth is highly inhomogeneous
since the elastic modulus of the enamel outer surface of
the tooth is about three times that of the inner dentin
material.
79

79.  The major contribution was made by
 W. Farah (1972),
 Thresher R.W (1973) and Yettram A.L (1976) who
modeled a tooth and studied the stresses in a tooth
structure using a finite element method. -
80

80. Stress distribution around implant
81
Three-dimensional finite element analysis of the stress distribution around the
implant and tooth in tooth implant-supported fixed prosthesis designs.
Journalof dental implants Year : 2011 | Volume : 1 | Issue : 2 | Page : 75-
79

81. After removing third molar
82
Finite Element Analysis of the Human Mandible to Assess the Effect of
Removing an Impacted Third Molar J Can Dent Assoc 2010;76:a72

82. Finite element analysis of stress concentration in
three popular brands of fiber posts systems used
for maxillary central incisor teeth
 Computer aided designing was used to create a 2-D
model of an upper central incisor.
 Post systems analyzed were the
DTLight Post (RDT, Bisco),
Luscent Anchor (Dentatus) &
RelyX (3M-ESPE).
The entire design assembly was subjected to analysis by
ANSYS for oblique loading forces of 25N, 80N & 125 N
83

83.  When a fiber-reinforced post is bonded within the root
canal, it dissipates functional and parafunctional
forces, reducing the stress on the root.
 Acute consequences of such forces in the assembly are
not anticipated, but there will be a gradual build-up of
destructive stresses that finally cause the failure of the
assembly.
 When a catastrophic force is placed on the crown of the
tooth, the crown will fracture instead of the
post, transmitting the energy of force down the root
and creating a vertical root fracture.
84

84.  Consequently, a post system should be able to dissipate
the function of energy and even overcome moderate
trauma.
 Fiber-reinforced posts have demonstrated the ability to
fracture at the coronal portion of a tooth restoration with
the presence of catastrophic forces without root fracture,
permitting scope of retreatment of the remaining root
structure.
85

85. 86

86. 87

87. Results
Materials Modulus of elasticity (Gpa)
DT LIGHT POST 13
LUSCENT ANCHOR 20
RELYX 37.5
88
Group C showed maximum stress distribution in the
entire structure and least forces generated (stress
concentration at apical third of the tooth model, which
was significantly different from other two groups.
Aggarwal S, Garg V. Finite element analysis of stress concentration
in three popular brands of fiber posts systems used for maxillary
central incisor teeth. J Conserv Dent 2011;14:293-6.

88. CUSPAL FLEXURE
 Magne and Oganesyan conducted one study to measure
cuspal flexure of intact and restored maxillary premolars
with different restorative materials:
 (mesio-occlusal-distal porcelain, and composite-inlay
restorations) and occlusal contacts (in enamel, at
restoration margin, or in restorative material).
 They concluded that a relatively small cuspal
deformation was observed in all the models.
 There is an increased cusp-stabilizing effect of ceramic
inlays compared with composite ones.
Magne P, Oganesyan T. Premolar cuspal flexure as a function of
restorative material and occlusal contact location. Quintessence Int
2009;40:363-70.
89

89. Tooth preparation design
 Zarone et al., evaluated the influence of tooth
preparation design on the stress distribution and
localization of critical sites in maxillary central incisor
restored by means of alumina porcelain veneers under
functional loading.
 They concluded that when restoring a tooth by means of
porcelain veneers, the chamfer with palatal overlap
preparation better restores the natural stress
distribution under load than the window technique.
Zarone F, Apicella D, Sorrentino R, Ferro V, Aversa R, Apicella A.Influence of
tooth preparation design on the stress distribution inmaxillary central
incisors restored by means of alumina porcelainveneers: A 3D-finite
element analysis. Dent Mater 2005;21:1178-88.
90

