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Research ArticleAn SMA Passive Ankle Foot Orthosis Design Modelingand Experimental Evaluation

Liberty Deberg12 Masood Taheri Andani13

Milad Hosseinipour13 and Mohammad Elahinia1

1 Dynamic and Smart Systems Laboratory The University of Toledo Toledo OH 43606 USA2 Ecole Superieure des Sciences et Technologies de lrsquoIngenieur de Nancy (ESSTIN) Nancy Lorraine France3 Center for Vehicle Systems and Safety Virginia Tech Blacksburg VA 24061 USA

Correspondence should be addressed to Masood Taheri Andani masoodtavtedu

Received 8 January 2014 Revised 17 April 2014 Accepted 22 April 2014 Published 2 June 2014

Academic Editor Yanjun Zheng

Copyright copy 2014 Liberty Deberg et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Shape memory alloys (SMAs) provide compact and effective actuation for a variety of mechanical systems In this work thedistinguished superelastic behavior of these materials is utilized to develop a passive ankle foot orthosis to address the dropfoot disability Design modeling and experimental evaluation of an SMA orthosis employed in an ankle foot orthosis (AFO) arepresented in this paper To evaluate the improvements achieved with this new device a prototype is fabricated and motion analysisis performed on a drop foot patient Results are presented to demonstrate the performance of the proposed orthosis

1 Introduction

Drop foot is amotor deficiency due to paralysis of the anteriortibial muscle or the muscles innervated by the commonperoneal nerve This neuromuscular disorder can be causedby stroke multiple sclerosis diabetes or neuromuscularinjuries as a result of surgeries A drop foot patient is unableto dorsiflex hence drags the toe during swing Moreoverthe same patient is unable to control the foot during heelstrike which leads to foot slap However these patients oftenhave a controlled normal plantarflexion So far differenttreatments have been developed to address this deficiencyOrthotics functional electrical stimulation (FES) physicaltherapy and surgery are among common treatments offeredto these patients Each method has specific advantages anddisadvantages and is prescribed to a patient based on healthconditions symptoms and requirements Extensive discus-sion on conventional approaches is provided in [1]

Ankle foot orthoses (AFO) have increased in popularityover the past two decadesThese orthotic devices have the twofunctions of providing stability and maintaining the range ofmotion When used for permanent assistance orthoses canenable the patient walk easier and more normally [2] AFOsare externally applied and are intended to control the motion

of the ankle compensate the weakness and correct thedeformities Conventional AFOs are passive mechanicalbraces that prevent the toe dragging by restricting the anklemovement Although these light orthoses provide some shortand long term biomechanical benefits disadvantages stillremain Lehmann et al [3] found that although a constantstiffness AFOwas able to prevent the toe dragging the devicedid not reduce the occurrence of foot slap These devicesalso lead to disuse atrophy of the ankle flexor muscles bycompletely restricting the ankle motion In order to addressthese concerns researchers have developed active AFOs inwhich the impedance (stiffness) of the orthotic joint can bemodulated throughout the gait Blaya andHerr [2] developedan active ankle foot orthosis (AAFO) based on a series ofelastic actuatorsThemain goal of this design is to change theorthosis impedance actively As a result the AFO minimizesthe walking kinematic difference compared to a normalgait This device includes a DC motor mechanical linkagesand springs Although lab tests showed promising resultsthe actuator weighs 26 Kg and requires bulky batteries andelectronics for operation

Another active AFO uses a pneumatically powered lowerlimb exoskeleton [4] This AFO is actuated by McKibben

Hindawi Publishing CorporationSmart Materials ResearchVolume 2014 Article ID 572094 11 pageshttpdxdoiorg1011552014572094

2 Smart Materials Research

pneumatic artificial muscles One pneumatic actuatorprovides the plantarflexion torque while another one assiststhe dorsiflexion A control algorithm adjusts the air pressurein each actuator independently The study showed promisingresults in gait rehabilitation human motor adaptationand muscle activation However the applicability of theseorthoses is limited to laboratory studies and rehabilitationsince on board power supplies and computers are requiredfor their operation Shape memory alloy (SMA) basedAAFOs have also been studied in recent years by severalresearch groups [1 5 6]

This paper presents the design modeling and evaluationof a passive AFO which utilizes the superelastic behaviorof SMA wires SMAs are a group of smart materials thatcan undergo large deformations and provide actuation byrestoring their memorized shape The reversible mechanismbehind shape memory alloy actuation is a solid-state phasetransformation that takes place in response to variationof temperature and stress The distinct thermomechanicalbehavior of SMAs is the result of a transformation fromthe austenite (parent) phase to martensite (product) phaseand vice versa [7] These alloys have higher energy densitycompared to other smartmaterials such as piezoceramics andelectroactive polymers Therefore actuators that implementthese alloys are compact and lightweight alternatives for otherconventional actuators such as DC motors and solenoidsBiocompatibility and elastic properties similar to body tissuesare among the other reasons why SMAs are promisingcandidates for biomechanical applications and rehabilitationdevices In the following sections the proposed design isfirst presented A modeling approach is then introducedto capture the behavior of SMA wires under the requiredloading conditions The proposed modeling approach isverified experimentally for a similar loading path as neededin practice Finally the fabricated device is experimentallytested to record the improvements in walking quality of a realdrop foot subject

2 SMA Passive AFO Design

A typical passive AFO is a brace with constant torsionalstiffness that limits the motion of the ankle as shown inFigure 1 The SMA passive AFO consists of a hinged braceand a series of SMA wires This concept is depicted inFigures 2 and 3 As mentioned above most drop foot patientsare able to plantarflex their foot normally Therefore thesuperelastic wires can store mechanical energy during plan-tarflexion and release it during dorsiflexion to compensatethe inability Since the SMA wire undergoes stress inducedphase transformation during loading and unloading itsmechanical stiffness changes It is further shown that thechange in the stiffness of the SMA wire is similar to thenatural change in stiffness of the ankle joint in normal gaitThis eliminates excessive loads on active muscles letting thepatient walk more naturally and feel less exhausted On theother hand this actuation mechanism does not require a

Figure 1 A conventional passive ankle foot orthosis (DJ Orthope-dics)

Elongation powered

plantarflexion Recovery dorsiflexion

Figure 2 The SMA passive AFO concept SMA wires store energyin plantarflexion and release it to assist during dorsiflexion

complex controllingmechanismMoreover using SMAwiresalong with a hinged brace reduces the number of mechanicalparts manufacturing cost and complexity of maintenance

