Analysing Mechanical Property of Two Different Closing Loops using Finite Element Analysis and Universal Testing Machine: A Comparitive Study

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ANALYSING MECHANICAL PROPERTY OF TWO

DIFFERENT CLOSING LOOPS USING FINITE

ELEMENT ANALYSIS AND UNIVERSAL TESTING

MACHINE - A COMPARITIVE STUDY

Dissertation submitted to

THE TAMILNADU Dr.M.G.R.MEDICAL

UNIVERSIT Y

In partial fulfillment for the Degree of

MASTER OF DENTAL SURGERY

BRANCH

–

V

ORTHODONTICS AND DENTOF ACIAL ORT HOPE DICS

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CERTIFICATE

This is to certify that the dissertation entitled

“Analysing mechanical pr operty of two different closing

loops using finite element analys is and universal

testing machine - A comparitive study done by

Dr. A. Dinesh K umar, post graduate student (M.D.S),

Orthodontics (branch V), Tamil Nadu Govt. Dental College

and Hospital, Chennai, submitted to the Tamil Nadu

Dr.M.G.R. Medical University in par tial fulfillment for the

M.D.S. degree examination (March 2010) is a bonafide

research work carried out by him under my supervis ion and

guidance.

Guided B y

D r. M .C. SAINATH M DS

Pro fe sso r,

Dept . o f Ort ho do nt ic s a nd De nt o fac ia l Ort ho ped ic s , Ta mil N adu Go vt De nt a l Co llege & Ho sp it al,

C he nna i - 3

D r. W.S.M ANJULA, M . D . S. , Dr. K.S.G.A. NASSER, M . D . S. ,

Pro fe sso r a nd Head o f De part me nt Princ ip a l,

Dept . o f Ort ho do nt ic s a nd Ta mil Nadu Go vt Dent a l De nt o fa c ia l Ort ho ped ic s, Co lleg e & Ho sp it a l, Ta mil N adu Go vt De nt a l Co llege Che nna i- 3

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DECLARATION

I, Dr.A.Di nes h k um ar d o hereb y d ec lare t ha t t he d isser ta t ion t it le d

“Analysing m echanica l proper ty of two d i fferent clos ing loops using f ini te

elem ent analys is and universa l tes ting m achine - A com paritive s tudy” was done in t he Depar tme nt of Ort hod ont ics, Tam il N adu Gover nme nt De nta l

Colle ge & H osp it a l, Che nna i 600 003. I ha ve ut iliz ed t he fac il it ies pr ovided

in t he G over nme nt De nta l C olleg e for t he stud y in p art ia l fu lfil lme nt of t he

requ ir em e nts for t he deg ree of Mast er of Denta l Surger y in t he sp ec ia lt y of

Orthod ont ics a nd De nt ofac ia l Ort hop ed ic s (Branc h V) dur ing t he c ours e

per iod 200 7 -2010 u nd er t he c onc ep tu a liz a t ion a nd gu id a nc e of m y

d issert at ion gu ide, Pr ofessor Dr.M.C.Sa ina th MDS. I de c lare t ha t no pa rt of

t he d issert at ion w ill be u t iliz ed for ga ini n g fina nc ia l ass ist a nc e for r ese arc h

or ot her pr om ot ions w it hou t obt a ining pr ior perm iss ion fr om t he Ta m il Nad u

Gove r nm e nt De nta l C olle ge & H osp ita l. I a ls o d ec lare t hat no par t of t his

wor k w il l be pub lis he d e it her in t he pr int or e le ctr onic m ed ia ex cep t w it h

t hose w ho ha ve bee n a ct ive l y invo lve d in t his d issert at ion w or k a nd I firm l y

a ffir m t ha t t he r ig ht t o pr eser ve or pub lis h t his wor k r ests s ole ly w it h t he

pr ior per m iss ion of t he Pr inc ipa l, Tam il Na du G over nme nt D e nt a l C olleg e &

Hosp ita l, C he nna i 600 003, b ut w it h t he vested r ig ht t hat I s ha ll b e c it ed as

t he aut hor(s).

S ig nat ure o f t he PG st ude nt Sig nat ure o f t he HO D

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ACKNOWLEDGMENT

My s incere thanks to Dr.K.S. G.A.NASSER, M.D.S.,

Principal, Ta mil Nadu Government De ntal College and

Hospital, C hennai-3, for his kind s upport and encourage ment.

I express my deep sense of gratitude and great honor

to my respected Pr ofessor Dr.W.S.MANJULA M.D.S, Head

of the Depar tment, Department of Orthodontics and

Dentofacial orthoped ics, Tamilnadu Govt. Dental College

and Hospital, Chennai -3, for her inspiration and

encouragement throughout the study and the entire course.

I consider as my privilege and a great honor to express my

gratitude to Dr. C.KARUNANI THI M.D.S., Professor Department of Orthodontics and Dentofacial orthopedics,

Tamilnadu Govt. Dental C ollege and Hospital, Chennai -3,

for his patient guidance, suppor t and encouragement

throughout the study.

I owe my thanks and gr eat honor to

Dr.M.C.SAINATH M.D.S, Professor, Dept of Orthodontics

and Dentofacial Orthopedics, Tamilnadu Govt. Dental

College and Hos pital, Chennai -3, for helping me with his

valuable and timely suggestions and encouragement.

I am gr ateful to Dr.S. PRE M KUMAR., M.D.S.,

Dr. S.NAGALAKSHMI., M.D.S., and Dr. USHA RAWA T,

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Orthodontics, Tamil N adu Government Dental C ollege and

Hospital, C hennai – 600 003 for their support and

encouragement.

I thank, Dr.G.RAVA NAN. M.Sc., M.Phil., P h.D., Professor of Statistics, Presidency College for helping me with the Statistics in the study.

A special mention of thanks to all my study subjects

for their consent, cooperation and participation.

I take this opportunity to express my gratitude to my

friends and colleagues for their valuable help and

suggestions thr oughout this study.

I offer my heartiest gratitude to my family members

for their selfless blessings.

