imechanica.orgimechanica.org/files/1658.pdf1658/1658.htm Answer ID 1658 Last Updated 09/07/2010 11:46 AM Access Level Cust wo support Print Answer Email AnswerUMAT and

Martensitic transformationlevel in retracted stent.

A N S W E R S T O C O M M O N A B A Q U S Q U E S T I O N S S P R I N G 2 0 0 1

C O N T E N T S1 Simulation of Implantable

Nitinol Stents

Hibbitt, Karlsson &

Sorensen, Inc.

1080 Main Street

Pawtucket, RI

02860-4847 usa

phone 401.727.4200

fax 401.727.4208

e-mail [email protected]

www.abaqus.com

ABAQUS

FEA Model courtesy of Nitinol Devices & Components, Cordis Corporation, a Johnson & Johnson Company.

Simulation of ImplantableNitinol Stents

Medical technology is advancing rapidly,particularly in the development ofadvanced medical implants. Traditionallynew products were developed byprototyping and evaluating; however,this process is very time consumingand often does not fully reveal potentialfailures. Finite element modeling andanalysis greatly reduces testing and timeto market by allowing the designer tosimulate product performance in advanceof any prototyping.

The superelastic and shape memoryproperties of Nitinol, a nickel-titaniumalloy, along with its biocompatibility andfatigue properties, have made thematerial attractive for cardiovascularstents. However, it is a complex materialand difficult to process. FEA hastens timeto market of Nitinol products by reducingthe number of design iterations required,hence expediting the design process.

Superelastic alloy materialbehavior

Nitinol is an extremely flexible metalalloy that can undergo very largedeformations without losing the ability

to recover its original shape uponunloading. At rest, the material presentsitself in an austenite phase, which behaveslinear elastically. Upon loading, thisaustenite phase transforms into amartensite phase, which is also linearelastic; however, the elasticity of eachphase has different constants. Thetransformation produces a substantialamount of strain and is triggered bystress over a relatively narrow range.Upon unloading, the transformation isreversible. However, the stress levels atwhich such reversible transformationoccurs are smaller than the stresses thatwere required to produce the originaltransformation. Because the materialrecovers its original shape uponunloading, it is described as elastic. Inaddition, because the transformationstrains are large (on the order of 6%)compared to elastic strains in typicalmetals (on the order of 0.1%), thematerial is said to be superelastic.

If a reverse loading is applied (forexample, in compression instead oftension), a similar behavior is observed,with the exception that the stress levelsrequired to produce the transformationsare higher, while the transformationstrain is lower.

ABAQUS/Answers

Von Mises stress intensityduring deployment.

0617.ANSWERS 4/5/01 8:35 AM Page 1

Nitinol is a difficult material tocharacterize numerically. Anapproximation, capable of modelingthe loading part of the model, ishyperelasticity, which is commonly usedto represent rubber behavior. Otherconstitutive models have been proposedrecently to address Nitinols behavior.However, a thorough verification of thesemodels has been difficult because themanufacturing requirements of Nitinolare complex. As a result, Nitinol istypically available as relatively thin wiresand tubes, from which most of the testingdata available are in the form of uniaxialdata. It is relatively straightforward toproduce a uniaxial model, but it is muchmore difficult to produce a model thatrepresents Nitinols three-dimensionalstress-strain behavior.

At Hibbitt, Karlsson & Sorensen(West) a user material routine(UMAT/Nitinol) was written followingthe model proposed by Auricchio andTaylor. This theory is based on theconcept of generalized plasticity andphysical principles. The theorydecomposes strain into two parts-apurely linear elastic component anda transformation component:

= el+

tr.

The austenite to twinned martensitetransformation is driven by theresolution of shear forces, and it takesplace within a range of stress levels thatare characteristic of the material.

tr

= a ,

FS

F FF,

where is the fraction of martensite andF is a transformation potential. The sameis true for the reverse transformation butat different stress levels. The intensity ofthe transformation follows a stresspotential law:

= f(, ) F .

Any change in stress direction producesa reorientation of the martensite withnegligible additional effort. Changes intemperature produce a shift in the stresslevels at which the transformations takeplace. This shift is linear in temperature.Because there is a volume increase

F

associated with the transformation, itrequires less stress to produce thetransformation in tension and more incompression. This is modeled with alinear Drucker-Prager approach for thetransformation potential:

F = - p tan + CT,

with being the Mises equivalentstress, p the pressure stress, and Tthe temperature.

A rule of mixtures is used to implementthe change in linear elasticity from theaustenite phase into the martensite phase.

In addition to the usual stresses andstrains, the UMAT routine tracks variablesspecific to the model. These variablesinclude the distribution of the fraction ofmartensite, transformation strains, andequivalent stresses and strains. Theseare points in the uniaxial tensile curveinto which material points that have athree-dimensional state, specificfractions of martensite, and a specificloading/unloading history are mapped.The material data required by the modelare obtained from straightforwardobservations of uniaxial tests in terms ofloading, unloading, reverse loading, andtemperature effects. The calibrationconsists of 13 values, as shown below.

.

2 ABAQUS/Answers

-

Mechanical behavior of Nitinol.

The ABAQUS algorithm forNiTi alloy modeling closelymatches experimentalmeasurements wheresuccessively larger strain loadsare applied in the alloy atdifferent temperatures.

Behavior of the model uponrepeated loading and unloadingof Nitinol.

temperature = 22C

temperature = 37C

Data required to define superelastic behav-ior in the ABAQUS model.

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0617.ANSWERSFOR PDF PAGE 2 4/5/01 9:09 AM Page 2

Stent analysis

Stents are cylindrical metal mesh tubesmade of materials such as Nitinol andinserted into blood vessels to counteractthe effects associated with vasculardiseases, such as narrowing of bloodvessels due to plaque build up.