A prototype is developed as shown in Figure 4 The mainelement of the device is an SMA superelastic wire that isfixed to the brace at one end and is connected to the carriage(Figure 4) at the other end The carriage provides sufficientfreedom by moving on a slider connected to a ball jointSeveral small pulleys are mounted on the brace to hold therequired length of wireThe length of the wire not only affectsthe range of motion but also determines the life time of theorthosis A longer wire undergoes less strain and thereforehas a longer fatigue life

Smart Materials Research 3

Figure 3 The SMA passive AFO CAD design

3 Kinematics and Dynamics

During a normal gait the average walking speed is 5 Kmhand the average number of steps during one minute is about100 [8] Hence one stride corresponds to 16m during 12 sThe time requirement for the AFO to provide a normal gait isthus 12 s It is notable here that different gait parameters arereported in some older classical works [9ndash11]

Considering that the swing phase takes about 40 of astride 048 s is the time to activate the wire Foot dorsiflexesat the beginning of the swing phase to avoid the toe draggingfollowed by plantarflexion prior to the heel strikeThis can beseen on the ankle angle diagram in Figure 5 Angle incrementcorresponds to dorsiflexion and decrement corresponds toplantarflexion

As the SMA wire embedded in the device is beingextended it provides the required rotation and torque tomove the foot In order to choose the appropriate wire it isnecessary to calculate the profile of force applied to the wireduring a gait cycle Calculations in this work are based on thetests andmeasurements done on amale patient in his eightieswho is 196m tall and is 943 Kg in weight [1] If the anklemoment (119872) is known then the force (119865) applied to the wirecan be found through

119872 = 119865119886 (1)

where 119886 is the distance between the rear of the heel and theaxis of rotation of the ankle For the subject of this study thisdistance is measured to be 85mmTherefore by knowing theanklemoment the required force can be calculatedHoweverthe moment has not been recorded during the swing phase(and it is shown as zero in Figure 5) while the value ofrotation has been recorded Considering the weight of thefoot and its acceleration (from the ankle angle diagram) themoment can be calculated during the swing phase from

119872 = 1198691198892120579

1198891199052+ 119898119892119889 cos 120579 (2)

where 119869 120579119898 and 119889 represent the second moment of inertiaangle of rotation mass of the foot and the distance betweenthe axis of rotation of ankle (119874) and center of gravity of thefoot (119866) Anthropometric data are used to calculate theseparameters as follows 119889 = 110mm 119898 = 136Kg and119869 = 00247Kgm2 [12]

The ankle angle data reported in Figure 5 is used tocalculate the ankle moment during the swing phase from (2)Then the force profile can be found through (1) As shown inFigure 6 the maximum force needed to lift the foot up andprovide the angular acceleration is 55N

The next step in designing the AFO is determiningthe length and configuration of SMA wires For such apurpose a semianalytical approach is developed to capturethe thermomechanical behavior of the SMA wire under thesubjected loading condition

4 Modeling

41 Coupled Constitutive Relations for the Uniaxial LoadingCase The modeling approach presented in this work isbased on the 3D phenomenological constitutive model forSMAs developed by Boyd and Lagoudas [13] and Qidwai andLagoudas [14] The coupled form of the model is analyticallystudied in several works [15ndash17] In this section a reducedsimple formulation of themodel is presented for the situationwhen a wire is under uniaxial loading and unloading which isthe case in the proposed SMA AFO In this study normal oraxial strain will be considered constant throughout the cross-section which is a valid assumption for small diameters Inthis case the stress strain and reversal transformation straintensors have the following forms

120590 = (

0 0 0

0 0 0

0 0 120590119911119911

) 120598 = (

120598119903119903

0 0

0 120598120579120579

0

0 0 120598119911119911

)

120598119905minus119903

= (

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(3)

where 120590119911119911 120598119911119911 and 120598119905minus119903

119911119911are the axial stress axial strain and

the axial strain at the reversal point respectively The terms120598119903119903 120598120579120579 120598119905minus119903119903119903

and 120598119905minus119903120579120579

represent the induced normal strainsand their corresponding reversal transformation strains inthe two mutual perpendicular directions due to the appliedaxial stress (120590

119911119911) and are introduced to meet the conservation

of mass The deviatoric stress tensor could be written as

1205901015840= (

minus120590119911119911

30 0

0 minus120590119911119911

30

0 02120590119911119911

3

) (4)


Pulley

SMA wire

Plasticbrace

Carriage

Ball joint

Figure 4 The SMA passive AFO prototype

0 20 40 60 80 100minus20

0

20

Controlled dorsiflexionAnk

le an

gle (

∘)

minus10

10

10 30 50 70 90

Powered plantarflexionControlled plantarexion

(a)

200 40 60 80 100minus2

minus15

minus1

minus05

0

Gait cycle ( )

Toe-off

Max dorsiflexion

Foot flat

10 30 50 70 90

05

(Nm

kg)

Ank

le m

omen

t(b)

Figure 5 Plots of ankle angle and ankle moment versus gait percentage for a normal gait [1]

0 01 02 03 04 0510

20

30

40

50

Time (s)

Forc

e (N

)

Figure 6 Calculated force needed during the swing phase for a drop foot patient enrolled in this study

The transformation tensor is expressed as

Λ119905

fwd =119867

2(

minus1 0 0

0 minus1 0

0 0 2

)

Λ119905

rev =1

120585119905minus119903(

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(5)

In (5)Λ119905fwd is the transformation direction tensor duringforward transformation and Λ119905rev is that form during thereverse It is well established that any change in the state ofthe system is only possible by a change in the martensiticvolume fraction 120585 Given this assumption the evolution of

the transformation strain tensor has the following form (flowrule) [13 14]

120598 = Λ119905 120585 (6)

Substitute (5) into the relations of thermodynamic forceand transformation function and use the following relationbetween the constitutive model parameters [18]

120588Δ1199060+ 1205831=

1

2120588Δ1199040(119872119904+ 119860119891)

119884 = minus1

2120588Δ1199040(119860119891minus 119872119904) minus 1205832

1205832=

1

4(120588119887119860minus 120588119887119872)

120588119887119860= minus120588Δ119904

0(119860119891minus 119860119904)

120588119887119872

= minus120588Δ1199040(119872119904minus 119872119891)

(7)


Then explicit expressions for the martensitic volume fractionin forward and reverse phase transformation are obtained as

120585fwd

=1

120588119887119872[120590119911119911119867 +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

120585rev

=1

120588119887119860[

1

120585119905minus119903(120590119911119911120598119905minus119903

119911119911) +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

(8)

where

119891fwd

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119872

119904)