I seek the blessings of the Almighty God without

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LIST OF GRAPHS

Graph

No Title

Page

No

1 Force obtained on activation of tear drop loop to 2mm in universal testing machine

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2 Force obtained on activation of t loop loop to 2mm in universal testing machine

41

3 Mean force tendency (n) for t loops and tear drop loops mechanical tes ting

45

4 Mean force tendency (n) for t loops and tear drop loops mechanical tes ting

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CLOUR PLATES

Fig 1 - Arma mentarium

Fig 2 - Template or millimeter jig for T loop

Fig 3 - T loop placed on the jig

Fig 4 - Measuring T loop dimens ion us ing

digital caliper

Fig5 - Modeling and mes hing of T loop

(co mputer s imulation)

Fig 6 - Template or millimeter jig for Tear drop loop

Fig 7 - Tear drop loop placed on the jig

Fig 8 - Measuring Tear drop loop dimens ion with

digital caliper

Fig 9 - Modeling and mes hing of Tear drop loop

(co mputer s imulation)

Fig 10 - Universal tes ting machine

Fig 11 - T loop before activation

Fig 12 - Tear drop loop before activation

Fig 13 - T loop after activation

Fig 14 - 2mm activation of T loop in finite

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Fig 15 - Tear drop loop after activation

Fig 16 - 2mm activation of Tear drop loop in finite

ele ment analys is

Fig 17 - Vonmises stress during 2 mm activation of

T loop in finite ele ment analys is

Fig 18 - Vonmises stress during 2 mm activation of

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Introduction

INTRODUCTION

Orthodontic bio mechanics invo lves controlled

application of mo ments and forces to bring about des ired

tooth move ment and favourable tiss ue response. To

understand the forces and mo ments generated on the teeth

and s urrounding tiss ues in respo nse to applied load, severa l

experiments were carried out.

The major goals of these experimental testing

methods were mainly to predict the optimal force levels that

can be applied to the teeth and supporting structures.

Among the various in vitro models created to s imulate the

complex oral environment, finite element analys is used in

recent past is t he near accurate model to analys e the

structural s tress /strain relations hip of the teeth and

surrounding structures in response to the force applied. This

method is based on the separation of the analys is s hape into

sub domains through finite elements. This separation allows

a point analys is of the phys ical behaviour of the object

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Introduction

In fixed orthodontic mechanotherapy, with adve nt o f

new orthodontic arch wires, various types of loops were

used for space clos ure. While selecting a loop for

orthodontic space clos ure, a great deal of attention must be

paid in ter ms of the individual clinical problem and

anato mical constrains. The co mmon variables that are

analysed in selecting loop mechanotherapy include the loop

des ign, its quantity of activation, wire thickness, the meta l

alloy used, type of movement des ired and the a mount of

force. When choos ing loops for clos ing spaces, it is of

utmos t importance for the professional to deter mine

precisely the force s ys tems generated, the magnitude of the

forces and the mo ments released when these loops are

activated.

Among the various arch wire materials used to

construct loops, beta titanium is the best material of choice.

β - Titanium wires have improved values of spring back

which markedly increases their working range for toot h

move ment. For a given cross section, it can be deflected

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Introduction

per manent defor mation. The hig h formability of β -titaniu m

allows the fabrication of clos ing loops with or without

helices.

In this study, ‘T’ and Tear drop retraction loops of

TM A 0.017 x 0.025 inch rectangular wire were used. Tear

drop loops are s imple in des ign with better complianc e and

flexible making this loop to be mos t widely us ed for space

clos ing in both arches. T loop by itself will have a

relatively low load-deflection rate and a large maximu m

spring back. Anchorage can be control led by varying the

location of loop pos ition. The large inter attachment

distance between the auxiliary tube on the first molar and

the vertical tube of the canine allows sufficient roo m for

the large activations required. Small errors in the s hape or

geometry of the loop will not radically change the forces.

The purpose of this study was to evaluate the

computer s imulation and compare it with that of mechanica l

testing to predict the force obtained from activation of ‘T’

loops and Tear drop loo ps. ‘T’ loop and Tear drop loop

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Introduction

and force were analysed. The Teardrop and ‘T’ loops were

als o manually made and force analysed with universal

testing machine. The res ults obtained in both the groups

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Aims and Objectives

AIMS AND OBJECTIVES

The aim of this study is to evaluate the force obtained

from activation of ‘T’ loop and Tear drop loop by

mechanical testing method and to compare it with force

obtained from activation of ‘T’ loop and Tear drop loop by

Finite Ele ment Analys is.

The objectives of the study are:

1. To measure the force exerted by 25‘T’ loops at

various levels of activation by mechanical testing

method.

2. To meas ure the force exerted by 25 Tear drop loops at

various levels of activation by mechanical testing

method.

3. To meas ure the force exerted by computer s imulated

‘T’ loop at various levels of activation using Finite

Ele ment Analys is.

4. To meas ure the force exerted by computer s imulated

Tear drop loop at various levels of activation us ing

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Aims and Objectives

5. To co mpare and analys e the force values obtained

from mechanical testing method and Finite Ele ment

Analysis for ‘T’ loops

6. To co mpare and analyse the force values obtained

from mechanical testing method and Finite Ele ment

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Review of Literature

REVIEW OF LITERATURE

BIOMECHANICS

Schwarz5 8 (1932) detailed the tissue response to the

magnitude of the applied force with the capillary bed blood

press ure. He concluded that the force delivered as part of

orthodontic treatment s hould not exceed the ca pillary bed

blood press ure (20 -26g/c m2 of root s urface).

Reitan5 1 (1957) s tated that the force exerted in a tipping

move ment perfor med with continuous forces will create

compressed, cell-free areas in the periodontal membrane

more frequently than in a bo dily mo ve ment, because of the

mechanical principles involved. The appropriate a mount of

force to be applied may vary cons iderably according to the

type of movement required. For example approximately

250 gra ms of force are required during the final stage s of a

continuous bodily move ment of canines, whereas only 25

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B urstone1 0 (1966) stated that, as an orthodontic appliance

is activated, the operator has control over three variables

which can dete r mine the s uccess of clinician‟s adjus tment.

They are the mo ment to force ratio, the magnitude o f

mo ment or force used, and the constancy of force or

mo ment. He concluded that the segmented mechanis m have

been des igned to control tooth movement which has k now n

mo ment to force ratio and to aim an optimal biological

response by delivery of relatively constant force at a n

optimal magnitude.