The present analysis considers both themanufacturing process and deployment ofa stent. One of the key issues in medicalimplants is device lifetime or, inengineering terms, fatigue life. Finiteelement analysis provides quantitativemeasures of stress and strain needed tomake fatigue estimates for these devices.This allows the optimization of designsand allows prediction of the devices life.

The large elastic strains possible inNitinol reduce the risk of damage to thestent both during delivery into the bodyand due to accidents while in operation.

One manufacturing process of Nitinolstents starts from a thin tube into which apattern is electromachined. The FEA modelis built from this machined tube. Since thepattern repeats itself, only a part of thestent with appropriate symmetry ismodeled. The stent is expanded to itsnominal dimensions, typically at adiameter many times larger than theoriginal tube diameter. While loaded, thestent is annealed to provide its newunloaded configuration. The stent is thencrimped from the outside and inserted intothe delivery system (usually a system ofcatheter tubes). Once inside a patientsbody, the delivery system pushes the stentout of its containment. Once delivered, theresponse to blood pressure pulsing loadsdetermines the fatigue life of the stent.

The calculation reveals stress-strainconcentrations during manufacturing,deployment, and service loading. Auxiliaryinformation is also available from thecalculation; for example, how muchmartensitic transformation has occurredand, therefore, how close the design is tothe limits of the material flexibility.

Summary

Finite element analysis is a method wellsuited to the needs of the product designer.The method allows designers to iteratedesigns on a computer before prototypesare made. The finite element method can

ABAQUS/Answers 3

solve mechanical problems involvingcomplex material behavior such as thoseof Nitinol alloys.

Complexity of stent designs and of theactions taken to deploy them requiressophistication in the finite element toolused. Proper material behavior is just onerequirement. Advanced modelingcapabilities such as contact with bothrigid tools and other flexible bodies, largedeformations, localized buckling, material removal, and simulation of complexloading sequences are needed. These basicrobust capabilities in ABAQUS make thecode particularly suitable for stent design.

Stress-strain curveresults based on loadingshown above.

Expanded

Retracted

Partiallydeployed

Behavior of the model subjected to an 18Ctemperature range while strainsare applied.

Initial configuration

Stent model.

Loading in terms of temperature and strain.

0617.ANSWERS 4/5/01 8:41 AM Page 3

nitinol_uni22_std.inp

*headingbuilt-in nitinol umatUniaxial test, c3d8,c3d10m,cps4,t3d2Loading in Y direction*preprint,echo=yes,model=yes,history=yes************************************************************node,nset=c3d81, 0., 3.2, 1., 3.3, 1., 4.4, 0., 4.5, 0., 3., 1.6, 1., 3., 1.7, 1., 4., 1.8, 0., 4., 1.*nset, nset=load-c3d83,4,7,8*element,type=c3d8,elset=c3d81,1,2,3,4,5,6,7,8*solid section,elset=c3d8,material=ABQ_super_elastic_1*boundary1,1,32,2,33,34,14,35,1,26,28,1************************************************************Node, nset=c3d10m 201, 4., 4., 1. 202, 4., 3., 1. 203, 4., 3., 0. 204, 4., 4., 0. 205, 3., 3., 1. 206, 3., 3., 0. 207, 3., 4., 0. 208, 3., 4., 1. 209, 3.499939, 3.5, 0.5 210, 3.749969, 3.25, 0.75 211, 3.5, 3., 1. 212, 3.249969, 3.25, 0.75 213, 3., 3.5, 1. 214, 3.249969, 3.75, 0.75 215, 3.5, 3.5, 1. 216, 3.249969, 3.25, 0.25 217, 3., 3., 0.5 218, 3.5, 3., 0.5 219, 3.249969, 3.75, 0.25 220, 3., 4., 0.5 221, 3., 3.5, 0.5 222, 3., 3.5, 0. 223, 3.749969, 3.75, 0.25 224, 3.5, 4., 0.5 225, 3.5, 4., 0. 226, 3.5, 3.5, 0. 227, 3.5, 3., 0. 228, 3.749969, 3.25, 0.25 229, 4., 3.5, 0. 230, 4., 4., 0.5 231, 3.749969, 3.75, 0.75 232, 3.5, 4., 1. 233, 4., 3.5, 0.5 234, 4., 3., 0.5 235, 4., 3.5, 1.*nset, nset=xfix 205, 206, 207, 208, 213, 217, 220, 221, 222*nset, nset=yfix 202, 203, 205, 206, 211, 217, 218, 227, 234*nset, nset=zfix 203, 204, 206, 207, 222, 225, 226, 227, 229*nset, nset=load-c3d10m 201, 204, 207, 208, 220, 224, 225, 230, 232*Element, type=C3D10M, elset=c3d10m201, 209, 205, 202, 208, 212, 211, 210, 214, 213, 215202, 209, 205, 206, 202, 212, 217, 216, 210, 211, 218203, 209, 208, 207, 205, 214, 220, 219, 212, 213, 221204, 209, 205, 207, 206, 212, 221, 219, 216, 217, 222205, 209, 208, 204, 207, 214, 224, 223, 219, 220, 225206, 209, 204, 206, 207, 223, 226, 216, 219, 225, 222207, 209, 203, 206, 204, 228, 227, 216, 223, 229, 226208, 209, 201, 204, 208, 231, 230, 223, 214, 232, 224209, 209, 201, 203, 204, 231, 233, 228, 223, 230, 229210, 209, 202, 203, 201, 210, 234, 228, 231, 235, 233211, 209, 208, 202, 201, 214, 215, 210, 231, 232, 235212, 209, 202, 206, 203, 210, 218, 216, 228, 234, 227*solid section,elset=c3d10m,material=ABQ_super_elastic_1*boundaryxfix,1yfix,2zfix,3************************************************************node,nset=cps4301, 0., 0.302, 1., 0.303, 1., 1.304, 0., 1.*nset, nset=load-cps4303,304*element,type=cps4,elset=cps4301,301,302,303,304*solid section,elset=cps4,material=ABQ_super_elastic_11.0,*boundary301,1,2302,2304,1************************************************************node, nset=t3d2401, 3.5, 0.402, 3.5, 1.0*nset, nset=load-t3d2402*element, type=t3d2, elset=t3d2401, 401, 402*solid section,elset=t3d2,material=ABQ_super_elastic_11.0,*boundary401,1,3402,1402,3************************************************************MATERIAL, NAME=ABQ_super_elastic_1*user material,consta=1540000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22.,6.7 ,250.,140.,,0.041,,*depvar24,*nset, nset=nallc3d8,cps4,t3d2,c3d10m*initial conditions,type=temperaturenall,22.*restart,write*nset,nset=noutload-c3d10m,load-c3d8,load-cps4,load-t3d2************************************************************step,nlgeom,inc=100*static0.02,1.,,0.02*boundaryload-c3d10m,2,2,0.0776load-c3d8,2,2,0.0776load-cps4,2,2,0.0776load-t3d2,2,2,0.0776 *output, field*element outputS,LE*Node outputU,*output,history,variable=preselect*node output,nset=noutU2,RF2*end step*step,nlgeom,inc=100*static0.02,1.,,0.02*boundaryload-c3d10m,2,2,0.load-c3d8,2,2,0.load-cps4,2,2,0.load-t3d2,2,2,0. *end step