119891rev

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119860

119891)

(9)

In (8) Δ11987833

= 1119864119872

minus 1119864119860 where 119864 is Youngrsquos

modulus The parameters 119872119904and 119860

119891are the martensitic

start and austenitic finish temperatures respectively andthe superscripts fwd and rev represent forward and reversetransformations By substituting the explicit expressions ofthemartensitic volume fraction equation (8) into (6) and afterintegrating from zero to an arbitrary time the transformationstrain can be calculated The constitutive equations for theforward transformation are now reduced to two algebraicexpressions as

120598119911119911

=1

119864119860+ 120585fwd (119864

119872minus 119864119860)120590119911119911

+ 119867120585fwd

+ 120572 (119879 minus 1198790) (10)

minus1

119863fwd (minus119884 + 120588Δ1199040119879)[

119867

120590119911119911

+ Δ11987833] 120590119911119911119911119911

+ [120588119888 minus120588Δ1199040

119863fwd (minus119884 + 120588Δ1199040119879)] = minus div (119902) + 120588119892

(11)

and for the reverse transformation the constitutive equationsare

120598119911119911

=1

119864119860+ 120585rev (119864

119872minus 119864119860)120590119911119911

+120598119905minus119903119911119911

120585119905minus119903120585rev

+ 120572 (119879 minus 1198790)

(12)

minus1

119863rev (119884 + 120588Δ1199040119879)[

120598119905minus119903119911119911

120585119905minus119903+ Δ11987833120590119911119911] 119911119911

+ [120588119888 minus120588Δ1199040

119863rev (119884 + 120588Δ1199040119879)] = minus div (119902) + 120588119892

(13)

where ] is Poissonrsquos ratio that is assumed to be the same forboth phases If there is no internal heat generation sourcelike Joule heating then 119892 = 0 Also due to Fourierrsquos lawof thermal conduction in a cylindrical element we can takediv(119902) = minus119896(12059721198791205971199032 + (1119903)(120597119879120597119903)) where 119903 is the radiusof the annular element in which the constitutive equationsare studied As shown in (11) and (13) both temperature andstress are functions of time and radiusThus it is necessary to

define initial and boundary conditions for the problem Initialtemperature and stress distributions are prescribed as

119879 (119903 0) = 119879infin 120590

119911119911(119903 0) = 0 (14)

where 119879infinis the ambient temperature Due to the convection

at the surface of the wire and axisymmetric distribution of thetemperature in the cross-section the boundary conditions atthe surface and the center of the rod can be defined as [15]

119896120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=119877119900

= ℎ [119879infin

minus 119879 (119877119900 119905)] 119896

120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=0= 0

(15)

where ℎ is the heat convection coefficient and 119877119900is the rod

radiusConstitutive (10) and (11) for the forward transformation

and (12) and (13) for the reverse transformation along withthe initial and boundary conditions of (14) and (15) mustbe solved simultaneously when transformation is occurringin the material Solving such equations is computationallyvery expensive using implicit schemes Instead an iter-ative approach based on the finite difference method isimplemented as a MATLAB code for solving the nonlineargoverning equations The developed code takes the materialproperties of the SMA wire and the applied displacementprofile as input and calculates the force and temperatureprofiles as output Interested readers are referred to [16 19]for further information on the solution procedure

5 Experiments

51 Validation of the CoupledModel Experiments are carriedout on superelastic nitinol samples to validate the capabilityof the model in capturing the coupled thermomechanicalbehavior of an SMAwire undergoing the proposedAFOactu-ation pattern An electromechanical testing machine (BoseElectroForce 3330) equipped with temperature-controlledenvironmental chamber (Applied Test Systems) was usedfor the mechanical tests An infrared camera (Micro-EpsilonoptoNCDT 1700) is used to measure the surface temperatureof the wire The apparatus is shown in Figures 7(a) and7(b) Two superelastic nitinol wires (NiTi number 1 providedby Fort Wayne Metals IN) with diameters of 1247mm(00491 in) and 0254mm (001 in) and with gauge lengths of27mm and 100mm are tested They are referred to as wire 1and wire 2 throughout the rest of the paper for convenienceWireswere previously annealed and surfacedwith light oxide

In order to implement the model it is first necessary tocalibrate the model with the required material propertiesAs a macromechanical based model all of the requiredparameters can be calibrated through mechanical testing atseveral temperatures In order to stabilize the stress-strainbehavior of the SMAwire a series of 30 loadunload cycles areconducted [18]Moreovermechanical training has to be doneat a very low frequency to simulate an isothermal behavior(to avoid the latent heating effects) For such a purposetraining was conducted at 60∘C inside the thermal chamberwith the strain rate of 120598 = 37 times 10minus4sminus1 and axial strain


Computerinterface

Axial actuator

Loadtorquecell

Environmentalchamber

Rotationalactuator

(a) Bose machine and environmental chamber

Computer interface

Wire IR camera

Black screen

(b) Temperature measurement setup

Figure 7 Test setup for the model verification experiments during the experiments the environmental chamber is closed with an opticalwindow for the IR camera

Figure 8 Apparatus of the free heat convection test

of 120598 = 0058 Uniaxial tests are then performed at 60∘C50∘C 40∘C and a room temperature of 23∘C and the recordedforce-displacement diagrams are used to calibrate the modelparameters

Once the wires were trained the AFO displacementpattern is simulated A sequence of ramps and square wavescorresponding to the real path and proportional to thelength of the wire is used to reproduce the strain whichwires undergo during the motion The total time period ofeach cycle is set to 12 s which results in a frequency of0083HzThemechanical response (force-displacement) andthe temperature variation of the wires are recorded They arediscussed and compared with the coupled model in the nextsections

52 Free Heat Convection of Vertical SMA Wires Experi-ments are carried out to find the best empirical equationwhich relates the free heat convection coefficient ℎ asa function of temperature and geometry of the wire Asuperelastic nitinol wire with a diameter of 0457mm and alength of 240mm is used for the test The wire is mountedvertically inside a box and hooked up to a power supply Asseen in Figure 8 the sample and box are painted in blackto attenuate the effect of ambient irradiation The wire isheated up to an elevated temperature (eg 70∘C) by applying

Table 1 Calibrated material properties through mechanical testingfor wire 1 and wire 2