Weins tein6 3 (1967) explained the efficiency of light forces

that is, force of s mall magnitude in orthodontics. He

suggested this by analys ing certain areas of the oral

musculature and their influence on tooth pos ition. He

concluded that there seems to be a genetic factor involved

in both the resting force and the stiffness of cheek

musculature in males. Masticatory forces produce a bucca l

tipping tendency on the lower premolar and contribute to

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Smith and B urstone9 (1984) explained about the bas ic

relations hips between force and tooth move ment and their

potential for clinical relevance. Forces produce trans lation

(bodily move ment), rotation, or a combination of

trans lation and rotation, depending upon the relations hip o f

the line of action of the force to the center of res istance o f

the tooth. Since most forces are applied at the bracket , it is

necessary to compute equivalent force sys tems at the center

of res is tance in order to predict tooth move ment.

Robert. Quinn, Ken Yos hikawa5 5 (1985) stated that the

force s yste ms developed by an ideal arch cannot be used

directly to estimate tooth move ment. They s hould first be

trans ferred to the centre of res is tance of the teeth and the

force s ystems at the centre of res istance may differ

significantly from the force sys tems at the brackets. The

relations hip between the force magnitude delivered b y

orthodontic appliances and the rate of orthodontic toot h

move ment is controvers ial. He concluded that appliances

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mo ment/force ratios allow the clinician to take advantage

of the type of tooth move men t proposed.

Birte Melsen, Giorgio Fiorelli. et al 3(1994), developed a

computer program that can help to des ign the optimal

orthodontic appliance. It involves several phases :

1. Identification of the required tooth move ment and its

center of rotation.

2. Deter mination of the force s yste m needed to produce

this movement.

3. Appliance des ign.

With statically indeterminate force s yste ms,

calculators are included in the progra m for co mplicated

calculations to deter mine forces based on the formulae

given by Burstone and Koenig and are available for all

poss ible wire selections.

Halazonetis1 4 (1998) studied the forces and mo ments

produced by a straight portion of an arch wire which were

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The purpose was to co mpare the force s yste m at the

brackets to the force s yste m at the center of res istance and

to assess whether bracket geometry can be applied to

predict initial tooth move ment. The res ults show that the

force sys tem at the center of res is tance may be of an

entirely different “geometry” type than that at the bracket.

Factors that influence the force s ystem include the

interbracket distance, the angulation of the teeth, the lengt h

of the tooth root, and the width of the bracket.

Yijin Ren, DDS, MSca; Jaap C. Maltha6 6 (2003) did a

study about the meta -analys is of the literature concerning

the optimal force or range of forces for orthodontic toot h

move ment. Articles on animal experiments were in the

majority. Bes ides variation in s pecies, there was also a

wide range of variation in force magnitudes, teeth under

study, directions of tooth move ment, duration of

experimental period, and force reactivation. Further more,

hardly any experiments were reported that provide

infor mation on the relation between the velocity of tooth

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from human research on the efficiency of orthodontic toot h

move ment appeared to be very limit ed. The large variation

in data fro m current literature made it imposs ible to

perfor m a meta-analys is. They had concluded that no

evidence about the optimal force level in orthodontics

could be extracted fro m literature. Well -controlled clinical

studies and more standardized animal experiments in the

orthodontic field were required to provide more ins ig ht into

the relation between the applied force and the rate of tooth

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RETRACTI ON LOOPS

B urrstone C.J7 (1961), stated that the most cons tant force

at optimal level are derived fro m spring possess ing low

deflection rate and high availa ble working loads. His stud y

concluded that Stainless steel have s lightly higher

maximum load than gold springs of identical rates.

B urstone and A. Jon Goldberg8 (1980) reviewed the gold

-based, stainless steel, chro me -cobalt-nickel, and nitino l

alloys, as well as beta titanium, a new material for

orthodontics. Mechanical properties and manipulative

characteris tics are s ummarized to develop a bas is for the

selection of the proper alloy for a given clinical s ituation.

Beta titanium offers an improve ment in t he properties of

presently des igned orthodontic appliances with its

increased spring back, reduced force magnitudes, good

ductility, and weldability, and also its excellent balance of

properties s hould per mit the des ign of future appliances

which deliver s uperior force s ys tems with s implified

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Scott R. Drake et al5 9 (1982) the mechanical properties of

three s izes of s tainless steel (SS), nickel -titanium (NT), and

titanium- mo lybdenum (TM ) orthodontic wires were studied

in tens ion, bending, and tors ion. The wires (0.016 inch,

0.017 by 0.025 inch, and 0.019 by 0.025 inch) were tes ted

in the as -received condition. The s tudy concluded that a

titanium- mo lybdenum teardrop clos ing loop delivers less

than one half of the force co mpared to stainless ste el loop

for similar activations.

B urstone6 (1982) s tudied the clinical application o f

frictionless attraction springs us ing the segmented arch

technique . He concluded the mos t important cons iderations

in the clinical use of attraction springs are the amo unt o f

distal activation, the angulation differential between the

anterior and posterior teeth, and the centricity or

eccentricity of the loop. Loop design lead to a more

efficient, hygienic, and comfortable mechanis m for space

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Poul Gjessing4 5 (1985) introduced new canine retraction

spring in orthodontics .On the bas is of a series o f

theoretical cons iderations described in the present report, a

canine -retraction spring was cons tructed from 0. 016 ´ 0.022

inch stainless steel wire, the principa l ele ment being a

double ovoid loop 10 mm in height . A "sweep" bend was

incorporated to avoid unwanted s ide effects at the second

pre molar. He concluded that load deflection and

mo ment/force curves were derived experimentally and

demons trated the ability o f the spring to generate and

maintain bio mechanical conditions necessary .

Faulkner et al3 3 (1989) studied the effects of severa l

parameters on the force/moment systems produced by „T‟

-loop retraction s prings. The springs are studied by us ing

the finit e element method and by experimentally meas uring

the forces and mo ments fro m the various des igns. The

res ults s howed that varying the spring height can produce

larger mo ment to force ratios as the height increases.

Changes in the pre activation bends resul t in as ymmetric

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intrus ive/extrus ive forces. The addition of helices at the

bends did little to alter the springs ' mechanica l

characteris tics.

S.J.Chaconas5 7 (1989) studied three contraction arch wires

na mely double delta spring, contraction torquing arch, and

contraction torquing utility arch wire. The activations

studied were intrus ion, retraction and torque. He s tated that

if deepening of the bite is indicated, the clinician s hould

use the double delta arch wire which would produce a

lingual crown tipping and poss ibly extrus ion of the incis ors

during retraction. However, if a deep overbite exists prior

to anterior tooth consolidation, the contraction torquing or

contraction torquing utility arch wires should be used s ince

they were s hown to produce the mos t effective lingual root

torquing during incis or retraction. This action would not

res ult in deepening of the bite.