nitinol_sax_xpl.inp

*headingUniaxial test sax1 element for the nitinol built-in vumatLoading in Y direction*preprint,echo=yes,model=yes,history=yes*node, nset=sax1101,3.5,0.102,3.5,1.*nset, nset=load-sax1102*element, type=sax1, elset=sax1101,101,102*shell section, elset=sax1, material=ABQ_super_elastic_N2d_10.0454728408834*transverse shear stiffness1.0,1.0,1.0*boundary101,2,************************************************************MATERIAL, NAME=ABQ_super_elastic_N2d_1*user material,consta=1440000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22.,6.7 ,250.,140.,,0.041,*depvar24,*density1.e-2*nset, nset=nallsax1,*initial conditions,type=temperaturenall,22.*restart,write, number=1*amplitude,name=smooth,time=totaltime,definition=smoothstep0.,0.,0.1,1.,0.2,0.*elset,elset=QA_TEST_ALLELEMENTSsax1************************************************************step*dynamic, explicit,0.1*boundary, amplitude=smoothload-sax1,2,2,0.0776*OUTPUT,FIELD,NUMBER INTERVAL=20,TIME MARKS=YES*ELEMENT OUTPUT,ELSET=QA_TEST_ALLELEMENTSS,LE*NODE OUTPUTU,*OUTPUT,HISTORY*ELEMENT OUTPUT,ELSET=sax1S,LE*NODE OUTPUT,NSET=NALLU,RF,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIME INTERVAL=0.025*end step*step*dynamic,explicit,.1,,*boundary,amplitude=smoothload-sax1,2,2,0.0776*end step

nitinol_cax_xpl.inp

*headingUniaxial test of cax4r for nitinol built-in vumatLoading in Y direction*preprint,echo=yes,model=yes,history=yes************************************************************node,nset=cax4301, 0., 0.302, 0.564189583548, 0.303, 0.564189583548, 1.304, 0., 1.*nset, nset=load-cax4303,304*element,type=cax4r,elset=cax4301,301,302,303,304*solid section,elset=cax4,material=ABQ_SUPER_ELASTIC_N3D_11.0,*boundary301,1,2302,2304,1************************************************************MATERIAL, NAME=ABQ_SUPER_ELASTIC_N3D_1*user material,consta=1440000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22.,6.7 ,250.,140.,,0.041,*depvar24,*density1.e-2*nset, nset=nallcax4*initial conditions,type=temperaturenall,22.*restart,write, number=1*amplitude,name=smooth,time=totaltime,definition=smoothstep0.,0.,0.1,1.,0.2,0.*elset,elset=QA_TEST_ALLELEMENTScax4************************************************************step*dynamic, explicit,0.1*boundary, amplitude=smoothload-cax4,2,2,0.0776*OUTPUT,FIELD,NUMBER INTERVAL=20,TIME MARKS=YES*ELEMENT OUTPUT,ELSET=QA_TEST_ALLELEMENTSS,LE*NODE OUTPUTU,*OUTPUT,HISTORY*ELEMENT OUTPUT,ELSET=cax4S,LE*NODE OUTPUT,NSET=NALLU,RF,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIME INTERVAL=0.025*end step*step*dynamic,explicit,.1,,*boundary,amplitude=smoothload-cax4,2,2,0.0776*end step

nitinol_beam_xpl.inp

*headingUniaxial test b31 element for the nitinol built-in vumatLoading in Y direction*preprint,echo=yes,model=yes,history=yes*node, nset=b31101,3.5,0.102,3.5,1.*nset, nset=load-b31102*element, type=b31, elset=b31101,101,102*beam section, elset=b31, material=ABQ_super_elastic_N1d_1,section=rectangular0.345,0.3048*transverse shear stiffness1.0,1.0,1.0*boundary101,2,************************************************************MATERIAL, NAME=ABQ_super_elastic_N1d_1*user material,consta=1440000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22.,6.7 ,250.,140.,,0.041,*depvar24,*density1.e-2*nset, nset=nallb31,*initial conditions,type=temperaturenall,22.*restart,write, number=1*amplitude,name=smooth,time=totaltime,definition=smoothstep0.,0.,0.1,1.,0.2,0.*elset,elset=QA_TEST_ALLELEMENTSb31************************************************************step*dynamic, explicit,0.1*boundary, amplitude=smoothload-b31,2,2,0.0776*OUTPUT,FIELD,NUMBER INTERVAL=20,TIME MARKS=YES*ELEMENT OUTPUT,ELSET=QA_TEST_ALLELEMENTSS,LE*NODE OUTPUTU,*OUTPUT,HISTORY*ELEMENT OUTPUT,ELSET=b31S,LE*NODE OUTPUT,NSET=NALLU,RF,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIME INTERVAL=0.025*end step*step*dynamic,explicit,.1,,*boundary,amplitude=smoothload-b31,2,2,0.0776*end step

