i

STUDY OF STRESS LEVELS IN VARIOUS

MATERIALS IN TOTAL KNEE REPLACEMENT UNDER

STATIC CONDITION

A PROJECT REPORTSubmitted by

SHREYAS HARSHA [REG.NO - 1021110129]

Under the guidance of

DR. RAMESH KANDADAI(Visiting Professor, Department of Mechanical Engineering)

in partial fulfillment for the award of the degreeof

BACHELORS IN TECHNOLOGYin

MECHANICAL ENGINEERING

of

FACULTY OF ENGINEERING & TECHNOLOGY

ii

S.R.M. Nagar, Kattankulathur, Kancheepuram District

APRIL 2015

i

ABSTRACT

With the increase in the number of people being

affected by Osteroarthritis, Rheumatoid Arthritis, and

other knee complication, Total Knee Replacement (TKR)

has emerged as one of the best solution for mobility

and to reduce the pain, stiffness etc, among people.

In TKR the affected portion of the Femur is fitted

with a metallic implant while the Tibia is fitted with

a implant made of a Polymer. The knee joint is

considered to be the most complex joint in the human

body. Accordingly the material utilized for knee

implant assumes an exceptionally important part for

survival of knee prosthesis. These implant materials

must meet the physical, mechanical and biological

necessary to serve its purpose. The materials that are

utilized incorporate Metals, Composites, Ceramics and

Polymers. Of these materials Co-Cr Alloy, Titanium

alloys, Stainless Steel, Zirconia and Tantalum are

ii

used for Femur and Ultra High Molecular Weight

Polyethylene (UHMWPE) for Tibia. The aim of this

project is to prepare a 3D model of the Knee

prosthesis and calculate the Stress, Contact and

Deformation for the various bio-materials used in the

TKR components. The 3D Modelling of knee prosthesis

was made using SolidWorks, while the pre-processing

was done using HYPERMESH and the FEA software ABAQUS

CAE was used as a solver for the contact pressure,

deformation on the knee. The aim is to find out by FEM

analysis results, for the various bio-materials under

static condition and find out the best materials for

the purpose of the Knee Implant.

iii

TABLE OF CONTENTS

CHAPTER TITLE PAGE NO.

BONAFIDE CERTIFICATE i

ABSTRACT ii

TABLE OF CONTENTS iii

LIST OF TABLES vi

LIST OF FIGURES vii

1. LITERATURE SURVEY 1

1.1 KNEE JOINT 1

1.2 FAILURE OF TKR 2

1.3 JOINT LOADING 2

1.4 MATERIALS 4

1.4.1 TITANIUM ALLOY 4

1.4.2 COBALT CHROMIUM ALLOY 5

1.4.3 STAINLESS STEEL 5

iv

1.4.4 ZIRCONIUM CERAMICS 5

1.4.5 POROUS TANTALUM 6

v

CHAPTER TITLE PAGE NO.

1.4.6 UHMWPE 6

1.5 PROBLEM STATEMENT 7

2. KNEE IMPLANT AND ITS MODELLING 8

2.1 KNEE IMPLANT 8

2.2 MODELLING OF KNEE IMPLANT 9

2.2.1 CAD MODELLING 9

2.2.2 FEM ANALYSIS 12

2.2.2.1 MESHING 12

2.2.2.2 CONTACT INTERFACE 13

2.2.2.3 MATERIAL PROPERTIES 14

2.2.2.4 BOUNDARY CONDITION 15

2.2.2.5 OUTPUT BLOCK 16

2.3 ANALYSIS 16

3. FINITE ELEMENT METHOD RESULTS 17

vi

3.1 VON-MISES STRESS 17

3.2 STRAIN/ DEFORMATION 20

CHAPTER TITLE PAGE NO.

3.3 YOUNGS MODULUS 22

4 RESULT AND CONCLUSION 25

5 BIBILOGRAPHY 29

vii

LIST OF TABLES

TABLE NAME PAGE

1 MATERIAL PROPERTIES 14

2 MINIMUM AND MAXIMUM STRESS

IN PROSTHESIS MADE OF DIFFERENT 19

MATERIAL (MPa)