Parameter Wire 1 Wire 2 Unit119864119860

500 times 103 370 times 103 MPa119864119872

270 times 103

270 times 103 MPa

119872119891

2230 2360 K119872119904

2380 2390 K119860119904

2680 2680 K119860119891

2750 2730 K119862119872

65 73 MpaK119862119860

72 68 MpaK] 033 033 mdash119867 0029 0038 mdash

a constant current After the temperature is achieved thepower supply is turned off and the wire is left to cooldown to room temperatureThe associated temperature-timediagrams are recorded

6 Results and Discussions

61 Coupled Model The force-displacement responses of thewires at four different temperatures are used to calibrate therequired material properties (the method of calibration isillustrated in [18]) These parameters are listed in Table 1Although both specimens are NiTi number 1 they do nothave exactly the same material properties due to variationin material batches and processing However as expectedvariations are small In addition to the properties displayed inTable 1 themodel needs twomore thermal parametersTheseterms and their values are specific heat 120588119888 = 26 times 10

minus6 Jm3kand thermal conductivity 119896 = 18W(mK) These adoptedvalues are for a general Ni50Ti50 reported in [20] recentlyThe modelrsquos prediction for the simple uniaxial response ofwire 2 is compared with the experiment in Figure 9 Themodel is in good agreement with the experiment showingthe accuracy of the calibrated parameters


0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel

Figure 9 Comparison of the modelrsquos prediction with the experi-mental data Uniaxial stress-strain response at room temperature forwire 2

02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel

Figure 10 Comparison of the modelrsquos prediction with the experi-mental data Displacement versus time diagramofwire 1 undergoingthe 12 s AFO actuation pattern

The recorded AFO actuation pattern during one normal-ized walking cycle is compared to the modelrsquos prediction inFigure 10 Although simple linear functions are used to definethe loading trajectories for the mechanical testing machinethe simulated path is acceptable Experimental stress-strainand the associated temperature-time responses of wire 1 andwire 2 are compared with the modelrsquos predictions in Figures11(a) 11(b) 12(a) and 12(b) Results are in good agreementshowing the capability of themodel in capturing the behaviorof the SMA wire undergoing the AFO complex pattern

Based on the modelrsquos prediction it was decided to usetwo superelastic wires with 0254mm diameter (wire 2) inparallel configuration The maximum force that each wireprovides at the end of loading is 25N which is enough fordorsiflexion of the foot

62 Motion Analysis Tests A prototype is fabricated at theDynamic and Smart Systems Laboratory The University of

0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel

(a) Stress versus strain diagram

0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)

(b) Temperature versus time diagram

Figure 11 Comparison of the modelrsquos prediction with the experi-mental data of wire 1 undergoing the 12 s AFO actuation pattern

Toledo In order to evaluate the performance of the prototypegait analyses are performed on a real subject Data is collectedto compare the ankle stiffness characteristics of a dropfoot patient with and without an AFO To demonstrate theimprovements achieved with the new device three sets oftests are performed without AFO with a hinged AFO andfinallywith the proposed SMAAFOThis patient is diagnosedwith left leg drop foot andwears a brace for his daily activitiesFigure 13 shows the patient wearing the SMA AFO for themotion analysis test

Ankle moment and angle data are collected for each testFigure 14 compares the ankle angle versus gait percentage forthe three cases In absence of any AFO there is a negativeangle at the end of the cycle which means that the patientis not able to raise his foot during dorsiflexion Althoughwearing a typical brace helped him raise his foot and walkmore naturally there is still a large amount of residualnegative angle at the end of the gait While wearing the SMA


0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)


Figure 12 Comparison of the modelrsquos prediction with the experimental data of wire 2 undergoing the 12 s AFO actuation pattern

(a)

Marker

(b)

Figure 13 Patient wearing the SMA AFO for the motion analysis test

0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )

Without braceWith braceSMA AFO

Figure 14 Ankle angle (mean value) versus gait percentage for threedifferent tests

AFO he was able to dorsiflex his foot as desired which ismuch closer to a normal gait

Since only one of the patientrsquos feet is diagnosed with dropfoot it is possible to compare the ankle angle and momentangle responses of the healthy foot with the other foot whilewearing the proposed AFO These comparisons are shownin Figures 15(a) and 15(b) Regardless of a small deviationfrom the desired pattern the important accomplishment forthe device is in giving the patient the ability to recover themoment and angle at the end of the gait A notable point hereis that due to atrophy muscles of the foot suffering from dropfoot are not as strong as those of a healthy one thus exactlythe same angle and moment profiles could not be expectedfor the two feet

7 Conclusions

A superelastic SMA wire was used to develop a passive anklefoot orthosis for addressing the drop foot disabilityThemainbenefit of the new AFO compared to the other conventionalones was providing fast and effective actuation stroke with a


0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )

Drop footSMA AFOHealthy foot

Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle

(a) Ankle angle versus gait percentage

0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)

Healthy footDrop footSMA AFO

20 40 60 80 1000

Gait cycle ()

1

(b) Ankle moment versus gait percentage

Figure 15 Comparison of normal angle (a) and moment (b) profiles with SMA AFO assisted drop foot condition

simple design A comprehensive coupled thermomechanicalmodel was used for the SMA that enabled design evaluationand optimization This model included the SMA latent heateffect and free heat convection phenomenon and capturedthe dynamic rate dependent response of the material Aprototype of the device was designed based on the modeland fabricated Motion analysis was conducted to evaluatethe effectiveness of the device The SMA AFO presented inthis work demonstrated the ability to meet the torque-anglerequirements of an ankle assistive device much better than atypical brace or a conventional passive AFO

Appendix

Heat Convection

Several sets of empirical formulas are given in the literature toobtain the free heat convection coefficient of a vertical slendercylinder The Nusselt number for a slender cylinder is shownby Popiel et al [21] to be found as

119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)

where 119889 and 119871 are the diameter and length of the wirerespectively Ra = GrPr is the Rayleigh number and Pris the Prandtl number of the air at ambient temperatureGr = 119892120573(119879 minus 119879

infin)1198713]2 is the Grashof number where 119892 is

the gravitational acceleration 120573 is the volume coefficient ofexpansion that is 120573 = 1119879 for ideal gases 119879 is the walltemperature 119879

infinis the ambient temperature and ] is the

kinematic viscosity of air Having theNusselt number the freeconvection coefficient is calculated by ℎ = (119873119906 sdot 119896)119871 where119896 is the air thermal conductivity of air Popiel [22] suggestedthat the Nusselt number of a vertical slender cylinder canbe found by calculating the Nusselt number of a flat plate

and then applying a correction He proposed the followingequation for the Nusselt number of a flat plate

119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)

and the correction he used is

119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)

Churchill and Chu [23] suggested another empiricalexpression to calculate the Nusselt number of a flat plate as

