Finit element in prosthodontics /certified fixed orthodontic courses by Indian dental academy

INDIAN DENTAL ACADEMY
Leader in continuing dental education
www.indiandentalacademy.com


EDENTULOUS STATE
Finite element analysis is a numerical method based on the principle of dividing
a structure into finite number of small elements that are interconnected with
each other at the corner points or nodes having 3 degrees of freedom which
translates in X, Y and Z directions.
Each element is assigned unique elastic properties (Poisson’s ratio and
Modulus of Elasticity) to represent the materials modeled and for each element
its mechanical behavior can be written as a function of displacement of the
nodes.
The nodes are submitted to certain loading conditions resulting in a behavior of
the model similar to the structures it represents. When a computer analysis is
performed a system of simultaneous equations can be solved to relate all forces
and displacements at the nodes.
From this stresses and stress contours can be established in each element and
thus for the whole body.


The study was divided into following heads


Construction of geometric model



Preparing the finite element mesh



Validation of model



Application of forces and boundary conditions



Analysis of stress pattern


Construction of Geometric Model


Modeling of Mandibular canine





Complete Geometric Model of Tooth with Surfaces United at Different Levels




Mandibular Canine Characteristics
Length of the Crown
Length of Root
Mesiodistal Diameter of crown
Mesiodistal Diameter at cervix
Buccolingual Diameter
Buccolingual Diameter at cervix
Curvature of cervical line – mesial
Curvature of cervical line – distal

= 10.5 mm
= 16.0 mm
= 7.0 mm
= 5.5 mm
= 7.5 mm
= 7.0 mm
= 2.5 mm
= 1.0 mm




Modeling of Attachment designs

Bar-Clip Attachment
Dimension of Bar : 3 mm wide x 1.5 mm depth
Coping : 0.5 mm
Post : 5 mm

Ball-Socket Attachment

Dimension of Ball: 2 mm dia.
Post :
www.indiandentalacademy.com10 mm



Modeling of Periodontal ligament




Modeling of Mandibular body (cortical and cancellous bone)

Total length of edentulous Mandibular body = 70 mm
Length of mandible posterior to canine = 35 mm
Inter-canine distance = 20 mm
Height = 23 mm
Width = 11.5 mm
Thickness of cortical bone
Labial = 1 mm
Lingual = 2 mm
Cranial = 1 mm
Caudal = 4 mm
Thickness of alveolar bone proper = 2 mm



Modeling of Mucosa and Overdenture

Thickness of Mucosa : 2 mm

Overdenture:
Height above abutment = 6 mm,
Width of overdenture = 12 mm

Preparation of Finite Element Mesh
A 3-D finite element model was generated using Cosmos Pre and
Post Processor GeoStar.
The structure except for periodontal ligament was idealized using 8noded 3-D solid brick elements (Hexahedral) having 3 degrees of
freedom per node (i.e. Mesial, Axial and Facial directions).
The periodontal ligament space was meshed by using 1-D spring
elements and the orientation of these spring element was duplicated
fro the orientation of principal fibers as seen in histological sections
and were uniformly spaced throughout the tooth.


Completed Finite Element Model

Bar-Clip Attachment


Distribution of Elements and Nodes
(Bar-Clip & Ball-Socket)

No. of Elements (3D + 1D)

No. of Nodes

Total degree of Freedom

Bar-Clip

29085

32859

95678

Ball Socket

29301

33056

95886


Material Properties Assigned to the Various
Components of Finite Element Model
Material

Modulus of Elasticity (Mpa)

Poisson’s ratio

Dentin

18000

0.31

Cementum

18000

0.31

69

0.45

Cortical bone

13700

0.30

Cancellous bone

1370

0.30

10

0.40

182000

0.30

Acrylic resin

2260

0.37

Gutta-percha

0.69

0.45

18000

0.31

Periodontal ligament

Mucosa
Ni-Cr metal

Zinc-Phosphate cement


VALIDATION OF MODEL
The mathematical model was verified by computation of the axial
displacement corresponding to 10 N vertical force to the canine.
A displacement of 0.02-0.03 mm was computed, were obtained by
assigning the physical constants to the elements in the models.
Displacements were used to judge the appropriate mesh size as it
provides a convenient and useful measure in most linear problem.