3 STAIN COMPARISON OF PROSTHESIS

MADE OF 5 DIFFERENT MATEIRAL 22

4 TABLE FOR EVALUATION OF AHP 25

5 SCORING TABLE FOR

OSSEOINTERGRATION 26

viii

6 SCORING TABLE FOR COEFFICIENT

OF FRICTION 27

7 ANALYTIC HIERARCHY PROCESS TABLE 28

LIST OF FIGURES

FIGURE NAME PAGE

1 MEDIAL VIEW OF THE RIGHT KNEE 1

2 REPRESENTATION OF TOTAL KNEE

REPLACEMENT 3

3 MOBILE BEARING PROSTHESIS 9

4 FIXED BEARING PROSTHESIS 9

5 2D MODEL OF FEMUR IMPLANT 10

ix

6 2D MODEL OF TIBIA IMPLANT 10

7 3D MODEL OF FEMUR IMPLANT USING

SOLIDWORKS 2014 11

8 3D MODEL OF TIBIAL IMPLANT USING

SOLIDWORKS 11

9 ASSEMBLED MODEL OF THE KNEE IMPLANT 12

10 MESHED MODEL OF KNEE PROSTHESIS 14

11 MASKED VIEW OF SOLID MODEL 14

12 BOUNDARY CONDITION OF SOLID MODEL 15

13 CONTOUR PLOT OF VON-MISES FOR ZIRCONIA

(JUMPING) 17

14 CONTOUR PLOT OF VON-MISES FOR

Ti6Al4V(JUMPING) 17

x

15 CONTOUR PLOT OF VON-MISES FOR POROUS

TANTALUM (JUMPING) 18

16 CONTOUR PLOT OF VON-MISES FOR Co-Cr

ALLOY (JUMPING) 18

17 CONTOUR PLOT OF VON-MISES FOR

316L SS (JUMPING) 18

18 STRESS LEVEL COMPARISON FOR THE THREE

LOADING CASE SCENARIO 20

19 CONTOUR PLOT OF STRAIN FOR 316L SS 20

(JUMPING)

FIGURE NAME PAGE

20 CONTOUR PLOT OF STRAIN FOR

Co-Cr ALLOY (JUMPING) 21

21 CONTOUR PLOT OF STRAIN FOR

POROUS TANTALUM (JUMPING) 21

xi

22 CONTOUR PLOT OF STRAIN FOR Ti6Al4V

(JUMPING) 21

23 CONTOUR PLOT OF STRAIN FOR ZIRCONIA

(JUMPING). 21

24 STRESS- STRAIN GRAPH OF 316L SS

OBTAINED FROM ABAQUS 23

25 316L SS SPECIMEN BEFORE TENSILE TEST 23

26 TENSILE TEST SPECIMEN DIAGRAM 23

27 FAILED SPECIMEN AFTER TESNSILE TEST 24

28 STRESS - STRAIN% GRAPH FROM UTM 24

1

CHAPTER 1

LITERATURE SURVEY

1.1 - KNEE JOINT

The knee joint joins the thigh with the leg and consists

of two articulations: one between the femur and tibia, and

one between the femur and patella. It is the largest joint in

the human body. The knee is a pivotal condylar joint, which

permits flexion and extension as well as a slight internal

and external rotation. The knee is a hinge type synovial

joint, which is composed of three functional compartments:

the femoro-patellar articulation, consisting of the patella,

or "kneecap", and the patellar groove on the front of

the femur through which it slides; and the medial and lateral

femoro-tibial articulations linking the femur, or thigh bone,

with the tibia, the main bone of the lower leg. The joint is

bathed in synovial fluid which is contained inside

the synovial membrane called the joint capsule.

2

Fig. 1 - Medial View of Right Knee

The knee consists of three more or less independent

articulations: one between each sphere-like condyle of

the femur and a corresponding but more planar condylar

surface of the tibia, with interposed menisci, and a

third between the patella and the patellar groove of

the femur. None of the pairs of bearing surfaces is

exactly congruent, which results in a combination of

rolling and gliding motions determined by the

restraints of a complex network of ligaments, capsular

structures, and the contours of the bones themselves.

This intricate arrangement of anatomic

interrelationships allows the knee six degrees of

freedom of motion: three rotations and three

translations. The translations are anteroposterior (5

to 10 mm), compression–distraction (2 to 5 mm), and

mediolateral (1 to 2 mm). These motions are limited by

the ligaments, capsul, The rotations are flexion–

extension, varus–valgus, and internal–external

rotation, and in general they are much more extensive

than the translations. Normal flexion and extension of

the knee is variable, ranging from 0° to 15° of

hyperextension to 130° to 150° of flexion. Internal and

external rotation ranges from little or no motion in

full extension to 20° to 30° with the knee flexed.[11]

1.2 - FAILURE OF TKR

Arthritis is a disorder that results in the

inflammation of one or more joints. There are over 100

3

different types of arthritis. The most common type,

osteoarthritis, is due to trauma to the joint, infection of

the joint, or age. Other forms of arthritis are- rheumatoid

arthritis, psoriatic arthritis, and other related autoimmune

diseases. Osteoarthritis (OA) and rheumatoid arthritis (RA)

largely affect joints present in the fingers, shoulders,

elbows and also specifically the knee joint. Osteoarthritis

ranks as the 4th leading cause of the Years Lived with

Disability (YLDs).

Joint replacement represents an appealing means to relieve

the pain and increase the mobility of arthritic patients.