nitinol_3d_xpl.inp

*headingpull a bar, c3d8r,cps4r for nitinol built-in vumat*node,nset=nall1,2,1.3,1.,1.4,,1.5,,,1.6,1.,,1.7,1.,1.,1.8,,1.,1.11,3.12,4.13,4.,1.14,3.,1.*element,type=c3d8r,elset=one1,1,2,3,4,5,6,7,8*solid section,elset=one,material=ABQ_SUPER_ELASTIC_N3D_1*element, type=cps4r, elset=two2,11,12,13,14*solid section,elset=two,material=ABQ_SUPER_ELASTIC_N2D_11.0,*material,name=ABQ_SUPER_ELASTIC_N3D_1*user material,consta=1440000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22.,6.7 ,250.,140.,,0.041,*depvar24,*density1.e-2*material,name=ABQ_SUPER_ELASTIC_N2D_1*user material,consta=1440000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22.,6.7 ,250.,140.,,0.041,*depvar24,*density1.e-2*initial conditions,type=temperaturenall,22.*boundary1,1,32,2,33,34,14,35,1,26,28,111,1,212,214,1*amplitude,name=smooth,time=totaltime,definition=smoothstep0.,0.,0.1,1.,0.2,0.*restart,write,number=1*elset,elset=eallone,two*elset,elset=QA_TEST_ALLELEMENTSeall*step*dynamic,explicit,.1,,*boundary,amplitude=smooth3,2,,0.07764,2,,0.07767,2,,0.07768,2,,0.077613,2,,0.077614,2,,0.0776*OUTPUT,FIELD,NUMBER INTERVAL=20,TIME MARKS=YES*ELEMENT OUTPUT,ELSET=QA_TEST_ALLELEMENTSS,LE*NODE OUTPUTU,*OUTPUT,HISTORY*ELEMENT OUTPUT,ELSET=eallS,LE*NODE OUTPUT,NSET=NALLU,RF,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIME INTERVAL=0.025*end step*step*dynamic,explicit,.1,,*boundary,amplitude=smooth3,2,,0.07764,2,,0.07767,2,,0.07768,2,,0.077613,2,,0.077614,2,,0.0776*end step

annealing-template-standard.inp

*HEADINGTemplate: Annealing with ABAQUS/Standard (Annealing in STEP 3).........*ELSET, NAME=ALLELEM.........*MATERIAL, NAME=SUPERELASTIC*USER MATERIAL, CONSTANTS=16 6800000., 0.3, 3600000., 0.3, 0.04, 650., 52000., 63500., 37., 650., 18000., 2600., 78000., 0.04, 1, 3*DEPVAR 24,.........*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*END STEP*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*MODEL CHANGE, REMOVEALLELEM,.........*END STEP*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*MODEL CHANGE, ADD=STRAIN FREEALLELEM,.........*END STEP*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*END STEP

annealing-template-explicit.inp

*HEADINGTemplate: Annealing with ABAQUS/Explicit (Annealing in STEP 2).........*ELSET, NAME=ALLELEM.........*MATERIAL, NAME=N3D_SUPERELASTIC*USER MATERIAL, CONSTANTS=14 6800000., 0.3, 3600000., 0.3, 0.04, 650., 52000., 63500., 37., 650., 18000., 2600., 78000., 0.04*DEPVAR 24,.........*****STEP*DYNAMIC, EXPLICIT.........*END STEP*****STEP*ANNEAL*END STEP*****STEP*DYNAMIC, EXPLICIT.........*END STEP

auc01_nitinol_stent_r1.pdf

2001 ABAQUS Users Conference 1

SIMULATION OF IMPLANTABLE NITINOL STENTS

Nuno Rebelo, Norm Walker, and Hoss FoadianHibbitt, Karlsson & Sorensen (West), Inc.

39221 Paseo Padre Parkway, Suite FFremont, California 94538-1611

Abstract

Finite element methods continue to play an ever expanding role in the design and validation of

medical devices. The ability of the finite element technique in dealing with both complex

geometries and materials is key to the success of this method in the medical field. This synergism

is clearly evident in the analysis of devices based on Nitinol, a nickel-titanium alloy, and a

complex superelastic material. The particular device explored here is a stent, which is a mesh tube

that is inserted into blood vessels to counteract the effects of vascular diseases. Both the

manufacturing process and deployment are considered.

Introduction

Medical technology continues to advance rapidly as physicians and engineers move closer to and

understand better each other's needs. Nowhere is this better evidenced than in the development of

advanced medical implants. Traditionally, new products were developed by prototyping and

evaluating. However, this process is very time consuming and often does not fully reveal potential

failures. Finite element modeling and analysis greatly reduce testing and time to market by

allowing the designer to simulate product performance in advance of any prototyping (Haridas,

1999). Algorithms have been developed which allow for the accurate predictive finite element

analysis of nickel-titanium alloys which have extremely complex but highly attractive mechanical

behavior for medical applications.