T homas R. Katona et al6 2 (1989) review article describes

the mechanical properties and cl inical applications of

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-Review of Literature

titanium, and multi stranded wires . Stainless steel wires

have re mained popular s ince their introduction to

orthodontics because of their forma bility, bioco mpatibility

and envir onmental stability, stiffness, resilience, and low

cost. Cobalt-chromium (C o---C r) wires can be manipulated

in a softened state and then s ubjected to heat treat ment.

Heat treat ment of C o ---C r wires results in a wire with

properties s imilar to those of stai nless steel. He found

Nitinol wires have a good s pring back and low stiffness.

This alloy, however, has poor for mability and weldability.

Beta-titanium wires provide a combination of adequate

spring back, average stiffness, good formability, and can be

welded to auxiliaries.

Fortschr Kieferorthop. B ourauel C 1 8 (1994) , based on

the favourable res ults achieved by the application o f

pseudoelastic „T‟ loops in the course of canine retraction,

investigated their application to the retra ction of maxillary

incisors. A modified Burstone „T‟ loop was made of a

pseudoelastic orthodontic nickel titanium wire and the n

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of the pseudoelastic spring was perfor med us ing an

individualized re traction arch enclos ing the whole front

segment. His study concluded that the location of the center

of res istance of the upper incisors has not been co mpletely

clarified. It is thus reco mmended that this matter s hould be

given further study.

D. W. Raboud, MSc, et al 1 2 (1997) studied the clinical

importance of the three -dimens ional effects of the force

syste ms s upplied by appliance des igns used for retraction .

His study concluded that the proposed numerical method

can accurately determine the force syst e ms res ulting from

this out -of-plane pre activation as well as the in -plane force

syste ms.

J. Halazonetis, DDS, MS et al1 5 (1997) tested the accuracy

of the computer s imulation, various loops that have bee n

evaluated experimentally in the literature were s imulated

and their res ponse were compared with the res ults reported

previous ly. In most cases, the res ults predicted by the

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values. Res ults obtained with wire specimens in an

experimental apparatus t hat meas ures forces and moments,

and values obtained from a computer s imulation, bot h

contain potential errors and can be different fro m the

values that can be expected in the clinical setting.

Development of the program is expected to address some o f

these proble ms and increase the validity of the s imulation.

Andrew J. Kuhlberg1. (1997) studied the effect of off

-center pos itioning on the force sys tem produced b y

segmented 0. 017 ´× 0.025 -inch TM A „T‟ -loops. A „T‟ -loop

was des igned to produce equal and o ppos ite mo ments in the

centered pos ition. The spring was tested in seven pos itions,

centered, 1, 2, and 3 mm toward the anterior attachment,

and 1, 2, and 3 mm toward the posterior attachments. The

horizontal force, vertical force, and alpha and beta

mo ments were meas ured over 6 mm of spring activation.

The res ults s howed that the alpha/beta mo ment ratio was

dependent only on the spring pos ition, and independent o f

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effectively produces a cons is tent moment differentia l

through the range of spring activation.

Demetrios J. Halazonetis1 6, (1998) stated that Control o f

the force s ys tem that is applied to teeth is one of the main

proble ms in the field of biomechanics. A major use of loops

is in the ret raction of canines, where a correct mo ment to

force ratio is essential for bodily mo ve ment. The des ign of

the loop influences both the force levels and the mo ment to

force ratio (M /F) in s uch a way that it is difficult to change

the one without adversely affecting the other.

Marcelo do Amaral Ferreira3 5,(1999) studied the

mechanical behaviour of orthodontics clos ing loops, wit h

three different wire materials (stainless steel, cobalt

-chro mium and titanium- molybdenum) and with different

cross-sections and a double delta des ign in tens ion tes ts. It

was hypothes ized that loads, after spring activation, and

spring rate, are dependent on cross -section, wire material,

and activation. The res ults s howed that the loads are

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Titanium- molybdenum 0. 017 × 0. 025 inch (Ormco) springs

showed the s mallest loads and the bes t spring rate.

(b = 84.9 g/mm) .

Jie Chen et al2 8 (2000) studied the e ffects of T-Loop

Geometry on Its Forces and M oments and de mons trated that

the mo ments and forces generated by a T -loop spring are

functions of its geometry and gable angle co mbined with

heat treat ment. This Study concluded that increas ing its

vertical or horizontal dimens ion reduces the load -deflectio n

rate and the moment -to-force ratio. Gable preactivation and

stress relieving heat treatment have the oppos ite effect.

Kwangchul Choy3 1 (2002), made a study on C ontrolled

Space C los ure with a Statically Deter minate R etraction

Syste m. SDRS uses frictionless mechanics, an d

its statically determinate force delivery s ys te m

(i.e, magnitude, direction, and point of force application)

can be eas ily establis hed by a s ingle force meas ure ment. He

stated that the cantilever spring has a low load-deflection

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reactivation is often not required. The force direction

changes minimally and re mains during s pace clos ure, as

does the axis of rotation. Therefore, unnecessary jiggling o f

teeth can be minimized.

Andrew J. Kuhlberg et al2 (2003) study was to compare

meas ured tooth movements with the theoretical force

syste m exerted by differential moment clos ing loops.

Tloop springs des igned to deliver a differential mo ment

-to-force ratio to the posterior Vs the anterior teeth were

used. The anterior teeth, as repres ented by the canines,

were retracted an average of 1. 73 mm, whereas the

posterior anchorage (molars) moved mes ially only 0.50

mm. Furthermore, the canine teeth exhibited tipping or

trans lation, and the molars s howed mesial root move ment.

Kum M , Quick A et al3 0 (2004) investigated the loads

("forces "), mo ments and mo ment:force ratios (M/F)

generated during activation and deactivation of three

clos ing loop des igns constructed from two different

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M/F ratios for trans lation are not poss ible with non -pre

activated vertical „U‟-Loops or symmetrical „T‟-Loops.

T hiesen G et al6 1 (2005) did a s tudy to determine the

mechanical characteristics of beta -titanium „ T‟ -loops w ith

and without helices, with 0 and 180 degree gable bends,

constructed from 0.017 inch x 0.025 inch and 0.019 inch x

0.025 inch wire. The horizontal forces and mo ment/force

ratios generated by plain „T‟ -loops with 180 degree gable

bends yielded more adequate force sys tems. He concluded

incorporation of helices in the design of „T‟ -loops seems to

be unnecessary.