119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)

and they used the same correction as (A3) to find the Nusseltnumber of a vertical slender cylinder

In order to calculate the experimental value of ℎ onemight start from the heat transfer equation Ignoring the heatconvention through the wire the heat transfer equation foran SMA element could be written as

119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)

where 119898 119862119901 119875 and ℎ are the mass heat capacity dissipated

power and free convective heat coefficient respectivelyParameters 120585 and Δ119867 represent the martensitic volumefraction and latent heat In the experiment conductedno transformation occurs and only the cooling period isrecorded thus the terms Δ119867 and 119875 are both zero Therefore(A5) can be rewritten as

1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)

Cebecirsquos equationChurchill and Chursquos equationLe Fevre and Edersquos equationExperiment

h(W

m2

K)

Figure 16 Comparison between the experimental data and theempirical equations available in the literature for the heat convectioncoefficient versus temperature

which results in the following expression for ℎ

ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)

In (A6) the term 120588 represents the material densityEquation (A7) is used to calculate ℎ from temperature-timeresponse of thewire recorded during the cooling period in theexperiment The experimental values of ℎ are then comparedagainst the predicted values by the empirical equations Asshown in Figure 16 all equations are in good agreement withthe experiment However Cebecirsquos equation is chosen since itdoes not underestimate the results and thus is more reliablefor design purposes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to acknowledge the financial supportprovided fromNitinol Commercialization Accelerator by theOhioDepartment ofDevelopment throughGrantWP 10-010NSF support through award 0731087 Research to Aid Personwith Disability is also appreciated Assistance of MichaelSteves from Marshall-Loene Orthopedics Inc MaummyOH in fabrication is also appreciated

References

[1] M Bhadane-Deshpande Towards a shape memory alloy basedvariable stiffness ankle foot orthosis [PhD thesis] University ofToledo Toledo Ohio USA 2012

[2] J A Blaya and H Herr ldquoAdaptive control of a variable-impedance ankle-foot orthosis to assist drop-foot gaitrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 12 no 1 pp 24ndash31 2004

[3] J F Lehmann S M Condon B J De Lateur and R PriceldquoGait abnormalities in peroneal nerve paralysis and theircorrections by orthoses a biomechanical studyrdquo Archives ofPhysical Medicine and Rehabilitation vol 67 no 6 pp 380ndash3861986

[4] D P Ferris J M Czerniecki and B Hannaford ldquoAn ankle-footorthosis powered by artificial pneumatic musclesrdquo Journal ofApplied Biomechanics vol 21 no 2 pp 189ndash197 2005

[5] S Pittaccio S Viscuso M Rossini et al ldquoSHADE a shape-memory-activated device promoting ankle dorsiflexionrdquo Jour-nal of Materials Engineering and Performance vol 18 no 5-6pp 824ndash830 2009

[6] S Pittaccio S Viscuso E Beretta A C Turconi and SStrazzer ldquoPilot studies suggesting new applications of NiTi indynamic orthoses for the ankle jointrdquo Prosthetics and OrthoticsInternational vol 34 no 3 pp 305ndash318 2010

[7] L C Brinson ldquoOne-dimensional constitutive behavior ofshape memory alloys thermomechanical derivation with non-constant material functions and redefined martensite internalvariablerdquo Journal of Intelligent Material Systems and Structuresvol 4 no 2 pp 229ndash242 1993

[8] C-C Yang Y-L Hsu K-S Shih and J-M Lu ldquoReal-time gaitcycle parameter recognition using a wearable accelerometrysystemrdquo Sensors vol 11 no 8 pp 7314ndash7326 2011

[9] J Perry and J RDavids ldquoGait analysis normal and pathologicalfunctionrdquo Journal of Pediatric Orthopaedics vol 12 no 6 p 8151992

[10] T Oberg A Karsznia and K Oberg ldquoBasic gait parametersreference data for normal subjects 10ndash79 years of agerdquo Journalof Rehabilitation Research and Development vol 30 no 2 pp210ndash223 1993

[11] J R Gage P A Deluca and T S Renshaw ldquoGait analysisprinciples and applicationsrdquo Journal of Bone and Joint SurgeryA vol 77 no 10 pp 1607ndash1623 1995

[12] L DebergA fast actuator using shapememory alloys for an anklefoot orthosis [Masterrsquos thesis] Ecole Superieure des Sciences etTechnologies de lrsquoIngenieur de Nancy 2012

[13] J G Boyd andDC Lagoudas ldquoA thermodynamical constitutivemodel for shape memory materials Part I The monolithicshape memory alloyrdquo International Journal of Plasticity vol 12no 6 pp 805ndash842 1996

[14] M A Qidwai and D C Lagoudas ldquoNumerical implementationof a shape memory alloy thermomechanical constitutive modelusing return mapping algorithmsrdquo International Journal forNumerical Methods in Engineering vol 47 no 6 pp 1123ndash11682000

[15] R Mirzaeifar R Desroches and A Yavari ldquoAnalysis of therate-dependent coupled thermo-mechanical response of shapememory alloy bars and wires in tensionrdquo ContinuumMechanicsand Thermodynamics vol 23 no 4 pp 363ndash385 2011

[16] M T Andani A Alipour and M Elahinia ldquoCoupled rate-dependent superelastic behavior of shape memory alloy barsinduced by combined axial-torsional loading a semi-analyticmodelingrdquo Journal of IntelligentMaterial Systems and Structuresvol 24 no 16 pp 1995ndash2007 2013

[17] R Mirzaeifar R Desroches A Yavari and K Gall ldquoCoupledthermo-mechanical analysis of shape memory alloy circular


bars in pure torsionrdquo International Journal of Non-LinearMechanics vol 47 no 3 pp 118ndash128 2012

[18] D Lagoudas Shape Memory Alloys Modeling and EngineeringApplications Springer New York NY USA 2008

[19] M T Andani A Alipour A Eshghinejad and M ElahinialdquoModifying the torque-angle behavior of rotary shape memoryalloy actuators through axial loading a semi-analytical studyof combined tension-torsion behaviorrdquo Journal of IntelligentMaterial Systems and Structures vol 24 no 12 pp 1524ndash15352013


[21] C O Popiel J Wojtkowiak and K Bober ldquoLaminar free con-vective heat transfer from isothermal vertical slender cylinderrdquoExperimental Thermal and Fluid Science vol 32 no 2 pp 607ndash613 2007

[22] C O Popiel ldquoFree convection heat transfer from verticalslender cylinders a reviewrdquo Heat Transfer Engineering vol 29no 6 pp 521ndash536 2008