2 2001 ABAQUS Users Conference

Since its discovery and first fabrication, Nitinol alloys have come to be used in a myriad of unique

ways. The superelastic and shape memory properties of the alloy along with its biocompatibility

and fatigue properties have given the material a wide range of applications from thermal switches

and electrical connectors to cardiovascular stents. However, the many benefits of the material

come at a cost. The complexity of its properties makes it difficult to process. Trial and error

techniques have been commonly employed in the past; it is, however, very time consuming; and in

today's market place, time is among the most valuable commodities. FEA can be employed to

hasten time to market of Nitinol products by greatly reducing the number of design iterations

required, hence expediting the design process. This article describes material models capable of

simulating the superelastic behavior of alloys such as Nitinol, and shows how they can be used to

simulate the fabrication and deployment of cardiovascular stents.

The purpose of FEA is to possibly expose and solve design flaws before a product is produced. It

does not normally preclude the manufacture of prototypes, but it should greatly reduce the number

of prototype iterations required, and in the best case, will reduce the number of prototypes to one.

In fact, in areas of high confidence of the materials and the model set-up, it is possible that

prototyping can be eliminated altogether.

Superelastic Alloy Material Behavior

While highly attractive for medical applications, Nitinol's behavior is complex, as can be seen in

the mechanical characterization provided in Figure 1. At rest, the material presents itself in an

austenite phase, which behaves linear elastically. Upon loading, this austenite phase transforms

into a martensite phase, which is also linear elastic; however, the elasticity of each phase has

different constants. The transformation produces a substantial amount of strain and is triggered by

stress, over a relatively narrow range. Upon unloading, the transformation is reversible.

However, the stress levels at which such reversible transformation occurs are smaller than the


stresses which were required to produce the original transformation. Because the material, upon

unloading, completely recovers its original shape, it is described as elastic. In addition, because

the transformation strains are so large (of the order of 6%) compared to the typical elastic strains

in a metal, the material is said to be superelastic.

If a reverse loading is applied (for instance in compression instead of tension), a similar behavior

is observed, with the exception that the stress levels required to produce the transformations are

higher, while the transformation strain is lower. The net result is that Nitinol is an extremely

flexible metal alloy that can undergo very large deformations without losing the ability to recover

its original shape upon unloading.

The constitutive laws used in simulations should embed the characteristics just described. It is

relatively straightforward to generate a material model that reproduces the desired behavior if the

deformation being simulated is uniaxial. Unfortunately, it rarely is in practice.

Until very recently, there were no generally accepted material models, which were capable of

reproducing all of the characteristics of the material just described. A popular close

approximation, capable of modeling the loading part of the model, is hyperelasticity, which is

commonly used to represent rubber behavior (Pelton, 1994). Several other models have recently

been proposed to address Nitinol's behavior (Auricchio, 1997; Auricchio, 1996; Qidwai, 2000).

However, a thorough verification of these models has been difficult. This is because the

manufacturing requirements of the material are complex. As a result, Nitinol is typically available

as relatively thin wires and tubes, from which most of the testing data available is uniaxial. While

it is relatively straightforward to produce a uniaxial model, it is much more difficult to produce a

model that represents Nitinols three-dimensional stress-strain behavior. At Hibbitt, Karlsson &

Sorensen (West), a user material routine (UMAT/Nitinol) was written following the model


proposed by Auricchio and Taylor (Auricchio, 1997; Auricchio, 1996). This theory is based on

the concept of generalized plasticity (Lubliner, 1996). The theory is deemed acceptable because it

is based on physical principles. The theory decomposes strain into two parts a purely linear

elastic component and a transformation component:

trel +=

The austenite to twinned martensite transformation is driven by the resolution of shear forces, and

it takes place within a range of stress levels that are characteristic of the material.

= F

a tr

FS FFF

where is the fraction of martensite, and F is a transformation potential. The same is true for the

reverse transformation, but at different stress levels. The intensity of the transformation follows a

stress potential law:

( ) F,f =

Any change in stress direction produces a reorientation of the martensite with negligible additional

effort. Changes in temperature produce a shift in the stress levels at which the transformations

take place. This shift is linear in temperature. Because there is a volume increase associated with

the transformation, it requires less stress to produce the transformation in tension, and more in

compression. This is modeled with a linear Drucker-Prager approach for the transformation

potential:

TCtanpF +=


with being the Mises equivalent stress, p the pressure stress, and T the temperature.

Although the original model does not take it into account, a rule of mixtures was used to

implement the change in linear elasticity from the austenite phase into the martensite phase; the

implementation is, at present, approximate.

In addition to the usual stresses and strains, the UMAT routine tracks variables specific to the

model. These variables include distribution of fraction of martensite, transformation strains, and

equivalent stresses and strains. These are points in the uniaxial tensile curve into which material

points that have a three-dimensional state, specific fractions of martensite, and a specific

loading/unloading history are mapped. The material data required by the model are obtained from

straightforward observations of uniaxial tests in terms of loading, unloading, reverse loading, and

temperature effects. The calibration consists of 13 values (Figure 2). In addition, the user may

anneal the material in the middle of an analysis.

Figure 3 displays a comparison of a set of experimental stress-strain curves, in which successively

larger strains were imposed, with the same curves obtained by a simulation of the uniaxial test.

Figure 4 shows the behavior of the model upon repeated loading and unloading. Figures 5 and 6

show the behavior of the model subjected to an 18C temperature range while strains are applied.

Stent Analysis

Stents are cylindrical metal mesh tubes made of materials such as Nitinol and inserted into blood

vessels to counter act the effects associated with vascular diseases, such as narrowing of blood

vessels due to the build up of plaque.

In this section, we present an example of a stent analysis in which both the manufacturing process

and deployment are considered, courtesy of Nitinol Devices & Components, Cordis Corporation, a

Johnson & Johnson company. One of the key issues in medical implants is device lifetime or, in


engineering terms, fatigue life. Fatigue testing normally takes such a long time that it is

incompatible with old-fashioned build-test design cycles. Finite element analysis provides

quantitative measures of stress and strain without the need to build the devices. This process not

only allows the optimization of designs, but also provides an opportunity to predict the device's

life.