90. Influence of cavity design preparation on
stress values in maxillary premolar:
a finite element analysis
 To analyze the influence of cavity design preparation on
stress values in three-dimensional (3D) solid model of
maxillary premolar restored with resin composite.
 3D solid model of maxillary second premolar was
designed using computed-tomography (CT) data.
 Based on a factorial experiment, 9 different mesio-
occlusal- distal (MOD) cavity designs were
simulated, with three cavity wall thicknesses (1.5
mm, 2.25 mm, 3.0 mm),
91

91. 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 resin
composite restoration (Gradia Direct
Posterior,GC, Japan).
 Finite element analysis (FEA) was used to calculate
von Mises stress values
92

92. 93

93.  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 design
parameters, cuspal reduction (92.97%) and cavity wall
thickness (3.06%) significantly (P < 0.05) determined
the magnitude of stress values in enamel.
94

94. The influence of cavity design parameters on stress values
in dentin and resin composite was not significant.
 When stresses for enamel, dentine, and resin composite
were considered all together, palatal cusp coverage was
revealed as an optimal option.
 Cavity wall thickness did not show a significant effect on
stress values.
Conclusion
 a palatal cusp reduction could be suggested for
revealing lower stress values in dental tissues and
restorative material.
Ivana Kantardžić, Darko Vasiljević, Larisa Blažić,Ognjan Lužanin
2012Influence of cavity designpreparation on stress values
inmaxillary premolar:a finite element analysis.
Croat Med J. 2012;53:568-76l. 95

95. Stress analysis on non carious
cervical lesions
 An extracted human upper canine tooth was scanned by
μCT machine (Skyscan,Belgium).
 These μCT scans were segmented, reconstructed, and
meshed using ScanIP (Simpleware, Exeter, UK) to create
a three dimensional finite element model.
 A 100N load was applied axially at the incisal edge and
laterally at 45◦ midpalatally to the long axis of the canine
tooth.
 Separately, 200N axial and non-axial loads were applied
simultaneously to the tooth.
96

96.  It was found that stresses were concentrated at the
CEJ in all scenarios.
 Lateral loading produced maximum stresses greater
than axial loading,and pulp
tissues, however, experienced minimum levels of
stresses.
 This study has contributed towards the understanding
of the aetiology of non-carious cervical lesions which is a
key in their clinical management.
97

97. Micro-CT imaging, modelling, and
developing FE model of canine
tooth
98

98. 3D model of canine, FE mesh
99

99. Lateral loading on 3D FEmodel
100

100. Von mises stress distribution caused by
100 N vertical load
Buccal view Lingual view
101

101. Stress distribution caused by
100 N lateral loading
Lateral view Buccal view
102

102. 200 N LATERAL VIEW, BUCCAL
VIEW
103

103. Enamel‘s displacement caused by
100 N
Vertical loading Lateral loading
104

104.  Enamel has suffered much higher stresses than dentine
especially at the cervical buccal CEJ region under lateral
loading
 The enamel tooth tissue is known to be thin, having a
very weak prismatic structure and low ultimate tensile
strength at the CEJ.
 In addition, the CEJ is usually subject to erosion and
abrasion, caused by acidic exposure and tooth
brushing, respectively, which further weaken and
undermine
the structure of cervical enamel and dentine
 Therefore, tensile stresses, along with other contributing
factors, concentrated at the CEJ seem to be most
105

105.  Conclusions of this study
(1) maximum stresses and crown displacement generated
by lateral loading were generally higher than the vertical
loading;
(2) peak stresses were concentrated at the CEJ in all
loading scenarios;
(3) the greatest levels of stress generated within enamel
and dentine were located at the CEJ when axial and
non-axial loadings were applied simultaneously;
106

106. (4) pulp tissues sustained the minimum level of
stress under all loading conditions
Shihab A. Romeed, RaheelMalik, and Stephen M. Dunne .Stress
Analysis of Occlusal Forces in Canine Teeth and Their Role in the
Development of Non-Carious Cervical Lesions: Abfraction.
International Journal of Dentistry Volume 2012, Article ID 234845, 7
pages
107

