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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.
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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
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Construction of Geometric Model ď ą
Modeling of Mandibular canine
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Construction of Geometric Model ď ą
Modeling of Mandibular canine
Complete Geometric Model of Tooth with Surfaces United at Different Levels www.indiandentalacademy.com
Construction of Geometric Model
Modeling of Mandibular canine
Mandibular Canine Characteristics Length of the Crown = 10.5 mm Length of Root = 16.0 mm Mesiodistal Diameter of crown = 7.0 mm Mesiodistal Diameter at cervix = 5.5 mm Buccolingual Diameter = 7.5 mm Buccolingual Diameter at cervix = 7.0 mm Curvature of cervical line – mesial = 2.5 mm Curvature of cervical line – distal = 1.0 mm
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Construction of Geometric Model ď ą
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 : 10 mm www.indiandentalacademy.com
Construction of Geometric Model ď ą
Modeling of Periodontal ligament
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Construction of Geometric Model ď ą
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 www.indiandentalacademy.com
Construction of Geometric Model ď ą
Modeling of Mucosa and Overdenture
Thickness of Mucosa : 2 mm
Overdenture: Height above abutment = 6 mm, www.indiandentalacademy.com 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.
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Completed Finite Element Model
Bar-Clip Attachment
Ball-Socket Attachment www.indiandentalacademy.com
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
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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
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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.
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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.
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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.
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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.
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Von Mises Stress Value (in Mpa) in Attachments for Two Attachment Designs under 70 and 120 Newton Force
70 Newton (Group I) 120 Newton (Group II)
Bar-Clip
Ball-Socket
90
109
53.45
80.14
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Under 70 Newton Force
Bar-Clip Attachment Ball-Socket Attachment www.indiandentalacademy.com
Under 120 Newton Force
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
120 Newton (Group II)
6.64
46.55
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Under 70 Newton Force
Bar-Clip Attachment Ball-Socket Attachment www.indiandentalacademy.com
Under 120 Newton Force
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
70 Newton (Group I) 120 Newton (Group II)
Apical Cortical Layer
Bar-Clip
Ball-Socket
Bar-Clip
Ball-Socket
17
23
4.5
6.7
15.54
16.24
8.82
8.27
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Under 70 Newton Force
Bar-Clip Attachment Ball-Socket Attachment www.indiandentalacademy.com
Under 120 Newton Force
Bar-Clip Attachment www.indiandentalacademy.comBall-Socket Attachment
Under 70 Newton Force
Bar-Clip Attachment Ball-Socket Attachment www.indiandentalacademy.com
Under 120 Newton Force
Bar-Clip Attachment www.indiandentalacademy.comBall-Socket Attachment
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.
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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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