Renato Parsekian Martinsa 5 3; (2008) stated that both

curvature and bend pre activated „T‟ loop produced

symmetrical mo ments with s mall vertical force. The

curvature pre activated „T‟ loops produced horizontal

forces that were lighter than the bend pre activated „T‟

loops. The curvature pre activated „T‟ loops produced MF

ratios that were approximately 2.5 mm higher than the bend

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activated T loops s howed less force decay per 0.5 mm of

deactivation (29.8 gf) than the bend pre activated „T‟ loops.

Poowadon Kos on-ittikul et al4 4 (2008) s tated that the

LDR (low deflection rate) for one clos ing loo p s hould be as

low as poss ible so that the force applied to the tooth will be

low to minimize pathological effects on the periodonta l

support and also maintain constant force over a large

deflection range. According to the tests, the helical loop

with reversed ar ms provided the lowest LDR among the

four s imple clos ing loops des igns studied. Wire bending to

change the s hape and configurations of the loop is the one

procedure to improve or change the force/deflectio n

properties of the orthodontics wire mater ial. The major

effect of the LDR co mes from the amount of the wire

incorporated into a clos ing loop.

Miceli Beck Guimaraes Blaya et4 1 (2009) analyzed the

mechanical behaviour of different orthodontic retractio n

loops. Two des igns of orthodontic loops for clos ing space

(35)

loop (C), of two different heights (6 and 8 mm), and two

types of orthodontic wires (s tainless steel – 0.19‟ × 0.25‟;

TM A – titanium mo lybdenum alloy – 0.016‟ × 0.016‟). The

group “teardrop -8 mm-TM A” together with the group

“circle-8 mm-TMA” presented the lowest mean value,

differing statistically from all of the other groups. It was

concluded that the alloy of the wire and the height of the

(36)

FINITE ELEMENT ANALYSI S

Osamu Miyakawa et al4 3 (1985) described a new

simulation method to analyze the initial behaviour of the

total s ys tem co mpris ing orthodontic appliance, teeth, and

their s upporting s tructures. It is bas ed on a finite ele ment

method which additionally takes account of a rotationa l

degree of freedo m. Bea m and rod ele ments are used for

finite ele ment idealization of orthodontic appliance.

Through spring ele ments it is connected with the teeth

supported by the alveolar structures. The technique of

„initial strain‟ is introduced so as to analyze the effects of a

gable bend and activation on the force s yste m which is

delivered by the orthodontic appliance. As co mpared with

the photo elastic technique hitherto used, this method

serves to investigate s yste matically and quantitatively the

initial aspect of orthodontic tooth movement.

Raymond E. Siatkows ki at al4 9 (1997) introduced new

clos ing loop us ing FEM (ANSYS soft ware -Swanson

(37)

capable of delivering a non varying target M/F within the

range of 8.0 -9.1 mm inherently, without adding res idual

mo ments by twist or bends (commo nly gable bends )

anywhere in the arch wire or loop before insertion. The

res ulting precise fo rce s ystems delivered with non varying

M/F can move groups of teeth more accurately to achieve

predeter mined anteroposterior treatment goals for esthetics

and/or stability. The experimental res ults s how that the

loops must be bent accurately to achieve the ir des ign

potential. The negative impact on M/F of various

dimens ional changes to the loop design is presented.

Experimental data is presented illus trating the improved

perfor mance of the new des ign over s tandard available

des igns. Suggested applications o f the des ign for varyin g

anchorage require ments are presented, along with a cas e

report in which rigorous protraction require ments were met.

Young –ll Chang et al 6 6(2004), compared the effects of a

multi loop edgewise archwire (M EAW) on dis tal en masse

move ment with a continuous plain ideal archwire(IA) us ing

(38)

models of the maxillary dentition was cons tructed

according to Wheeler and aligned with reference to the

facial axis point of Andrews and als o standard edgewis e

bracket and stainless steel IA and MEAW. The stress

distribution and displacement of the maxillary dentition

were analyzed when classII inter maxillary elas tics

(300gm/s ide) were applied. The results s howed that the

MEAW produced low amo unt of tooth displacement.

Individual tooth move ment was more uniform and balanced

and less vertical displacement was seen with M EAW.

Rodrigo F. Viecilli et al5 6(2006) studied about

Self-corrective „T‟ -loop design for differential space closure

.The effects of steps, angles, and vertical forces were

combined to produce an ideal „T‟ -loop des ign that would

provide a more deter minate force sys tem. The effects and

force s yste ms are estimated based on s implified locations

of the centers of res istance, ass uming relatively constant

behavior of the centers of rotation. These s implifications

might differ s lightly fro m what happens in vivo. The s tud y

(39)

spring tester capable of reproducing the geo metric

corrections s hould be used to ens ure a precise force s ys tem.

Mohd. Reza safavi4 2 (2006) studied M/F ratio of four

different clos ing loops us ing FEM. The objective of the

study was to co mpare the forces, mo ments and

mo ment/force (M /F) ratios of the opus loop, „L‟ –loop,

„T‟–loop and vertical helical closing loop (VHC loop) in a

segmented arch with the finite element method (FEM).

Results s howed that the highest horizontal and vertical

forces were produced by the „ L‟–loop (with and without pre

activation bends) and in most cases the lowest forces were

produced by the VHC loop. He concluded Loops with pre

activation bends produced marked changes in the M /F ratio

and loops without pre activation bends low, but relat ively

constant, M/F ratios over the full range of activation.

Maria Elisa Rodrigues Coimbra3 8 et al (2008), studied

about Mechanical tes ting and Finite ele ment analys is o f

orthodontic teardrop loop. The purpose of this study was to

(40)

and the tors ion obtained after the activation of teardrop

loops of 3 heights. The co mputer simulation accurately

predicted the experimentally deter mined mechanical

behaviour of teardrop loops of different heights and s hould

be cons idered an alternative for des igning orthodontic

(41)

Materials and Methods

MATERIALS AND METHODS

The present study was conducted to evaluate and

compare the force obtained after activation of Tear drop

and “T” loops by mechanical method and by finite element

method (Co mputer s imulation). Retraction loops of TM A

0.17x 0.25inch rectangular wire were used.