107. CAST POST, FIBRE POST
108

108. 109

109. ENDOCROWNS, CONVENTIONAL
CROWNS
110

110. 111

111.  The stress values on the dentin and luting cement for
the endocrown restoration were lower than those for the
crown configuration.
 Weibull analysis revealed that the individual failure
probability in the endocrown dentin and luting cement
diminished more than those for the crown restoration.
112

112.  While the overall failure probabilities for the endocrown
and the classical crown were similar, fatigue fracture
testing revealed that the endocrown restoration had
higher fracture resistance than the classical crown
configuration (1,446 vs. 1,163 MPa)
Finite element and Weibull analyses to estimate failure risks in the
ceramic endocrown and classical crown for endodontically treated
maxillary premolar Eur J Oral Sci 2010; 118: 87–93 .
113

113. Carbon post
 The analysis of the von
Mises stress values for
carbon post model showed
that maximum stress
concentrations were
noted on the coronal
third and the cervical
area of the root in the
range of 353.149 and
13.878 MPa
114
Özkan ADIGÜZEL, Sadullah KAYA, Senem YİĞİT ÖZER, Yalçın DEĞER.
Three-dimensional Finite Element Analysis of Endodontically Treated Tooth
Restored with Carbon and Titanium Posts (Int Dent Res 2011;2:55-59)

114. Titanium post
 Titanium post model
showed that maximum
stress concentrations
were noted on the
coronal third and the
cervical area of the root
in the range of 540.736
and 22.777 MPa.
115

115.  This study shows that titanium posts
yields larger stresses than carbon post.
Özkan ADIGÜZEL, Sadullah KAYA, Senem YİĞİT ÖZER, Yalçın
DEĞER.Three-dimensional Finite Element Analysis of
Endodontically Treated Tooth Restored with Carbon and
Titanium Posts (Int Dent Res 2011;2:55-59
116

116. Conclusion
 Finite element analysis has proved to be the most
adaptable, accurate, easy and less time consuming
process as compared to the other experimental analysis.
It has provided clinicians with useful information to
achieve higher degree of success and satisfaction to the
patients
117

117. Thank you
118

118. 119

119. Good morning!
121

120. Stress analysis
 Strain guages
 Photoelastic method
 Holography.
 Brittle coating analysis
122

121. Strain guage
A strain gauge is a device used to measure
deformation (strain) of an object
 Invented by Edward E. Simmons and Arthur C.
Ruge in 1938
 The most common type of strain gauge consists
of an insulating flexible backing which supports
a metallic foil pattern .
 The gauge is attached to the object by a
suitable adhesive 123

122.  A strain gauge is a long length of conductor
arranged in a zigzag pattern on a membrane.
 When it is stretched, its resistance increases.
124

123. 125

124.  They use the principle that when a certain electrical
resistance is subjected to an object, it produces strain .
 Tension produces an increase in resistance; compression
causes a decrease in resistance .
 Therefore, if such a strain gauge were bonded to the
surface of a structure under a load, monitoring the
resistance changes would yield knowledge of the strain
characteristics at that point
126

125. Photoelastic methods
127

126.  Photoelasticity is a nondestructive, whole-field, graphic
stress-analysis technique based on an optomechanical
property called birefringence, possessed by many
transparent polymers.
 Noonan was the first to apply photoelasticity
to restorative dentistry
128
TAM 326—Experimental Stress Analysis
James W. Phillips

127.  Based on the property of some transparent materials to
exhibit colorful patterns when viewed with polarized
light.
 These patterns occur as the result of alteration of the
polarized light by internal stresses into two waves that
travel at different velocities
 The pattern that develops is consequently related to the
distribution of the internal stresses and is called
Photoelastic effect
129
TAM 326—Experimental Stress Analysis
James W. Phillips

128.  To use this special characteristic, a model of the
structure of interest must be fabricated in the right
dimensions and proportions .
 The model should be made from a transparent material
capable of exhibiting a photoelastic response .
 The stresses that develop in the model as the result of
the applied loads can then be visualized by examining
the model with polarizing filters
131