The large elastic strains possible in Nitinol reduce the risk of damage to the stent both during

delivery into the body, and due to accidents while in operation. The large elastic strains also

permit the deployed configuration to be close to the unloaded configuration.

A possible manufacturing process of Nitinol stents starts from a thin tube in which a pattern is

electromachined. The FEA model is built from this machined tube. Since the pattern repeats

itself, only a part of the stent with appropriate symmetry boundary conditions is considered in

order to simplify the complexity of the models (Figure 7). The stent is expanded to its nominal

dimensions, typically at a diameter many times larger than the original tube diameter (Figure 8).

While loaded, the stent is annealed to provide its new unloaded configuration. The stent is

crimped from the outside, and inserted into the delivery system (usually a system of catheter

tubes), as shown in Figure 9. Once inside a patient's body, the delivery system pushes the stent

out of its containment (Figure 10). Once delivered, the response to blood pressure pulsing loads

may be used to determine the fatigue life of the stent. The calculation reveals stress or strain

concentrations during all three aspects of manufacturing, deployment, and service loading (Figure

11). Auxiliary information is also available from the calculation; such as how much martensitic

transformation has occurred, and therefore, how close the design is to the limits of the material

flexibility (Figure 12).


Conclusion

Finite element analysis is a method well suited to the needs of the product designer. The method

allows the designer to quickly assess his or her design and to iterate the design on a computer

before a single piece of metal is ever touched. The finite element method's ability to quickly and

accurately solve complex material problems, such as those of Nitinol alloys, makes it an ideal

candidate for such situations. Complexity of stent designs and of the actions taken to deploy them

requires sophistication in the finite element tool used. Proper material behavior is just one

requirement. Quite often, advanced capabilities are required in terms of contact with both rigid

tools and other flexible bodies, large deformations, localized buckling, material removal, complex

loading sequences and synchronization. These basic robust capabilities in ABAQUS make the

software particularly suitable for stent design.

References

1. Auricchio F, Taylor RL. Shape-memory alloys: modeling and numerical simulations ofthe finite-strain superelastic behavior Comp Meth in Appl Mech and Engnrg 1996; 143:175-194.

2. Auricchio F, Taylor RL, Lubliner J. Shape-memory alloys: macromodelling andnumerical simulations of the superelastic behavior Comp Meth in Appl Mech andEngnrg 1997; 146: 281-312.

3. Haridas B, Haynes C. Predictive analysis at the forefront of medical productdevelopment Med Devc and Diag Indsty, Oct 1999: 112-119.

4. Lubliner J, Auricchio F. Generalized plasticity and shape memory alloys Int J SolidsStruct 1996; 33: 991-1003.

5. Qidwai MA, Lagoudas DC. Numerical implementation of a shape memory alloythermomechanical constitutive model using return mapping algorithms Int J Num MethEngnrg 2000; 47: 1123-1168.

6. Pelton AR, Rebelo N, Duerig TW, Wick A. Experimental and FEM analysis of thebending behavior of superelastic tubing In: Pelton AR, Hodgson D, Duerig TW, editors,The First International Conference on Shape Memory and Superelastic Technologies.Pacific Grove: MIAS, 1994: 353-358.


1. Mechanical behavior of Nitinol.

2. Data required to define superelastic behavior in the ABAQUS model.


3. The ABAQUS algorithm for NiTi alloy modeling closely matches experimentalmeasurements where successively larger strain loads are applied to the alloy at different

temperatures, 22C (top) and 37C (bottom).


4. Model showing the effects of repeated loading and unloading of Nitinol.

5. Model showing loading in terms of temperature and strain.


6. Stress-strain curve results for Nitinol based on loading shown in Figure 5.

7. Stent model in its initial configuration.


8. Expanded stent.

9. Retracted stent.


10. Partially deployed stent.

11. Von Mises stress intensity during deployment.


12. Martensitic transformation level in retracted stent.

nitinol_3d_xpl_plastic.inp

*headingpull a bar, c3d8r,cps4r for nitinol built-in vumat*node,nset=nall1,2,1.3,1.,1.4,,1.5,,,1.6,1.,,1.7,1.,1.,1.8,,1.,1.11,3.12,4.13,4.,1.14,3.,1.*element,type=c3d8r,elset=one1,1,2,3,4,5,6,7,8*solid section,elset=one,material=ABQ_SUPER_ELASTIC_N3D*element, type=cps4r, elset=two2,11,12,13,14*solid section,elset=two,material=ABQ_SUPER_ELASTIC_N2D1.0,*material,name=ABQ_SUPER_ELASTIC_N3D*user material,consta=1940000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22 ,6.7 ,250.,140.,,0.041,2,800.,0.07,1200.,0.2,*depvar31,*density1.e-4*material,name=ABQ_SUPER_ELASTIC_N2D*user material,consta=1940000,0.33,32000,0.33,0.041,6.7 ,440.,540.,22 ,6.7 ,250.,140.,,0.041,2,800.,0.07,1200.,0.2,*depvar31,*density1.e-4*initial conditions,type=temperaturenall,22.*boundary1,1,32,2,33,34,14,35,1,26,28,111,1,212,214,1*amplitude,name=smooth,time=totaltime,definition=smoothstep0.,0.,0.1,1.,0.2,0.*restart,write,number=1*elset,elset=eallone,two*elset,elset=QA_TEST_ALLELEMENTSeall*step*dynamic,explicit,.1,,*boundary,amplitude=smooth3,2,,0.07764,2,,0.07767,2,,0.07768,2,,0.077613,2,,0.077614,2,,0.0776*OUTPUT,FIELD,NUMBER INTERVAL=40,TIME MARKS=YES*ELEMENT OUTPUT,ELSET=QA_TEST_ALLELEMENTSS,LE*NODE OUTPUTU,*OUTPUT,HISTORY*ELEMENT OUTPUT,ELSET=eallS,LE*NODE OUTPUT,NSET=NALLU,RF,*OUTPUT,HISTORY,VARIABLE=PRESELECT,TIME INTERVAL=0.025*end step*step*dynamic,explicit,.1,,*boundary,amplitude=smooth3,2,,0.07764,2,,0.07767,2,,0.07768,2,,0.077613,2,,0.077614,2,,0.0776*end step

1658/Templates_InputFiles_References/abqanswersspring2001_r1.pdf

Martensitic transformationlevel in retracted stent.