Nearly 200,000 Total Knee Replacements (TKR) are implanted

annually in the United States. Most TKR designs incorporate a

polished metallic femoral component, usually made from a

cobalt- chrome alloy or Titanium Aluminum alloy in contact

with a tibial bearing made from Ultra- High Molecular Weight

Polyethylene (UHMWPE). Femoral component are also made up of

Zirconium Oxide, Stainless Steel, pure Titanium and pure

Tantalum in certain cases. The loading conditions in knee

joints are cyclic in nature, and they vary with the flexion

and extension angle. Owing to inertia forces during the human

gait, loads of more than 2-3 times body weight can be

supported by the knee during a typical walk cycle and other

research has shown that loads can exceed 8 times body weight

in many cases. These loads cause high contact pressures in

the concentrated contact between the metallic femoral

component and the UHMWPE tibial bearing. Therefore, after

implantation the non conforming TKR bearings are subjected to

4

many cycles of high contact stress during oscillatory

rolling/sliding contact. Although many implanted knee

prostheses have withstood 10 or even 20 years of activity

without substantial surface damage many other tibial bearings

of TKR have shown evidence of significant wear and contact

fatigue damage, requiring early replacement (5 years after

implantation). The replacement procedures are costly and can

have serious health consequences.[12][13][14][16]

1.3 - JOINT LOADING

It has been estimated that femoro-patellar contact forces

can range from 300 to 2000 N during normal walking. This

translates to a compressive stress of 2-4 MPa on the contact

surface. When considering joint loading on the knee, it is

important to note that load on the knee joint is rarely

constant for an extending period of time. Proper loading

analysis must consider spatial dimensions, position of the

joint, and muscle groups most active in loading activity. The

walk cycle is broken into four phases: stance, swing, heel

strike, and toe off. For most of the walk cycle, one leg is

in swing phase and one is in stance. The leg in stance phase

is weight bearing and in contact with the ground. [1] The

walking cycle becomes more complex when considering the five

separate motions involved: pelvic rotation, pelvic tilt, knee

flexion, ankle flexion, and toe flexion. These five motions

result in a center of gravity path that oscillates left to

right and up and down creating a figure 8 motion.

5

Fig.2

-

Representation of Total Knee Replacement

Maximum load on the knee occurs during the heel strike and

just before toe off phases of the walk cycle, where it

reaches about 1500 N. [2] Sliding velocity in the knee varies

with load and increases as load on the knee decreases. Forces

in the knee are highly dependent on the position of the

tibia, as a 1-degree change in angle moves the knee by 10mm.

Joint force can be calculated with 2-D or 3-D analysis and

static or dynamic analysis of horizontal force balance,

vertical force balance, and moment balance in the joint. [2] A

real time experiment performed on knee shows, 1.5 - 1.8 times

the body weight being transmitted on the tibial part of the

knee.

1.4 - MATERIALS

1.4.1 - TITANIUM ALLOY

6

Titanium alloys are metals that contain a mixture of

Titanium and other chemical elements like Vanadium, Aluminum,

Niobium, Iron and oxygen. Such alloys have very high tensile

strength and toughness. They are light in weight, have

excellent corrosion resistance and the ability to withstand

extreme temperatures. This makes the alloys most suitable for

aircraft, spacecrafts, medical devices, sports cars etc.

Although pure titanium has acceptable mechanical properties

and has been used for orthopedic implants, for most

applications titanium is alloyed with small amounts of

aluminum and vanadium, typically 6% and 4% respectively by

weight. Grade 5, also knows as Ti6Al4V is most commonly used

alloy. It has a chemical composition of 6% aluminum,

4%vanadium, 0.25% Iron and 0.2 % oxygen, while the rest is

Titanium. This grade of Titanium alloy has an excellent

combination of strength, corrosion resistance, weld and

fabricability. Ti6Al4V is used in application up to 400

degrees Celsius. It has a density of 4430 kg/m3, Young's

Modulus of 115 GPa and Poission’s ratio of 0.342. Ti6Al7Nb was

developed as a bio-medical replacement of Ti6Al4V because

Ti6Al4V contains vanadium, an element that has demonstrated

cytrotxic outcomes when isolated. Ti6Al7Nb contains 6%

Aluminum and 7% Niobium.[28][29]

1.4.2 - COBALT-CHROMIUM ALLOY

Cobalt-Chromium also known as Cobalt-Chrome is a metallic

alloy made up up Cobalt and Chromium. Because of its high

strength, it is extensively used in gas turbines, Orthopedic

7

and Dental implants. Co-Cr alloys show high resistance to

corrosion due to the spontaneous formation of a protective

passive film composed of Cr2O3. Because of its bio-compartable

property, it finds wide application in Bio-medical industry.

Good Mechanical properties that are similar to stainless

steel are a result of multi-phase structure which increases

the hardness of the alloy. Co-Cr alloys are most commonly

used to make artificial joints including knee and hip joints

due to high wear-resistance and bio-compatibility.[18][19]Co-Cr

alloys tend to be corrosion resistance, which reduces

complication with the surrounding tissues when implanted, and

chemically inert that they minimize the possibility of

irritation, allergic reaction, and immune response.  Co-Cr

alloy has also been widely used in the manufacture of stent

and other surgical implants as Co-Cr alloy demonstrates

excellent bio-compatibility with blood and soft tissues as

well. The alloy composition used in orthopedic implants is

described in industry standard ASTM-F75: cobalt with 27 to

30% chromium, 5 to 7% molybdenum, and limits on other

important elements such as manganese and silicon, less than

1%, iron, less than 0.75%, nickel, less than 0.5%, and

carbon, nitrogen, tungsten, phosphrous, sulphur and boron[20]

[23][24]

1.4.3 - STAINLESS STEEL

Stainless steel, also know as inox steel is a steel alloy

with a minimum of 10.5% chromium content by mass. Low-carbon

versions, for example 316L or 304L, are used to avoid

8

corrosion problems caused by welding. Grade 316L is preferred

where biocompatibility is required such as body implants and

piercings.  The "L" means that the carbon content of the

alloy is below 0.03%, which reduces the sensitization effect

caused by the high temperatures involved in welding. Grade

316 is the standard molybdenum-bearing grade, second in

importance to 304 amongst the austenitic stainless steels.