[23] S W Churchill and H H S Chu ldquoCorrelating equations forlaminar and turbulent free convection from a vertical platerdquoInternational Journal of Heat and Mass Transfer vol 18 no 11pp 1323ndash1329 1975

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


pneumatic artificial muscles One pneumatic actuatorprovides the plantarflexion torque while another one assiststhe dorsiflexion A control algorithm adjusts the air pressurein each actuator independently The study showed promisingresults in gait rehabilitation human motor adaptationand muscle activation However the applicability of theseorthoses is limited to laboratory studies and rehabilitationsince on board power supplies and computers are requiredfor their operation Shape memory alloy (SMA) basedAAFOs have also been studied in recent years by severalresearch groups [1 5 6]

This paper presents the design modeling and evaluationof a passive AFO which utilizes the superelastic behaviorof SMA wires SMAs are a group of smart materials thatcan undergo large deformations and provide actuation byrestoring their memorized shape The reversible mechanismbehind shape memory alloy actuation is a solid-state phasetransformation that takes place in response to variationof temperature and stress The distinct thermomechanicalbehavior of SMAs is the result of a transformation fromthe austenite (parent) phase to martensite (product) phaseand vice versa [7] These alloys have higher energy densitycompared to other smartmaterials such as piezoceramics andelectroactive polymers Therefore actuators that implementthese alloys are compact and lightweight alternatives for otherconventional actuators such as DC motors and solenoidsBiocompatibility and elastic properties similar to body tissuesare among the other reasons why SMAs are promisingcandidates for biomechanical applications and rehabilitationdevices In the following sections the proposed design isfirst presented A modeling approach is then introducedto capture the behavior of SMA wires under the requiredloading conditions The proposed modeling approach isverified experimentally for a similar loading path as neededin practice Finally the fabricated device is experimentallytested to record the improvements in walking quality of a realdrop foot subject

2 SMA Passive AFO Design

A typical passive AFO is a brace with constant torsionalstiffness that limits the motion of the ankle as shown inFigure 1 The SMA passive AFO consists of a hinged braceand a series of SMA wires This concept is depicted inFigures 2 and 3 As mentioned above most drop foot patientsare able to plantarflex their foot normally Therefore thesuperelastic wires can store mechanical energy during plan-tarflexion and release it during dorsiflexion to compensatethe inability Since the SMA wire undergoes stress inducedphase transformation during loading and unloading itsmechanical stiffness changes It is further shown that thechange in the stiffness of the SMA wire is similar to thenatural change in stiffness of the ankle joint in normal gaitThis eliminates excessive loads on active muscles letting thepatient walk more naturally and feel less exhausted On theother hand this actuation mechanism does not require a

Figure 1 A conventional passive ankle foot orthosis (DJ Orthope-dics)

Elongation powered

plantarflexion Recovery dorsiflexion

Figure 2 The SMA passive AFO concept SMA wires store energyin plantarflexion and release it to assist during dorsiflexion

complex controllingmechanismMoreover using SMAwiresalong with a hinged brace reduces the number of mechanicalparts manufacturing cost and complexity of maintenance

A prototype is developed as shown in Figure 4 The mainelement of the device is an SMA superelastic wire that isfixed to the brace at one end and is connected to the carriage(Figure 4) at the other end The carriage provides sufficientfreedom by moving on a slider connected to a ball jointSeveral small pulleys are mounted on the brace to hold therequired length of wireThe length of the wire not only affectsthe range of motion but also determines the life time of theorthosis A longer wire undergoes less strain and thereforehas a longer fatigue life







119872 = 119865119886 (1)


119872 = 1198691198892120579

1198891199052+ 119898119892119889 cos 120579 (2)




4 Modeling


120590 = (

0 0 0

0 0 0

0 0 120590119911119911

) 120598 = (

120598119903119903

0 0

0 120598120579120579

0

0 0 120598119911119911

)

120598119905minus119903

= (

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(3)

where 120590119911119911 120598119911119911 and 120598119905minus119903



and 120598119905minus119903120579120579




1205901015840= (

minus120590119911119911

30 0

0 minus120590119911119911

30

0 02120590119911119911

3

) (4)


Pulley

SMA wire

Plasticbrace

Carriage

Ball joint


0 20 40 60 80 100minus20

0

20


le an

gle (

∘)

minus10

10

10 30 50 70 90


(a)

200 40 60 80 100minus2

minus15

minus1

minus05

0

Gait cycle ( )

Toe-off

Max dorsiflexion

Foot flat

10 30 50 70 90

05

(Nm

kg)

Ank

le m

omen

t(b)


0 01 02 03 04 0510

20

30

40

50

Time (s)

Forc

e (N

)



Λ119905

fwd =119867

2(

minus1 0 0

0 minus1 0

0 0 2

)

Λ119905

rev =1

120585119905minus119903(

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(5)



120598 = Λ119905 120585 (6)


120588Δ1199060+ 1205831=

1

2120588Δ1199040(119872119904+ 119860119891)

119884 = minus1

2120588Δ1199040(119860119891minus 119872119904) minus 1205832

1205832=

1

4(120588119887119860minus 120588119887119872)

120588119887119860= minus120588Δ119904

0(119860119891minus 119860119904)

120588119887119872

= minus120588Δ1199040(119872119904minus 119872119891)

(7)



120585fwd

=1

120588119887119872[120590119911119911119867 +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

120585rev

=1

120588119887119860[

1

120585119905minus119903(120590119911119911120598119905minus119903

119911119911) +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

(8)

where

119891fwd

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119872

119904)

119891rev

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119860

119891)

(9)

In (8) Δ11987833

= 1119864119872





120598119911119911

=1

119864119860+ 120585fwd (119864

119872minus 119864119860)120590119911119911

+ 119867120585fwd

+ 120572 (119879 minus 1198790) (10)

minus1

119863fwd (minus119884 + 120588Δ1199040119879)[

119867

120590119911119911

+ Δ11987833] 120590119911119911119911119911

+ [120588119888 minus120588Δ1199040


(11)


120598119911119911

=1

119864119860+ 120585rev (119864

119872minus 119864119860)120590119911119911

+120598119905minus119903119911119911

120585119905minus119903120585rev

+ 120572 (119879 minus 1198790)

(12)

minus1

119863rev (119884 + 120588Δ1199040119879)[

120598119905minus119903119911119911

120585119905minus119903+ Δ11987833120590119911119911] 119911119911

+ [120588119888 minus120588Δ1199040

119863rev (119884 + 120588Δ1199040119879)] = minus div (119902) + 120588119892

(13)