The testing apparatus cons is ted of co mputer with

ANSYS software and universal testing machine (S H IM ADZ U

Model;AG -IS 50 KN) (Fig 10 )

Fifty clos ing loops made of TM A 0. 017 × 0.025 -inch

rectangular wires were bent. Based on the d es ign of the

loops, they were divided into 2 groups na mely 25 Tear drop

loops4 0 (Fig 7) and 25 T loops (Fig 3 ). Dimens ion of Tear

drop loop was 7 mm height and 2.5mm internal arch

circumference. Geometry of T loop was 5mm anterior (α)

vertical height and 4 mm posterior (β) vertical height.

Posterior vertical height was made to be in level wit h

(42)

10mm. The sa me operator prepared the specimens us ing a

template or millimetre jig4 1.

A light wire plier with TC tip (Dentronix, US A) and

Tweed loop for ming plier ( R ocky M ountain G ERMAN Y) were

used for making the loops. After preparation, each loop had

28 mm of total length of which anterior and posterior 5mm

of wire allowed its attachment to a universal tes ting

ma chine (Fig 10 ). Remaining 18mm represented the

standard inter bracket dis tance (IBD)2 and loops were

placed centrally 3 6 .A D igital Vernier Caliper (fig 1) was

used to check the dimens ions of the loops to main tain a

standard dimens ion (fig 4&8 .) Pre activation bends were

not given in any loop s.

MATERIALS

1. 0.017× 0.025 TM A (Omrco, Glendora,C A ) straight

wire (Fig 1).

2. Orthodontic light arch plier with TC tip (Dentronix,

USA) (Fig 1).

3. Tweed loop for ming plier ( Rocky M ountain GERM AN Y)

(43)

4. Orthodontic arc h wire cutter (heavy duty) (Fig 1).

5. Template or millimeter jig (Fig 2&6 ). Template

prepared with a help of Solid Works software 2005

(DWG -Editor).

6. Digital Vernier Caliper (M itutoya, Japan) (Fig 1).

7. A Personal computer with the following configuration

was used:

Monitor -- IBM TFT M onitor

CPU -- IBM (Intellis tation Z Pro)

Processor -- Intel Xeon (Dual Processor)

Memory Capacity -- Primary -2 GB, Secondary –

80 GB

Graphics card -- ATI FireGL V 71

Software -- ANSYS (vers ion 11,)

Operative s ys tem -- Windows vista

METHODOL OGY:

Evaluation with Universal testing machine.

The s prings were then s ubjected to a tens ile load on

the universal testing machine. (S HI MAD Z U model: AG-IS

(44)

purpose, one end of the specimen was fixed to the machine,

and the other end was displaced. The loops were s ubjected

to activation s teps with increments of 0.5 mm at a rate of

1.0 mm per minute up to a maximum displace ment of 2mm.

The forces were meas ured and recorded.

Evaluation using Computer simulation:

The geo metry of the s prings used in the computer

simulation was obtained with the help of jig dimen s ion. The

Tear drop loop (Fig 9) and „T‟ loop models (Fig 5 ) were

created in ANSYS software accordi ng to the characteristics

of the loop structures and also cons idering the s pecific

move ments imposed by the intended mechanical activation.

BEAM 4 ele ments were used for cons tructing loop models

for analys is3 6. This (finite) uni axial element could respond

to tens ion, compress ion, traction, and tors ion move ments.

The BEAM 4 element has 6 degree of freedo m,

3 trans lation and 3 rotation points around the axis3 6.The

modulus of elas ticity of the orthodontic wire used in the

(45)

coefficient of 0.130 (Siatkows ki,AJO 1997)4 8. Both the

Tear drop loop and the „T‟ loop models were discretized

into finite elements, and an average of 237 ele ments were

used for modelling. To s imulate the activation s i milar to

universal testing machine, the boundary conditions were

defined so that the terminal node in the alpha segment

(anterior) was restrained (i.e. it was not able to move in the

X, Y or Z axes, and it was not able to rotate around these

axes )4 1 , 3 6. The terminal node of the beta segment (posterior)

was restrained in a s imilar way to the alpha segment,

except that it was free to move along the horizontal leg of

the posterior segment. This movement s imulated the wire

sliding distally through a molar tube. Force exerted on the

horizontal axis during every 0.5mm incre mental activation

of the loop was deter mined up to a maximum of 2 mm

activation (Fig 14 & 15 ). Both the Tear drop loop mode l

and the „T‟ loop model were subjected to this simulated

activation and the forces exerted by these loops were

(46)

[image:46.595.168.431.151.374.2]

FIG 1- ARMAMENTARIUM

[image:46.595.123.475.543.749.2]

(47)

[image:47.595.139.460.152.350.2]

FIG 3- T LOOP PLACED ON THE JIG MANUALLY MADE

[image:47.595.162.437.470.677.2]

(48)

[image:48.595.150.445.119.344.2]

FIG 5 - MODELING AND MESHING OF T LOOP (COMPUTER SIMULATION)

FIG 6- TEMPLATE OR MILLIMETER JIG FOR TEAR DROP LOOP

[image:48.595.148.450.525.713.2]

(49)

[image:49.595.155.447.133.267.2]

FIG 7- TEAR DROP LOOP PLACED ON THE JIG MANUALLY MADE

[image:49.595.161.437.435.640.2]

FIG 8 - MEASURING TEAR DROP LOOP DIMENSION WITH DIGITAL CALIPER

(50)

[image:50.595.149.445.74.297.2]

FIG 10 - UNIVERSAL TESTING MACHINE

[image:50.595.194.405.416.693.2]

(51)

[image:51.595.153.446.97.319.2]

FIG 12 - TEAR DROP LOOP BEFORE ACTIVATION

[image:51.595.152.445.460.684.2]

(52)

[image:52.595.153.443.96.314.2]

FIG 14 - 2MM ACTIVATION OF T LOOP (COMPUTER SIMULATION)

[image:52.595.168.476.460.695.2]

(53)

[image:53.595.152.446.71.293.2]

FIG 16 - 2MM ACTIVATION OF TEAR DROP LOOP (COMPUTER SIMULATION)

[image:53.595.143.450.437.669.2]

(54)

[image:54.595.148.444.72.299.2]

FIG 18- VONMISES STRESS DURING 2MM ACTIVATION OF TEAR DROP LOOP

(55)

Results

RESULTS

1. Force value at various levels of activation (from 0.5 mm

to 2 mm) for ‘T’ loop and Tear drop loop of the 25

samples each were obtained fro m mechanical testing.