The molybdenum gives 316 better overall corrosion resistant

properties than Grade 304, particularly higher resistance to

pitting and crevice corrosion in chloride environments. The

austenitic structure also gives these grades excellent

toughness, even down to cryogenic temperatures. Compared to

chromium-nickel austenitic stainless steels, 316L stainless

steel offers higher creep, stress to rupture and tensile

strength at elevated temperatures.[17]

1.4.4 - ZIRCONIUM CERAMICS

Yttria-stabilized zirconia (YSZ) is a ceramic in which the

crystal structure of zirconium dioxide is made stable at room

temperature by an addition of yttrium oxide. These oxides are

commonly called "zirconia" (ZrO2) and "yttria" (Y2O3).

Yttria-stabilized zirconia (YSZ) is a form of Zirconiumceramic that is most commonly used as bio-materials in human

body as implants. These materials are used extensively for

the purpose of Dental implants as Crowns and as Hip and Knee

9

implants. Zirconia is best known among ceramics as being both

hard and fracture-tough at room temperature. [26]Additionally,

its fine grain size enables excellent surface finishes and

the ability to hold a sharp edge. Althought it retains many

properties including corrosion resistance at extremely high

temperature, Zirconia does exhibit structural change that can

limit its use at high temperatures of about 500 degree

Celsius. Zirconia is tough because it has a teragonal

structure that precipitates a stress induced phase

transformation near an advancing crack tip. [27][30][31]

1.4.5 - POROUS TANTALUM

With the advancements in the field of Material Science and

Bio-Materials, Porous Tantalum has come into the picture as

an alternative metal for primary and revision Total Knee

Arthroplasty, because of its several unique properties.

Tantalum is a transition metal, which in its bulk nature

shows excellent biocompatibility. It is safe to use it in

vivo as Porous Tantalum finds its application in pacemaker

electrodes, cranioplasty plates, and radiopaque markers.

Porous Tantalum as a orthopedic implant maintain a high

columetric porosity (70%-80%), low modulus of elasticity,

making it a good fit for biologic fixation. Because of its

low modulus of elasticity, it allows a more physiologic load

transfer and relative preservation of bone stock. Although

porous tantalum is in its early stages of evolution, the

initial clinical data and studies support of its use as an

10

alternative to traditional orthopedic implant materials.[25][32]

[33]

1.4.6 - UHMWPE

Ultra high molecular weight polyethylene is a subset of

the thermosplastic polyethylene. Also known as high modulus

polyethylene, it has extremely long chains, with a molecular

mass usually between 2 and 6 million atomic mass unit. [10]The

longer chain serves to transfer load more effectively to the

polymer backbone by strengthening intermolecular

interactions. This results in a very tough material, with the

highest impact strength of any thermoplastic presently made.

UHMWPE is odorless, tasteless, and nontoxic.[11 It is highly

resistant to corrosive chemicals except oxidizing acids; has

extremely low moisture absorption and a very low coefficient

of friction; is self-lubricating; and is highly resistant

to abrasion, in some forms being 15 times more resistant to

abrasion than carbon steel. Its coefficient of friction is

significantly lower than that of nylon and acetal, and is

comparable to that of PTFE but UHMWPE has better abrasion

resistance than PTFE. [12]

1.5 - PROBLEM STATEMENT

The aim of this project is to find out the Stress, Strain

and Deformation for the various materials that are used as

femoral implants in Total Knee Arthroplasty using Finite

Element Analysis (FEA). Also taking into consideration other

11

factors such as Density and Osseointergration, to find the

material that is best suited as a femoral implant, when

UHMWPE is taken as the material for Tibia. In order to find

the best material for femoral implant, a Multi- Criteria

Decision Making procedure known as Analytic Hierarchy Process

(AHP) is used.

The analytic hierarchy process (AHP) is a structured

technique developed by Thomas. L. Saaty in 1970 for

organizing and analyzing complex decisions. This process is

generally used to make group decision making and is used

around the world in large scale for a variety of decision

situations, in the field of government, business, industry,

health care, shipbuilding, education etc. In this process,

rather than suggesting the “Correct” decision, it helps the

decision makers to find that alternative that best suits

their goal. It provides a comprehensive and rational

framework for structuring a decision problem, for

representing and quantifying its elements, for relating those

elements to overall goals and for evaluating alternative

solutions.[21][22]

Users of the AHP, first dissect their decision problem

into a sub-problems that are easier to comprehend. This way

each of the sub-problems can be analyzed independently. The

elements of this sub-problems can relate to any aspect of the

decision problem, carefully measured or roughly estimated,

well or poorly understood- anything at all that applies to

the decision at hand.