129.  The general procedure for photoelastic analysis involves
bonding a special plastic coating onto the
structure, shining polarized light onto the plastic, and
then analyzing the resultant images.
132

130. 133

131.  The polarizer has the property of passing only those
components of the incident light waves which are
parallel to the polarizing axis.
 Consequently, plane polarized light is produced which
impinges upon the stressed model made of a material
exhibiting temporary double refraction under stress.
134

132. 136

133. Selecting the material.
Many polymers exhibit sufficient birefringence to be used
as photoelastic specimen material.
However, such common polymers as
polymethylmethacrylate (PMMA) and polycarbonate may
be either too brittle or too intolerant of localized
straining.
 Homalite®-100 (araldite) has long been a popular
general purpose material, available in various
thicknesses in large sheets of optical quality.
137

134.  PSM-1® is a more recently introduced material that has
excellent qualities, both for machining and for fringe
sensitivity.
 Another good material is epoxy, which may be cast
between plates of glass, but this procedure is seldom
followed for two-dimensional work
138

135. Advantages and
disadvantages
Advantages.—Photoelasticity, as used for two dimensional
plane problems,
• provides reliable full-field values of the difference
between the principal normal stresses in the plane of the
model
• provides uniquely the value of the nonvanishing
principal normal stress along the perimeter(s) of the
model, where stresses are generally the largest
139

136.  furnishes full-field values of the principal stress
directions (sometimes called stress trajectories)
 is adaptable to both static and dynamic Investigations .
 requires only a modest investment in equipment and
materials for ordinary work
 is fairly simple to use
140

137. Disadvantages.—
On the other hand, photoelasticity requires that a model of
the actual part be made (unless photoelastic coatings
are used)
• requires rather tedious calculations in order to separate
the values of principal stresses at a general interior point
• can require expensive equipment for precise analysis of
large components
• is very tedious and time-consuming for three-dimensional
work
141

138. Two-dimensional Photoelastic Stress
Analysis of
Traumatized Incisor
 Two homogeneous two-dimensional central incisor
models were prepared from Araldite B (Ciba-Geigy S.A.,
Bale, Switzerland), a birefringent plastic material with a
modulus of elasticity within the range of human dentin.
142
Braz Dent J (2001) 12(2): 81-84 Two-dimensional Photoelastic
Stress Analysis of Traumatized Incisor

139.  Each specimen was 5 mm thick. Alveolar bone was also
prepared from Araldite B. The models were loaded with
a 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

140.  When photoelastic material is subjected to force, optical
properties change in direct proportion to the stresses
developed.
 The material becomes ―birefringent‖ and a colorful
interference pattern is observed when polarized light
passing through the stressed material splits into two
beams.
 A fringe is defined as a line separating the red and green
color bands
144

141.  A fringe order will consist of a sequence of color
bands, including fringe line.
 The zero fringe order is black and indicates no stress.
Stress can be quantified and localized by counting the
number of fringes and density. The closer the
fringes, the steeper the stress gradient, indicating an
area of stress concentration
145

142.  This case shows that the normal forces applied to teeth
on the apical area cause more stress than those applied
at an angle.
 It has been observed that the highest stress value is
obtained under F2 loading.
 This fact clearly shows that pulp dies when the effected
force is transferred to the apical third of the tooth that
has not been fractured after trauma.
When crown fracture occurs, the force affecting the tooth
divides into its components and causes less damage to
the pulp.
146

143.  A fracture occurs if the effecting force exceeds the
resistance against the sliding force of hard tissue.
 Otherwise the resistance depending on the strength and
direction of the force may cause pathological damages
 Finally, the forces exerted horizontally to the labial side
of the tooth caused more stress on the tooth and
alveolar bone than inclined forces
147