The res ults are presented in Table 1 and 2 respectively.

2. Computer s imulated force val ue of ‘T’ loop and Tear

drop loop were obtained and presented in Table 3 and 4

respectively.

3. Unpaired ‘t’ test showed statistically significant

difference between T loop and Tear drop loop force

values. The data is presented in table 5.

4. Paired ‘t’ test analysis for computer simulation and

experimental testing of ‘T’ loop and Tear drop loop were

(56)

Results

[image:56.595.108.529.201.760.2]

TABLES

Table 1. Force values obtained from T loops at various

levels of activation in universal testing machine (Newton).

T loop Sample no 0.5mm

Activation 1mm Activation

1.5mm

Activation 2mm Activation

1 0.53 1.024 1.546 2.165

2 0.403 1.085 1.446 2.435

3 0.512 0.987 1.418 2.45

4 0.516 0.906 1.616 2.21

5 0.501 0.916 1.483 2.333

6 0.511 0.953 1.439 1.904

7 0.416 1.09 1.442 1.867

8 0.523 0.952 1.341 1.849

9 0.609 0.932 1.372 1.911

10 0.458 0.963 1.392 1.891

11 0.556 0.961 1.462 1.54

12 0.512 0.966 1.468 2.354

13 0.534 0.956 1.429 1.825

14 0.509 0.903 1.421 1.834

15 0.514 0.912 1.425 1.815

16 0.52 0.916 1.556 2.435

17 0.59 0.953 1.486 2.45

18 0.454 1.09 1.468 2.21

19 0.553 0.961 1.586 2.333

20 0.619 0.928 1.462 1.954

21 0.459 0.953 1.466 1.967

22 0.566 0.963 1.458 1.849

23 0.512 0.956 1.437 1.891

24 0.534 0.957 1.432 1.54

25 0.509 0.913 1.473 2.454

(57)

Results

Table 2. Force values obtained from Tear drop loops at various

levels of activation in universal testing machine (Newton).

0.5 1 1.5 2

1 0.995 1.76 2.78 3.24

2 0.831 1.47 1.92 3.6

3 0.841 1.545 2.359 3.227

4 0.842 1.86 2.743 3.515

5 0.825 2.08 2.99 3.49

6 0.805 1.77 2.12 3.306

7 0.902 1.436 1.859 3.617

8 0.934 1.352 2.001 3.054

9 0.801 1.647 2.125 3.232

10 0.729 1.551 2.75 3.251

11 0.847 1.391 2.05 3.598

12 0.742 1.669 2.078 3.263

13 0.745 1.496 2.161 3.004

14 0.732 1.379 2.005 3.058

15 0.807 1.352 1.974 3.021

16 0.835 1.536 2.752 3.543

17 0.835 1.353 2.152 3.317

18 0.85 1.648 2.118 3.582

19 0.827 1.553 2.151 3.091

20 0.815 1.431 2.015 3.242

21 0.892 1.659 1.963 3.241

22 0.934 1.486 2.121 3.599

23 0.728 1.369 1.959 3.252

24 0.837 1.472 2.091 3.015

25 0.741 1.535 2.152 3.148

(58)

[image:58.595.103.527.228.404.2]

Results

Table 3. Descriptive statis tics for the force level (in N)

related during varying activation levels for ‘T’ loop

Table 4. Descriptive statis tics for the force level (in N)

related during varying activation levels for Tear drop loop.

Activation

(mm) Mean(N) Maximum(N) Minimum(N) SD

0.5 0.827 0.995 0.728 0.068

1.0 1.584 2.08 1.352 0.208

1.5 2.261 2.08 1.859 0.342

2.0 3.298 3.617 3.004 0.322

Activation(mm) Mean (N) Maximum(N) Minimum(N) SD

0.5 0.507 0.619 0.403 0.05

1.0 0.967 1.09 0.903 0.053

1.5 1.448 1.616 1.341 0.06

[image:58.595.103.513.548.712.2]

(59)

[image:59.595.162.451.185.352.2]

Results

Table 5. Co mputer s imulation res ults for T loop

Activation ( mm) Force in Fx (N)

0.5 0.481

1.0 0.960

1.5 1.4416

2.0 1.920

x- Force in hor izontal axis, N - Newton,

Table 6. Co mputer s imulation res ults for Tear drop loop

Activation (mm) Force in Fx (N)

0.5 0.809

1.0 1.618

1.5 2.427

2.0 3.236

[image:59.595.168.444.510.676.2]

(60)

[image:60.595.136.514.585.663.2]

Results

Table 7. Tear Drop and T Loop Unpaired Students T test

0.5mm activation

Loop Mean SD P

T loop Teardrop loop 0.5168 0.826 0.05193 0.06893 ˂ 0.001

1mm activation

T loop Teardrop loop

0.96384 1.552

0.05422

0.17866 ˂ 0.001

1.5mm activation

T loop

Teardrop loop

1.460

2.245

0.060

0.0318 ˂ 0.001

2mm activation

T loop

Teardrop loop

2.05

3.300

0.28

0.20 ˂ 0.001

(61)

[image:61.595.137.509.514.703.2]

Results

Table 8. Paired ‘t’ test for T loop between co mputer

stimulation and experiment.

Activation

(mm)

Experimental valve

for T loops (N)

Computer

simulation value(N)

0.5 0.507 0.48

1.0 0.967 0.96

1.5 1.448 1.44

2.0 2.026 1.92

P value = 0.1915 (not statis tically significant.)

Table9. Paired ‘t’ test for Tear drop loop between

computer stimulation and experiment.

Activation

( mm)

Experimental value

for Tear drop

loops(N)

Computer

simulation value

(N)

0.5 0.827 0.809

1.0 1.584 1.618

1.5 2.261 2.426

2.0 3.298 3.236

(62)

Results

GRAPHS

Graph- 1: F orce obtained on activation of T ear drop

loop to 2mm in univers al tes ting machine

0 330

30 60 90 120 150 180 210 240 270 300

F

o

rc

e

(g

f)

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.5

Stroke(mm)

Max

(63)

Results

Graph – 2: F orce obtained on activation of

T loop to 2mm in universal tes ting machine

0 210 20 40 60 80 100 120 140 160 180 200 F o rc e (g f)

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.5

Stroke(mm)

Max

Sample: 8

(64)

Results

Graph- 3: Mean f orce tendency (n) for T loops and tear

drop loops (mechanical tes ting)

Graph-4: Mean force tendency (n) for T loops and tear

(65)

Discussion

DISCUSSION

Biomechanics is the study and analysis of mechanica l

function in living bodies and the effect of the force on the

form and motion of living bodies. Forces are load or

external influences applied to a body that changes or tends

to change the pos ition of that body. If a force is applied to

the center of the res istance the whole body moves equally

in the direction of force applied. When orthodontic forces

are applied and when the line of the force does not pass

through the center of the res istanc e a moment is created.