12

CHAPTER 2

KNEE IMPLANT AND ITS M

2.1 KNEE IMPLANT

The earliest Total Knee Arthroplasty can be dated back to

1860, when a German surgeon by the name Themistocles Gluck

implanted the first artificial knee. It was based on the

principle of Hinge Joint and was made up of Ivory. In 1960s

John Charnley’s cemented metal on polyethylene total hip

arthroplasty inspired the development of the modern total

knee replacement.

With improvement in the field of Biomechanics, cruciate

and collateral ligaments began to be preserved intact, which

helped in maintaining the stability of unlinked femoral and

tibial components. Throughout the 1970s and 1980s incremental

improvement in component material, geometry and fixation

continued. The early efforts of McKeever and Eliott to

develop a Unicompartmental Knee Arthroplasty was being

pursued even in the 80s. However because the unicompartmental

procedure replaces only the diseased part of the joint with

more natural kinematics , the indications for its use are

more limited.

In the modern Total Knee Arthroplasty, the affected

portion of the knee are precision cut by the surgeon using

13

special cutting instruments, for the implant to fit on the

knee properly. Then the implants are fixed on to the knee

either using bone cement (polymethylmethacrylate) or by means

of screws. In most of the cases the Posterior Cruciate

Ligament (PCL) are removed along with the Anterior Cruciate

Ligament (ACL), while in some cases the the PCL is retained

with provision in the knee implants to accommodate the PCL,

to give better stability to the knee. The latter model is

more appropriate for patients who have a strong and healthy

PCL, and it needs no external support.

The other variation the knee implant provides is Fixed

Bearing Prosthesis and Mobile Bearing Prosthesis. In fixed

bearing prosthesis , the polyethylene of the tibial component

is attached firmly to the metal implant beneath. The femoral

component then rolls over the tibial component which acts as

a cushioned surface. While the other model namely Mobile

bearing prosthesis consists of the polyethylene of tibia

rotating over the metallic implant beneath it. Compared with

fixed-bearing designs, mobile-bearing knee implants require

more support from soft tissues, such as the ligaments

surrounding the knee. [1]

Fig.3- Mobile

Bearing Prosthesis

Fig.4- Fixed Bearing

Prosthesis

14

In the late 1980’s and early 1990’s, there have been tests

performed to introduce all polymer implant. Polyethylene was

used as the femur and Polyacetal was used as the tibial

plate. Though it showed significant reduction in the wear (up

to 20% improvement), issues of load bearing capacity were

reported among few patients. This accounts to the low load

bearing capacity of the Polymers. Similarly an all metal

implant may also face problems in terms of the excessive

wear, when a metal slides over another metal. For this

reason, a combination of metal and polymer is used. The

femoral head made up of metal acts as a load bearer, thereby

transmitting the load to the tibia efficiently,and the

Polymeric Tibia act as a lubricating part. The Polymer

(generally UHMWPE) used in the tibia also acts as a shock

absorber. This excellent combination helps in the functioning

of the artificial knee.[15]

2.2 - MODELLING OF KNEE IMPLANT

2.2.1 - CAD MODELLING

The geometry of the knee implant has a significant

influence in the performance of the implant. Thus it is

necessary to model the implant according to the standard

procedure. The 2D model of the knee implant can be made using

CT scan of the knee and with the help of MIMICS software. For

the purpose of this project, the 2D model of the knee implant

was referred from the research paper “Finite Element M and

15

Analysis of Prosthetic Knee Joint” by G.Mallesh and

Sanjay.S.J.[3] 2D model of the Femur and Tibia implants are

shown below in Fig.5 and Fig.6

Fig.5- 2D Model

of Femur Implant

Fig.6- 2D Model of Tibia Implant

The 3D model of the implant was

made using SolidWorks 2014 X 64 Edition.SolidWorks is a solid

modellingComputer Aided Design (CAD) that runs on Microsoft

Windows. It is a powerful 3D design solution for rapid

creation of parts, assembly and 2D drawing. Application

specific tools for sheet metals, surfacing, welding, mold

tools etc and also available in SolidWorks. The Solid

modelling of the Knee Implant is shown below in Fig7, Fig.8

and Fig.9

16

Fig.7- 3D Model of Femur Implant using SolidWorks 2014

17

Fig.8- 3D model of Tibial Implant using SolidWorks 2014

18

Fig.9- Assembled model of the Knee Implant

2.2.2 - FEMANALYSIS

Finite Element Method (FEM) analysis of the prosthetic

joint for various bio-materials of the femur was performed

partly in HYPERMESH and partly in ABAQUS. The meshing,

defining interfaces and boundary conditions of the model was

performed on Hypermesh.[4][5][6]

19

2.2.2.1 - MESHING

The assembled solid model of the knee implant was imported

into HYPERMESH in the form of IGES format. ABAQUS user

profile was used when working on Hypermesh. Upon importing,

all the solids from the model is deleted, with only the

surface of model remaining. Then the Femur part of the model

is offset by 2mm towards the Tibia to bring about the

Condylar shape of the implant. At this point, some amount of

surface of both the Tibia and Femur is being overlapped.

Hence to remove any possible errors, the shared surface of

the Tibia is deleted. Tetrahedral elements were used to mesh

the complete knee prosthesis. Tetrahedral elements were

chosen over the brick elements because tetrahedral elements

better approximate the shape around the sharp corners, with

minimal error. The size of the elements were chosen to be 0.5

mm. Meshed model of the Knee Implant is shown below in Fig.