119879 (119903 0) = 119879infin 120590

119911119911(119903 0) = 0 (14)



119896120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=119877119900

= ℎ [119879infin

minus 119879 (119877119900 119905)] 119896

120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=0= 0

(15)




5 Experiments




Computerinterface

Axial actuator

Loadtorquecell


Rotationalactuator


Computer interface

Wire IR camera

Black screen









500 times 103 370 times 103 MPa119864119872

270 times 103

270 times 103 MPa

119872119891

2230 2360 K119872119904

2380 2390 K119860119904

2680 2680 K119860119891

2750 2730 K119862119872

65 73 MpaK119862119860

72 68 MpaK] 033 033 mdash119867 0029 0038 mdash






0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel


02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel





0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel


0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)






0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









119872 = 119865119886 (1)


119872 = 1198691198892120579

1198891199052+ 119898119892119889 cos 120579 (2)




4 Modeling


120590 = (

0 0 0

0 0 0

0 0 120590119911119911

) 120598 = (

120598119903119903

0 0

0 120598120579120579

0

0 0 120598119911119911

)

120598119905minus119903

= (

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(3)

where 120590119911119911 120598119911119911 and 120598119905minus119903



and 120598119905minus119903120579120579




1205901015840= (

minus120590119911119911

30 0

0 minus120590119911119911

30

0 02120590119911119911

3

) (4)


Pulley

SMA wire

Plasticbrace

Carriage

Ball joint


0 20 40 60 80 100minus20

0

20


le an

gle (

∘)

minus10

10

10 30 50 70 90


(a)

200 40 60 80 100minus2

minus15

minus1

minus05

0

Gait cycle ( )

Toe-off

Max dorsiflexion

Foot flat

10 30 50 70 90

05

(Nm

kg)

Ank

le m

omen

t(b)


0 01 02 03 04 0510

20

30

40

50

Time (s)

Forc

e (N

)



Λ119905

fwd =119867

2(

minus1 0 0

0 minus1 0

0 0 2

)

Λ119905

rev =1

120585119905minus119903(

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(5)



120598 = Λ119905 120585 (6)


120588Δ1199060+ 1205831=

1

2120588Δ1199040(119872119904+ 119860119891)

119884 = minus1

2120588Δ1199040(119860119891minus 119872119904) minus 1205832

1205832=

1

4(120588119887119860minus 120588119887119872)

120588119887119860= minus120588Δ119904

0(119860119891minus 119860119904)

120588119887119872

= minus120588Δ1199040(119872119904minus 119872119891)

(7)



120585fwd

=1

120588119887119872[120590119911119911119867 +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

120585rev

=1

120588119887119860[

1

120585119905minus119903(120590119911119911120598119905minus119903

119911119911) +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

(8)

where

119891fwd

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119872

119904)

119891rev

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119860

119891)

(9)

In (8) Δ11987833

= 1119864119872





120598119911119911

=1

119864119860+ 120585fwd (119864

119872minus 119864119860)120590119911119911

+ 119867120585fwd

+ 120572 (119879 minus 1198790) (10)

minus1

119863fwd (minus119884 + 120588Δ1199040119879)[

119867

120590119911119911

+ Δ11987833] 120590119911119911119911119911

+ [120588119888 minus120588Δ1199040


(11)


120598119911119911

=1

119864119860+ 120585rev (119864

119872minus 119864119860)120590119911119911

+120598119905minus119903119911119911

120585119905minus119903120585rev

+ 120572 (119879 minus 1198790)

(12)

minus1

119863rev (119884 + 120588Δ1199040119879)[

120598119905minus119903119911119911

120585119905minus119903+ Δ11987833120590119911119911] 119911119911

+ [120588119888 minus120588Δ1199040

119863rev (119884 + 120588Δ1199040119879)] = minus div (119902) + 120588119892

(13)



119879 (119903 0) = 119879infin 120590

119911119911(119903 0) = 0 (14)



119896120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=119877119900

= ℎ [119879infin

minus 119879 (119877119900 119905)] 119896

120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=0= 0

(15)




5 Experiments




Computerinterface

Axial actuator

Loadtorquecell


Rotationalactuator


Computer interface

Wire IR camera

Black screen









500 times 103 370 times 103 MPa119864119872

270 times 103

270 times 103 MPa

119872119891

2230 2360 K119872119904

2380 2390 K119860119904

2680 2680 K119860119891

2750 2730 K119862119872

65 73 MpaK119862119860

72 68 MpaK] 033 033 mdash119867 0029 0038 mdash






0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel


02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel





0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel


0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)






0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Pulley

SMA wire

Plasticbrace

Carriage

Ball joint


0 20 40 60 80 100minus20

0

20


le an

gle (

∘)

minus10

10

10 30 50 70 90


(a)

200 40 60 80 100minus2

minus15

minus1

minus05

0

Gait cycle ( )

Toe-off

Max dorsiflexion

Foot flat

10 30 50 70 90

05

(Nm

kg)

Ank

le m

omen

t(b)


0 01 02 03 04 0510

20

30

40

50

Time (s)

Forc

e (N

)



Λ119905

fwd =119867

2(

minus1 0 0

0 minus1 0

0 0 2

)

Λ119905

rev =1

120585119905minus119903(

120598119905minus119903119903119903

0 0

0 120598119905minus119903120579120579

0

0 0 120598119905minus119903119911119911

)

(5)



120598 = Λ119905 120585 (6)


120588Δ1199060+ 1205831=

1

2120588Δ1199040(119872119904+ 119860119891)

119884 = minus1

2120588Δ1199040(119860119891minus 119872119904) minus 1205832

1205832=

1

4(120588119887119860minus 120588119887119872)

120588119887119860= minus120588Δ119904

0(119860119891minus 119860119904)

120588119887119872

= minus120588Δ1199040(119872119904minus 119872119891)

(7)



120585fwd

=1

120588119887119872[120590119911119911119867 +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

120585rev

=1

120588119887119860[

1

120585119905minus119903(120590119911119911120598119905minus119903

119911119911) +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

(8)

where

119891fwd

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119872

119904)

119891rev

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119860

119891)

(9)

In (8) Δ11987833

= 1119864119872





120598119911119911

=1

119864119860+ 120585fwd (119864

119872minus 119864119860)120590119911119911

+ 119867120585fwd

+ 120572 (119879 minus 1198790) (10)

minus1

119863fwd (minus119884 + 120588Δ1199040119879)[

119867

120590119911119911

+ Δ11987833] 120590119911119911119911119911

+ [120588119888 minus120588Δ1199040


(11)