In orthodontic mechanotherapy, several orthodontic

mechanis ms were des igned for clos ing loops. Among the

various devices described there are many ranges of loops,

which may be used, incorporated into continuous or

segmented arches, for vertical and saggital dental

move ment. Due to the large number of options, a great deal

of attention must be paid when selecting the mos t

(66)

Discussion

In this choice, certain variables mus t be analyzed,

among the m the loop des ign, it quantity of activation, wire

thickness, the metal alloy used, type of move ment des ired

and the quantity of force necessary. When us ing loops for

clos ing s paces, it is of the ut most importance for the

profess ional to determine precisely the s ys tem of fo rces

generated; that is, it is important for the orthodontist to

know the magnitude of Orthodontic forces a nd the mo ments

released when these devices are activated.

Orthodontic forces applied by means of orthodontic

appliances are dependent on various fac tors that determine

the s uccess of the treatment. The operator has control over

a few factors like moment: force ratio, magnitude of force

and constancy of force B urstone (1966)1 0

Optimum control of tooth move ment requires

application of specific orthodon tic force s yste ms.

Therefore, the knowledge of the mechanics of orthodontic

appliances is essential to achieve desirable and predictable

(67)

Discussion

Load deflection rate is also important for a n

orthodontic spring as its mo ment to force ratio. Force

produced per unit deflection is the load deflection rate. A

low load deflection rate is preferred for orthodontic springs

(P oowadon Kos on –ittikul et al. 2008)4 4 Low load

deflection is preferred for two reas ons : 1) it maintains a

des irab le force level in the PDL 2) It offers greater

accuracy in controlling force magnitude. Hence an ideal

orthodontic spring s hould have a greater M/F ratio and a

lower load deflection rate. (B urstone 1966)1 0

Crown tipping, trans lation and root mov e ment are

exa mples of different types of tooth movement that can be

produced with proper mo ment to force ratio (Graber,

Vanarsdall)2 2 An important aspect of orthodontic treat ment

is to unders tand tooth movement in response to mechanical

loads and the assoc iated adjacent tiss ue res ponse at bot h

clinical and histological levels (Prof fit)6 5.

To move teeth in a controlled fas hion, correct

mechanical principles and an ideal orthodontic appliance

(68)

Discussion

of malocclus ion to better align the teeth to be moved and

ease of place ment in the mouth. While the final goal of a

retraction s ys tem is efficient, effective clos ure of s pace

within the dental arch, the des igns and materials of the

appliances used to accomplis h this effect vary

cons iderably.(M.G.Faulkner et al 1991)3 3

To provide the appropriate force s ys tem, the appliance

must have the following mechanical characteris tics : 1. It

must provide appropriate levels of force and mo ment

-to-force (M /F) ratios to achieve the tooth displacement

des ired.2. It must be able to undergo a reasonable range of

activation/deactivation in which the appliance delivers

relatively cons tant forces and mo ments.3. It mus t be s mall

enough to fit comfortably in the space available for

intraoral treat ment. (M.G.Faulkner et al 1991)3 3

Number of procedures is used for retraction o f

anterior segments in treatment of extraction case. In s liding

mechanics, force diss ipates due to friction which is

(69)

Discussion

undes irable effects the retraction of anterior teeth b y

frictionless s yste m is based upon the incorporation of loop.

(Charles B urstone et al 1976)5

In frictionless mechanics, teeth are moved without the

brackets s liding along the arch wire. Retract ion is

accomplis hed with loops or springs, which offer more

controlled tooth move ment than s liding mechanics. The

force of a retraction s pring is applied by pulling the dista l

end through the molar tube and cinching it back. The

mo ment is deter mined by the wire configuration and by the

presence of pre activation or gable bends, which produce an

activation mo ment.

The addition of helices lowers the load/deflectio n

rate without s ignificantly affecting the mo ment to force

ratio (M.G.Faulkner1991)3 3. Reducing the load deflection

rates of orthodontic springs is important for it provides a

relative constancy of the mo ment - to- force ratio applied to

the teeth with concomitant , force a stable dental

(70)

Discussion

mo me nt to force ratio can be improved by increas ing its

height, horizontal length, and loop diameter of the spring.

The sa me is true of a T -loop, but once the horizonta l

section beco mes equal in length to the vertical section, no

improvement in the mo ment to force ratio is gained b y

lengthening the horizontal section. (B urstone et al 1976)5

Biomechanical cons ideration requires that arch wire

stiffness be an important criterion upon which rests the

relations hip between orthodontic forces and deflection

within the elastic working range. Stiffness is directly

related to the cross sectional s ize and s hape of the wire and

affected by bracket width, interbracket distance, the length

of the wire, wire material, hardness and the incorporatio n

of loops.

B urstone et al 19826 concluded that the most

important cons ideration in the clinical use of attraction

springs are the amount of distal activation, the angulations

differential between the anterior and posterior teeth and

(71)

Discussion

Loop des ign lead to a more efficient, hygienic, and

comfortable mechanis m for space clos ure. Principles of

loop des ign include use of a rectangular wire for preventing

the rolling of loop arch wire in the bracket s lots, use of a

simple des ign, a failsafe mechanis m and adequate range of

action to deliver continuous controlled force. (Wick

Alexander)6 4

The different biomaterials used in orthodontic wires

can be s tainless steel, nickel titanium or beta -titanium.

When for med into different configuration, they genera te

bio mechanical forces which are trans mitted to the appliance

to produced tooth move ment. The ideal arch wire s hould

deliver a low constant force, good spring back and

bioco mpatible. (Nanda)4 6 β - Titanium wires have

improved values of spring back which markedly increases

their working range for tooth movement. For a given cross

section, it can be deflected approximately twice as far as

stainless steel wire without permanent defor mation

Analysing Mechanical Property of Two Different Closing Loops using Finite Element Analysis and Universal Testing Machine: A Comparitive Study