10. All the elements are then checked for any possible errors

such as max length, min length, min and max angles, skew,

jacobian etc, and corrected if error exists.

20

Fig.10- Meshed model of Knee Prosthesis

2.2.2.2- CONTACT INTERFACE

In order for the load/pressure/force to be transmitted

from one part of the model to another part of the same model,

it is necessary for the two parts to have some kind of

surface interaction. For this purpose Hypermesh provides

various types of surface interaction such as Frictional

Contact, Tie constrain, Shell Coupling, General Contact. In

this model, Tie Constrain is defined between the contacting

surfaces of the Femur and Tibia.

A tie constrain ties two separate surfaces together so

that there is zero relative motion between them. This type of

constrain allows us to fuse together two parts even if the

meshes created on their surfaces are dissimilar. Tie

constrain can be defined between edges of wire, or solids or

21

between faces or shells.

Fig.11- Masked view of Solid Model

2.2.2.3 - MATERIAL PROPERTIES

Both parts of the solid model were defined by a material. And

for each of the material, their respective material properties such

as Density, Young’s Modulus, Poissions Ratio etc were defined. In

total, 5 Femoral materials were considered i.e 316 L Stainless

Steel, Cobalt-Chrome Alloy, Titanium Aluminum Alloy (Ti6Al4V),

Porous Tantalum and Zirconia (ZrO2). The Tibial material always

remained constant i.e Ultra High Molecular Weight Polyethylene

(UHMWPE). The material properties of these materials are tabulated

below in Table.1 [11][12][17][20][23][24][25][27][28][29][30][31][32][33]

MATERIAL DENSITY (Kg/m3) YOUNGS

MODULUS (MPa) POISSIONS RATIO

22

316L SS 8000 1.97E+5 0.3

Co-Cr Alloy 8300 2.3E+5 0.3

Ti6Al4V 4430 1.15E+5 0.342

Porous Tantalum 16700 1.86E+5 0.34

Zirconia 6040 2.1E+5 0.3

UHMWPE 930 6.9E+3 0.29

TABLE.1 MATERIAL PROPERTIES

2.2.2.4 - BOUNDARY CONDITION

Load on the model is applied in the form of force.

According to ISO 14243-1, an axial compressive load is one

which acts while standing and thus needs to be applied on the

model. Also according to 14243-1, maximum load should be

applied for testing of the knee implant. In this study, 3

loading case scenario are considered i.e Walking ( 2.84 X

Body weight), Running (5.5 X Body Weight), Jumping (9 X Body

Weight). Thus the load being applied on each knee while

Walking, Running and Jumping are 994N, 1925N and 3150N

respectively considering a person of 70Kg weight. The Tibial

part of the prosthesis was constrained of all degrees of

freedom (DOF) from the bottom surface.[10]

The Tibial portion is constrained of all degrees of

freedom by creating a “Load Collector” in the name of

CONSTRAINS. By selecting “CONSTRAINTS” option available in

“ANALYSIS”, all elements of the bottom surface of the Tibia

23

are selected and the constraints are created in all the 6

DOF. Similarly another “Load Collector” is created in the

name of LOAD. The load is applied on the flat surface of the

Femoral implant that is parallel to the Tibial surface. A

Master node was created and all the nodes of the flat surface

of femur (on which load is to be acted) is connected to the

master node by means of rigid links. To apply the load,

“FORCES” option is selected from “ANALYSIS”, following which

the master node is selected on which the force is to be

acted. Then the magnitude of the forces is specified along

with direction of force.

Fig.12- Boundary Condition of Solid Model

24

2.2.2.5 - OUTPUT BLOCK

In order to obtain and view results, it is necessary to

define the OUTPUT BLOCK. Output Block is an option in

Hypermesh that requests for the output of the analysis for

either some or all the entities in the model. In order to

define the Output block, two Output blocks are created, one

each for Tibia and Femur. For each of this, “Node Output (to

obtain the results of displacements)” and “ Element Output

(to obtain the results of Stress and Strain)” are selected.

In the Element Output, the required outputs are selected for

eg. ‘S’, ‘SINV’, ‘E’ and similarly in the Node Output, ‘U’ is

selected. This way all the required outputs are selected

which would be displayed upon the completion of the analysis.

2.2.3 - ANALYSIS

Once the meshing, interface conditions, boundary

conditions, material properties and output block have been

defined, the model is exported as Solverdeck in Abaqus File

Format (.inp). Upon importing the model is run in ABAQUS, by

opening the command window and giving the following command “

ABAQUS ANALYSIS JOB= “FILE NAME” INT ”. Once the analysis has

been completed, the results can be viewed using .odb file.

25

CHAPTER - 3

FINITE ELEMENT METHOD RESULTS

3.1 - VON-MISES STRESS

26

Stress is the force per unit area that some particles in a

body exert on adjacent particles. In prosthesis such as the

knee, lower the value of stress better is the prosthesis.

The following 5 figures shows the Contour Plot of Von-

Mises Stress for the five different materials that were used

as femoral implants. The scenario considered for loading was

Jumping with a load of 3150N.