A N S W E R S T O C O M M O N A B A Q U S Q U E S T I O N S S P R I N G 2 0 0 1

C O N T E N T S1 Simulation of Implantable

Nitinol Stents

Hibbitt, Karlsson &

Sorensen, Inc.

1080 Main Street

Pawtucket, RI

02860-4847 usa

phone 401.727.4200

fax 401.727.4208

e-mail [email protected]

www.abaqus.com

ABAQUS

FEA Model courtesy of Nitinol Devices & Components, Cordis Corporation, a Johnson & Johnson Company.

Simulation of ImplantableNitinol Stents

Medical technology is advancing rapidly,particularly in the development ofadvanced medical implants. Traditionallynew products were developed byprototyping and evaluating; however,this process is very time consumingand often does not fully reveal potentialfailures. Finite element modeling andanalysis greatly reduces testing and timeto market by allowing the designer tosimulate product performance in advanceof any prototyping.

The superelastic and shape memoryproperties of Nitinol, a nickel-titaniumalloy, along with its biocompatibility andfatigue properties, have made thematerial attractive for cardiovascularstents. However, it is a complex materialand difficult to process. FEA hastens timeto market of Nitinol products by reducingthe number of design iterations required,hence expediting the design process.

Superelastic alloy materialbehavior

Nitinol is an extremely flexible metalalloy that can undergo very largedeformations without losing the ability

to recover its original shape uponunloading. At rest, the material presentsitself in an austenite phase, which behaveslinear elastically. Upon loading, thisaustenite phase transforms into amartensite phase, which is also linearelastic; however, the elasticity of eachphase has different constants. Thetransformation produces a substantialamount of strain and is triggered bystress over a relatively narrow range.Upon unloading, the transformation isreversible. However, the stress levels atwhich such reversible transformationoccurs are smaller than the stresses thatwere required to produce the originaltransformation. Because the materialrecovers its original shape uponunloading, it is described as elastic. Inaddition, because the transformationstrains are large (on the order of 6%)compared to elastic strains in typicalmetals (on the order of 0.1%), thematerial is said to be superelastic.

If a reverse loading is applied (forexample, in compression instead oftension), a similar behavior is observed,with the exception that the stress levelsrequired to produce the transformationsare higher, while the transformationstrain is lower.

ABAQUS/Answers

Von Mises stress intensityduring deployment.

0617.ANSWERS 4/5/01 8:35 AM Page 1

Nitinol is a difficult material tocharacterize numerically. Anapproximation, capable of modelingthe loading part of the model, ishyperelasticity, which is commonly usedto represent rubber behavior. Otherconstitutive models have been proposedrecently to address Nitinols behavior.However, a thorough verification of thesemodels has been difficult because themanufacturing requirements of Nitinolare complex. As a result, Nitinol istypically available as relatively thin wiresand tubes, from which most of the testingdata available are in the form of uniaxialdata. It is relatively straightforward toproduce a uniaxial model, but it is muchmore difficult to produce a model thatrepresents Nitinols three-dimensionalstress-strain behavior.

At Hibbitt, Karlsson & Sorensen(West) a user material routine(UMAT/Nitinol) was written followingthe model proposed by Auricchio andTaylor. This theory is based on theconcept of generalized plasticity andphysical principles. The theorydecomposes strain into two parts-apurely linear elastic component anda transformation component:

= el+

tr.

The austenite to twinned martensitetransformation is driven by theresolution of shear forces, and it takesplace within a range of stress levels thatare characteristic of the material.

tr

= a ,

FS

F FF,

where is the fraction of martensite andF is a transformation potential. The sameis true for the reverse transformation butat different stress levels. The intensity ofthe transformation follows a stresspotential law:

= f(, ) F .

Any change in stress direction producesa reorientation of the martensite withnegligible additional effort. Changes intemperature produce a shift in the stresslevels at which the transformations takeplace. This shift is linear in temperature.Because there is a volume increase

F

associated with the transformation, itrequires less stress to produce thetransformation in tension and more incompression. This is modeled with alinear Drucker-Prager approach for thetransformation potential:

F = - p tan + CT,

with being the Mises equivalentstress, p the pressure stress, and Tthe temperature.

A rule of mixtures is used to implementthe change in linear elasticity from theaustenite phase into the martensite phase.

In addition to the usual stresses andstrains, the UMAT routine tracks variablesspecific to the model. These variablesinclude the distribution of the fraction ofmartensite, transformation strains, andequivalent stresses and strains. Theseare points in the uniaxial tensile curveinto which material points that have athree-dimensional state, specificfractions of martensite, and a specificloading/unloading history are mapped.The material data required by the modelare obtained from straightforwardobservations of uniaxial tests in terms ofloading, unloading, reverse loading, andtemperature effects. The calibrationconsists of 13 values, as shown below.

.

2 ABAQUS/Answers

-

Mechanical behavior of Nitinol.

The ABAQUS algorithm forNiTi alloy modeling closelymatches experimentalmeasurements wheresuccessively larger strain loadsare applied in the alloy atdifferent temperatures.

Behavior of the model uponrepeated loading and unloadingof Nitinol.

temperature = 22C

temperature = 37C

Data required to define superelastic behav-ior in the ABAQUS model.