120598119911119911

=1

119864119860+ 120585rev (119864

119872minus 119864119860)120590119911119911

+120598119905minus119903119911119911

120585119905minus119903120585rev

+ 120572 (119879 minus 1198790)

(12)

minus1

119863rev (119884 + 120588Δ1199040119879)[

120598119905minus119903119911119911

120585119905minus119903+ Δ11987833120590119911119911] 119911119911

+ [120588119888 minus120588Δ1199040

119863rev (119884 + 120588Δ1199040119879)] = minus div (119902) + 120588119892

(13)



119879 (119903 0) = 119879infin 120590

119911119911(119903 0) = 0 (14)



119896120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=119877119900

= ℎ [119879infin

minus 119879 (119877119900 119905)] 119896

120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=0= 0

(15)




5 Experiments




Computerinterface

Axial actuator

Loadtorquecell


Rotationalactuator


Computer interface

Wire IR camera

Black screen









500 times 103 370 times 103 MPa119864119872

270 times 103

270 times 103 MPa

119872119891

2230 2360 K119872119904

2380 2390 K119860119904

2680 2680 K119860119891

2750 2730 K119862119872

65 73 MpaK119862119860

72 68 MpaK] 033 033 mdash119867 0029 0038 mdash






0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel


02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel





0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel


0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)






0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





120585fwd

=1

120588119887119872[120590119911119911119867 +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

120585rev

=1

120588119887119860[

1

120585119905minus119903(120590119911119911120598119905minus119903

119911119911) +

1

21205902

119911119911Δ11987833

+ 119891fwd

(119879)]

(8)

where

119891fwd

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119872

119904)

119891rev

(119879) = 120588Δ119888 [(119879 minus 1198790) minus 119879 ln(

119879

1198790

)] + 120588Δ1199040(119879 minus 119860

119891)

(9)

In (8) Δ11987833

= 1119864119872





120598119911119911

=1

119864119860+ 120585fwd (119864

119872minus 119864119860)120590119911119911

+ 119867120585fwd

+ 120572 (119879 minus 1198790) (10)

minus1

119863fwd (minus119884 + 120588Δ1199040119879)[

119867

120590119911119911

+ Δ11987833] 120590119911119911119911119911

+ [120588119888 minus120588Δ1199040


(11)


120598119911119911

=1

119864119860+ 120585rev (119864

119872minus 119864119860)120590119911119911

+120598119905minus119903119911119911

120585119905minus119903120585rev

+ 120572 (119879 minus 1198790)

(12)

minus1

119863rev (119884 + 120588Δ1199040119879)[

120598119905minus119903119911119911

120585119905minus119903+ Δ11987833120590119911119911] 119911119911

+ [120588119888 minus120588Δ1199040

119863rev (119884 + 120588Δ1199040119879)] = minus div (119902) + 120588119892

(13)



119879 (119903 0) = 119879infin 120590

119911119911(119903 0) = 0 (14)



119896120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=119877119900

= ℎ [119879infin

minus 119879 (119877119900 119905)] 119896

120597119879(119903 119905)

120597119903

10038161003816100381610038161003816100381610038161003816119903=0= 0

(15)




5 Experiments




Computerinterface

Axial actuator

Loadtorquecell


Rotationalactuator


Computer interface

Wire IR camera

Black screen









500 times 103 370 times 103 MPa119864119872

270 times 103

270 times 103 MPa

119872119891

2230 2360 K119872119904

2380 2390 K119860119904

2680 2680 K119860119891

2750 2730 K119862119872

65 73 MpaK119862119860

72 68 MpaK] 033 033 mdash119867 0029 0038 mdash






0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel


02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel





0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel


0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)






0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Computerinterface

Axial actuator

Loadtorquecell


Rotationalactuator


Computer interface

Wire IR camera

Black screen









500 times 103 370 times 103 MPa119864119872

270 times 103

270 times 103 MPa

119872119891

2230 2360 K119872119904

2380 2390 K119860119904

2680 2680 K119860119891

2750 2730 K119862119872

65 73 MpaK119862119860

72 68 MpaK] 033 033 mdash119867 0029 0038 mdash






0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel


02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel





0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel


0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)






0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 001 002 003 004 005 0060

100

200

300

400

Strain

Stre

ss (M

Pa)

ExperimentModel


02 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

Disp

lace

men

t (m

m)

ExperimentModel





0 001 002 003 004 0050

100

200

300

400

500

600

Strain

Stre

ss (M

Pa)

ExperimentModel


0 2 4 6 8 10 1222

24

26

28

30

32

34

36

38

40

Time (s)

ExperimentModel

Tem

pera

ture

(∘C)






0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 001 002 003 004 0050

50

100

150

200

250

300

350

400

450

500

Strain

Stre

ss (M

Pa)

ExperimentModel


ExperimentModel

0 2 4 6 8 10 1224

26

28

30

32

34

36

Time (s)

Tem

pera

ture

(∘C)



(a)

Marker

(b)


0 20 40 60 80 100minus20

minus15

minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )





7 Conclusions



0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

20 40 60 80 100minus10

minus5

0

5

10

15

20

Gait cycle ()

Ank

le an

gle(

∘ )


Maximumcontrolled

dorsiflexionangle

Maximumpowered

plantarflexionangle


0

minus02

02

04

06

08

Ank

le m

omen

t (N

mk

g)


20 40 60 80 1000

Gait cycle ()

1




Appendix

Heat Convection


119873119906 =4

3[

7RaPr5(20 + 21Pr)

]

025

+4119871 (272 + 315Pr)35119889 (64 + 63Pr)

(A1)







119873119906FP = [0825 +0387Ra16

(1 + (0492Pr)916)827]

2

(A2)


119873119906

119873119906FP= 1 + 03 (32

05Grminus0025 119871119863) (A3)


119873119906FP = [

[

068 +067Ra025

(1 + (049Pr)056)044

]

]

(A4)



119898119862119901

120597119879

120597119905= 119875 + ℎ119860 (119879 minus 119879

infin) + 119898Δ119867

120597120585

120597119905 (A5)



1205881205871198892

4119871119862119901= minusℎ120587119889119871 (119879 minus 119879

infin) (A6)


40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




40 45 50 55 60 65 7020

40

60

80

100

120

140

Temperature (∘C)


h(W

m2

K)



ℎ = minus120588119889119862119901

4 (119879 minus 119879infin)

Δ119879

Δ119905 (A7)




Acknowledgments


References

































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials


















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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