Fig.13 - Contour Plot of Von-Mises for Zirconia (Jumping)

27

Fig.14 - Contour Plot of Von-Mises for Ti6Al4V (Jumping)

Fig.15 - Contour Plot of Von-Mises for Porous Tantalum (Jumping)

28

Fig.16 - Contour Plot of Von-Mises for Co-Cr Alloy (Jumping)

Fig.17 - Contour Plot of Von-Mises for 316L Stainless Steel (Jumping)

MATERIAL/

LOADING

WALKING

(994N)

RUNNING

(1925N)

JUMPING

(3150N)

MAX MIN MAX MIN MAX

29

MIN

(MPa) (MPa) (MPa) (MPa) (MPa) (MPa)

316L SS 1.3E-7 7.6 2.518E-714.8 4.120E-724.21

Co-Cr Alloy 1.307E-7 7.649 2.531E-714.81 4.141E-724.21

POROUS

TANTALUM 1.59E-7 7.49 3.005E-714.51 5E-7 23.74

Ti6Al4V 1.535E-7 7.452 2.972E-714.43 4.064E-723.62

ZIRCONIA 1.303E-7 7.644 2.523E-714.80 4.129E-724.22

The Maximum and Minimum stress induced in the five TKR are

tabulated below

TABLE.2 - Minimum and Maximum Stress in Prosthesis Made of Different

Material (MPa)

Upon comparing the stress levels, it shows that all the 5

bio-materials show almost the same stress levels. Also each

of these materials have similar contour plot of Von-Mises

Stress. However, Ti6Al4V is the best suited material in terms

of the stress induced in the prosthesis, as it induces the

least amount of stress in comparison to the other four bio-

materials.

30

Fig.18 - Stress Level Comparison for the three loading case scenario

3.2 - STRAIN/ DEFORMATION

Strain/Deformation in continuum mechanics is the

transformation of a body from a reference configuration to a

current configuration. A Configuration is a set containing

the positions of all particles of the body. A Deformation may

be caused by external loads, body forces, or change in

temperature, moisture, etc. In terms of the prosthesis, lower

the value of stress, safer and better is the prosthesis.

The following five figures, show the contour plotting of

the strain induced in each of the 5 prosthesis. The loading

condition is considered to be Jumping where the load applied

is 3150 N.

31

Fig.19 - Contour Plot of Strain for 316L Stainless Steel (Jumping)

Fig.20 - Contour Plot of Strain for Co-Cr Alloy (Jumping)

32

Fig.21 - Contour Plot of Strain for Porous Tantalum (Jumping)

Fig.22 - Contour Plot of Strain for Ti6Al4V (Jumping)

33

Fig.23- Contour Plot of Strain for Zirconia (Jumping)

MATERIAL/LOADING CONDITIONWALKING RUNNING JUMPING

316L SS 0.000416 0.0008066 0.001320

Co-Cr Alloy 0.000416 0.0008059 0.001320

Porous Tantalum 0.000416 0.0008064 0.001320

Ti6Al4V 0.0004156 0.0008050 0.001317

Zirconia 0.0004166 0.0008067 0.001320

TABLE.3 - STRAIN COMPARISON OF PROSTHESIS MADE OF 5 DIFFERENT

MATEIRAL

Upon comparison of the five different materials used in

the femoral insert of the knee prosthesis, the maximum

variation in strain levels is about 0.000016. As this value

is too small, the variation in the strain level is assumed to

be negligible.

3.3 - YOUNGS MODULUS

Young's modulus, also known as the tensile

modulus or elastic modulus, is a measure of the stiffness of

an elastic material. It is defined as the ratio of

the stress (force per unit area) along an axis to

the strain (ratio of deformation over initial length) along

that axis in the range of stress in which Hooke's law holds.

The unit of measurement is the same as that of Pressure (MPa

34

or N/mm2)

In order to validate the results obtained from ABAQUS, the

Youngs Modulus of 316L SS was calculated by plotting the

Stress-Strain graph from the values obtained from ABAQUS

. Thus obtained value of the Young’s Modulus was compared

with the value that was obtained by performing Tensile Test

on a specimen of 316L SS using a Universal Testing Machine

(UTM).

The Stress Strain graph obtained from ABAQUS is shown

below in Fig.24

Fig.24

- Stress

Strain

graph of

316L SS

obtained

from ABAQUS

The

Youngs

Modulus

thus

obtained of Stress-Strain through ABAQUS was 2.26 X 105 MPa.

35

Fig.25 - 316L SS Specimen before Tensile Test

In order to perform the Tensile Test, a 316L SS rod of

20mm diameter and 250mm Length was machined as per the

dimensions given in Fig.26

Fig. 26 - Tensile Test Specimen Dimension

36

Fig.27 - Failed Specimen After Tensile Test

The Stress - Strain% graph obtained upon performing the

Tensile Test using Universal Testing Machine is shown in

Fig.28

37

Fig.28 - Stress-Strain% graph from UTM

The Young’s Modulus thus obtained from the Tensile Test

performed using UTM is 1.014 X104 MPa.