APPLICATION OF BOUNDARY CONDITIONS
Symmetric boundary conditions were imposed at the mid symphyseal
region since only half of the mandible was modeled. On the distal side all
the three translation were fixed to simulate the exact physiologic situation.


APPLICATION OF FORCES
•

Two different types of forces were applied:

– Static distributed load of 70 N consistent with incisal bite force in denture
wearers applied to the incisal third of the abutment.

– As during bilateral biting, a distributed load of 120N, directed anteriorly and
downward at an angle of 15 degrees to the vertical was applied in first molar
region.


ANALYSIS OF STRESS PATTERN
The stress distribution in the structure is presented in the form of contour
plots of different cases of model studied. In order to get clear picture of
the stress status the contour plots of Von Mises Stress have been made
separately for the areas of special interest i.e. in the attachment design,
tooth, cortical bone around the tooth and the bone at the back separately
by using Iterative Solver of Cosmos M / Ver. 2.5 of Finite Element
Software.


Von Mises Stress Value (in Mpa) in Attachments
for Two Attachment Designs under 70 and 120
Newton Force
Bar-Clip
70 Newton (Group I)
120 Newton (Group II)

Ball-Socket

90

109

53.45

80.14


Under 70 Newton Force

Bar-Clip Attachment


Bar-Clip Attachment www.indiandentalacademy.comBall-Socket Attachment

Von Mises Stress Value (in Mpa) in Abutment
Tooth for Two Two Attachment Designs under
70 and 120 Newton Force
Bar-Clip

Ball-Socket

70 Newton (Group I)

26.4

47.2


6.64

46.55



Bar-Clip Attachment
www.indiandentalacademy.comBall-Socket Attachment

Von Mises Stress Value (in Mpa) in Top and
Apical Cortical Layer for Two Attachment
Designs under 70 and 120 Newton Force
Top Cortical Layer

Apical Cortical Layer

Bar-Clip
70 Newton (Group I)

Ball-Socket

Bar-Clip

Ball-Socket

17

23

4.5

6.7

15.54

16.24

8.82

8.27


RESULTS
• The stress transmitted to the abutment tooth using two different
attachment designs varied from 2-47.2 Mpa for two different
masticatory loads applied. The maximum of 47.2 Mpa was transmitted
in case of Ball-Socket Design and that of 43.50 in Bar-Clip Design.
• The stress transmitted to the cortical bone using two different
attachment designs varied from 2-22 Mpa for two different masticatory
loads applied. In top cortical layer it was 22 Mpa maximum, while in
apical cortical layer it was 43 Mpa and in posterior cortical layer it was
11.5 Mpa
• For the top cortical layer, maximum stress of 23 Mpa was transmitted
in case of Ball-Socket Design, while 17 Mpa was transmitted in case of
Bar-Clip Design.


RESULTS
• For the apical cortical layer, Bar-Clip design transmitted a little high
value of 14.3 Mpa than 12.50 as transmitted by Ball-Socket design.
• There was no difference in the stress transmitted to the posterior
cortical layer in the first molar region for the two attachment designs
under masticatory loads.
• Among the two masticatory forces, 70 N incisal force transmitted the
maximum stresses to the abutment tooth and cortical bone. At this
load Ball and Socket Design showed maximum stress value of 47.2
Mpa in abutment tooth and 23 Mpa in cortical bone, while the Bar-Clip
design, the value was 26.4 Mpa and 17 Mpa respectively.
• The stress transmitted to the two attachment designs varied from 6 to
121.07 Mpa. The maximum stress 121.07 Mpa was found in BallSocket, while Bar-Clip showed a value of 90 Mpa.


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Finit element in prosthodontics /certified fixed orthodontic courses by Indian dental academy

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