144. Comparison between FEM and
PEM
FEM
 All stress components are
calculated.
 Changes of relavant
parameters and loads can
be easily incorporated
into calculation program .
 Allowance can be made
for any homogeneity and
anisotropy in material
photoelasticity
 All stress components are
not calculated.
 Only fringe patterns
represent stress values.
 Model should mimic
actual structure
148

145. FEM
 Super computers and
highly expensive
softwares are needed.
 Based on meshing and
imaging of nodes and
elements
PHOTOELASTICITY
 It uses a polariscope,and
photoelastic polymers
only for evaluation of
stress patterns
 Based on wave theory of
light and polarization
principle.
149

146. Holography
 Holographic interferometry, a non-
destructive full-field technique that
measures small static or dynamic
deformations occurring in an object, is
based upon standard holographic
principles
150

147.  Holography was previously used to investigate various
deformations of dentures or dental implants
 Holography is a method for recording three-dimensional
information on a two-dimensional recording medium
(photographic emulsion, thermoplastics, etc)
 Unlike a photograph, the hologram contains all the
information about the surface of the object .
T. Puškar, et al., Holographic interferometry as a method
for measuring strain caused... Contemporary Materials,
I–1 (2010) 151

148.  Holography follows a different principle from
conventional photography.
 A laser is needed to produce a coherent, monochromatic
light beam.
 The difference in phase between a reference ray and the
object ray (to be analyzed) produces an interference
pattern that is recorded on a high-resolution
photographic plate (hologram).
 When developed and suitably exposed to laser light, this
hologram reconstructs a three-dimensional image of the
object.
 Resolution is that of the order of the laser wavelength
or that of a photographic film
152

149. 153

150.  The hologram is an interference pattern of
coherent wave fronts scattered from the object
and recorded by the medium .
 The basic principles of holography underly the
technique in double-exposure holographic
interferometry .
154

151. 156

152.  Because tension moves perpendicularly to the fringes, it
is possible to evaluate tension distribution within the
body of the mandible quantitatively .
 The higher the number of fringes, the greater the
tension transmitted.
 Qualitative evaluation is achieved by observing the
aspect and direction of the fringes
157

153.  Real-time holography is a dynamic method
through which the deformations can be
monitored during the entire experiment .
Detection and recording of the interference
pattern can be done with CCD camera and
computer .
158

154. BRITTLE COATING ANALYSIS
 Brittle Lacquer stress analysis makes use of a
brittle coating also known as brittle lacquer
or StressKote.
 The brittle coating will fracture in response to
the surface strain beneath it.
 The coating indicates the direction and
magnitude of stress within the elastic limit of the
base material.
159

155.  Stresscoat coatings provide a graphic picture of
the distribution, direction, location, sequence
and magnitude of tensile strains.
 The coating cracks at a predetermined value.
 This value is determined by a simple calibration
method.
160

156. 161
Craig and Peyton Measurement of
Stresses in Fixed-Bridge Restorations
Using a Brittle Coating Technique.
J. dent. Res. July-A list 1965

157.  The bridges were cleaned with carbon disulfide and
sprayed with the desired brittle lacquer.
 The selection of the lacquer depends
on the humidity, temperature, and sensitivity.
 The lacquer is sprayed so that a uniform coating of
0.005- 0.006 inches is applied to the bridge.
 An air pressure of 20-psi gauge was adequate, and
3-4 passes of the lacquer spray at a distance
of 2.5 inches produced the proper coatings
162

158.  The stress may be calculated by multiplying the
sensitivity of the lacquer by the modulus of elasticity of
the material which is coated.
 For example, if a crack is observed in the lacquer coating
on one of the gold-alloy bridges during loading, the
strain at this position is 800 micro inches/inch and the
stress 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 of
elasticity of the alloy.
163

159. Conclusion
Stress analysis techniques are invaluable for clinicians and
manufacturers of dental materials as they help in
evaluating critical stress levels of various materials .They
help in evaluating the mechanical properties of dental
materials under laboratory conditions and also give a
three dimensional view .Their accuracy has been a point
of confrontation for many years
164

160. Thank you
165