Possible source of errors while performing Tensile Test

are :

Alignment Error

Improper Calibration of Elongation Measuring Instrument in

UTM

38

CHAPTER - 4

RESULT AND CONCLUSION

According to the results obtained for stress using FEM, it

suggests that Ti6Al4V >

Porous Tantalum > Co-Cr Alloy > 316LSS > Zirconia, where ‘>’

is the symbol used to indicate ‘ better than’. However as per

the results obtained from the strain analysis, it suggests

that Ti6Al4V > Co-Cr Ally > Porous Tantalum > 316L SS >

Zirconia. However, while finding out the better/best

material,stress and strain are not the only factors that

needs to be taken into consideration. Other factors such as

Osseointergration, Coefficient of Friction, Density, etc also

needs to be considered.

Criteria/

MaterialOsseointergration

Coefficient

of Friction

Stress

(MPa)

Percentage

Elongation

Density

(N/mm3)

316L SS Above average 0.156 7.6 0.416 8000

Co-Cr Alloy High 0.012 7.649 0.416 8300

Ti6Al4V Very High 0.112 7.452 0.4156 4430

Porous

Tantalum Very High 0.14 7.49 0.416 16690

39

Zirconia Extremely High 0.082 7.644 0.416 6040

While considering multiple factors and multiple

alternatives, the task of choosing the best material becomes

tedious. To solve such a problem, the use of Multi Criteria

Decision Making (MCDM) process is made. Of the available

methods under MCDM, Analytic Hierarchy Method (AHP) is used

to solve the problem of determining the best material from

five options available. To start of with this method, firstly

a tabular column is made listing all the alternative and

criteria. Following this, the tabular column is filled with

appropriate data. The filled tabular column is shown below in

Table 4.[11][12][17][20][23][24][25][28][29][30][31][32][33][34][35][36][37]

TABLE.4 - Table for evaluation of AHP

After filling up of all the required data in the table, the

following steps are to be followed:

I. Each of the five criteria are assigned weight-age. The

criteria that holds the most importance, is given the

highest weight-age, while the least weight-age is given

to the criteria that holds the least importance of all

the criteria.

II. Each of the alternative are relatively ranked or

given a relative score for each of the five criteria. (

The ranking/score is given on the basis that the most

suitable material in a particular criteria is given the

lowest score/value) Scoring tables of Osseointergration

and Coefficient of Friction is given below in Table 5 and

Table 6

40

III. The AAHP for each of the material is calculated my

multiplying the weight-age of each criteria and its

respective score/rank.

The calculation is performed as shown below:

AAHP(316L SS) =(5*0.3) + (4*0.15) + (3*0.15) + (2*0.2)

+ (3*0.2) = 3.55

AAHP(Co-Cr Alloy) = (3.75*0.3) + (1*0.15) + (5*0.15) +

(2*0.2) + (2*0.2) = 2.825

AAHP(Ti6Al4V) = (2.5*0.3) + (4*0.15) + (1*0.15) + (1*0.20)

+ (5*0.2) = 2.7

AAHP(Porous Tantalum) = (2.5*0.3) + (4*0.15) + (2*0.15) +

(2*0.2) + (1*0.2) = 2.25

AAHP(Zirconia) = (1.25*0.3) + (3*0.15) + (4*0.15) +

(2*0.2) + (4*0.2) = 2.5875

OSSEOINTERGRATION

Extremely High 1.25

Very High 2.5

High 3.75

Above Average 5

Average 6.25

Low 7.5

Very Low 8.75

Extremely Low 10

41

TABLE 5 - Scoring table for Osseointergration

COEFFICIENT OF FRICTION

0 - 0.025 1

0.025 - 0.05 2

0.05 - 0.1 3

0.1 - 0.2 4

0.2 - 0.3 5

0.3 - 0.5 6

0.5 - 1 7

>1 8

TABLE 6 - Scoring Table for Coefficient of Friction

The completed AHP table is tabulated below in Table.7

By performing the AHP method, considering

Osseointergration, Coefficient of Friction, Stress induced,

Percentage of Elongation and the Density of the material, it

can be concluded that preference of materials for the Femoral

insert of the Knee Prosthesis is as follows:

Porous Tantalum > Zirconia > Ti6Al4V > Co-Cr Alloy > 316L

Stainless Steel

42

Criteria Osseo-

intergration

Coff.

of Friction

Stress

(MPa)

Percentage

Elongation

Density

(N/mm3)AAHP

Material Weight-

age 30% 15% 15% 20% 20% 100%

316L SS

Value/

Data

Above

Average 0.156 7.6 0.416 8000

3.55

Rank 5 4 3 2 3

Co-Cr

Alloy

Value/

Data High 0.012 7.649 0.416 8300

2.825

Rank 3.75 1 5 2 2

Ti6Al4V

Value/

Data Very High 0.112 7.452 0.4156 4430

2.7

Rank 2.5 4 1 1 5

Porous Value/ Very High 0.14 7.49 0.416 16690 2.25

43

Tantalum Data

Rank 2.5 4 2 2 1

Zirconia

Value/

Data

Extremely

High 0.082 7.644 0.416 6040

2.587

Rank 1.25 3 4 2 4

TABLE 7 - Analytic Hierarchy Process Table

CHAPTER 5

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