-

0617.ANSWERSFOR PDF PAGE 2 4/5/01 9:09 AM Page 2

Stent analysis

Stents are cylindrical metal mesh tubesmade of materials such as Nitinol andinserted into blood vessels to counteractthe effects associated with vasculardiseases, such as narrowing of bloodvessels due to plaque build up.

The present analysis considers both themanufacturing process and deployment ofa stent. One of the key issues in medicalimplants is device lifetime or, inengineering terms, fatigue life. Finiteelement analysis provides quantitativemeasures of stress and strain needed tomake fatigue estimates for these devices.This allows the optimization of designsand allows prediction of the devices life.

The large elastic strains possible inNitinol reduce the risk of damage to thestent both during delivery into the bodyand due to accidents while in operation.

One manufacturing process of Nitinolstents starts from a thin tube into which apattern is electromachined. The FEA modelis built from this machined tube. Since thepattern repeats itself, only a part of thestent with appropriate symmetry ismodeled. The stent is expanded to itsnominal dimensions, typically at adiameter many times larger than theoriginal tube diameter. While loaded, thestent is annealed to provide its newunloaded configuration. The stent is thencrimped from the outside and inserted intothe delivery system (usually a system ofcatheter tubes). Once inside a patientsbody, the delivery system pushes the stentout of its containment. Once delivered, theresponse to blood pressure pulsing loadsdetermines the fatigue life of the stent.

The calculation reveals stress-strainconcentrations during manufacturing,deployment, and service loading. Auxiliaryinformation is also available from thecalculation; for example, how muchmartensitic transformation has occurredand, therefore, how close the design is tothe limits of the material flexibility.

Summary

Finite element analysis is a method wellsuited to the needs of the product designer.The method allows designers to iteratedesigns on a computer before prototypesare made. The finite element method can

ABAQUS/Answers 3

solve mechanical problems involvingcomplex material behavior such as thoseof Nitinol alloys.

Complexity of stent designs and of theactions taken to deploy them requiressophistication in the finite element toolused. Proper material behavior is just onerequirement. Advanced modelingcapabilities such as contact with bothrigid tools and other flexible bodies, largedeformations, localized buckling, material removal, and simulation of complexloading sequences are needed. These basicrobust capabilities in ABAQUS make thecode particularly suitable for stent design.

Stress-strain curveresults based on loadingshown above.

Expanded

Retracted

Partiallydeployed

Behavior of the model subjected to an 18Ctemperature range while strainsare applied.

Initial configuration

Stent model.

Loading in terms of temperature and strain.

0617.ANSWERS 4/5/01 8:41 AM Page 3

1658/Templates_InputFiles_References/annealing-template-explicit.inp

*HEADINGTemplate: Annealing with ABAQUS/Explicit (Annealing in STEP 2).........*ELSET, NAME=ALLELEM.........*MATERIAL, NAME=N3D_SUPERELASTIC*USER MATERIAL, CONSTANTS=14 6800000., 0.3, 3600000., 0.3, 0.04, 650., 52000., 63500., 37., 650., 18000., 2600., 78000., 0.04*DEPVAR 24,.........*****STEP*DYNAMIC, EXPLICIT.........*END STEP*****STEP*ANNEAL*END STEP*****STEP*DYNAMIC, EXPLICIT.........*END STEP

1658/Templates_InputFiles_References/annealing-template-standard.inp

*HEADINGTemplate: Annealing with ABAQUS/Standard (Annealing in STEP 3).........*ELSET, NAME=ALLELEM.........*MATERIAL, NAME=SUPERELASTIC*USER MATERIAL, CONSTANTS=16 6800000., 0.3, 3600000., 0.3, 0.04, 650., 52000., 63500., 37., 650., 18000., 2600., 78000., 0.04, 1, 3*DEPVAR 24,.........*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*END STEP*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*MODEL CHANGE, REMOVEALLELEM,.........*END STEP*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*MODEL CHANGE, ADD=STRAIN FREEALLELEM,.........*END STEP*****STEP, NLGEOM, AMPLITUDE=RAMP*STATIC.........*END STEP

1658/Templates_InputFiles_References/auc01_nitinol_stent_r1.pdf


SIMULATION OF IMPLANTABLE NITINOL STENTS

Nuno Rebelo, Norm Walker, and Hoss FoadianHibbitt, Karlsson & Sorensen (West), Inc.

39221 Paseo Padre Parkway, Suite FFremont, California 94538-1611

Abstract

Finite element methods continue to play an ever expanding role in the design and validation of

medical devices. The ability of the finite element technique in dealing with both complex

geometries and materials is key to the success of this method in the medical field. This synergism

is clearly evident in the analysis of devices based on Nitinol, a nickel-titanium alloy, and a

complex superelastic material. The particular device explored here is a stent, which is a mesh tube

that is inserted into blood vessels to counteract the effects of vascular diseases. Both the

manufacturing process and deployment are considered.

Introduction

Medical technology continues to advance rapidly as physicians and engineers move closer to and

understand better each other's needs. Nowhere is this better evidenced than in the development of

advanced medical implants. Traditionally, new products were developed by prototyping and

evaluating. However, this process is very time consuming and often does not fully reveal potential

failures. Finite element modeling and analysis greatly reduce testing and time to market by

allowing the designer to simulate product performance in advance of any prototyping (Haridas,

1999). Algorithms have been developed which allow for the accurate predictive finite element

analysis of nickel-titanium alloys which have extremely complex but highly attractive mechanical

behavior for medical applications.


Since its discovery and first fabrication, Nitinol alloys have come to be used in a myriad of unique

ways. The superelastic and shape memory properties of the alloy along with its biocompatibility

and fatigue properties have given the material a wide range of applications from thermal switches

and electrical connectors to cardiovascular stents. However, the many benefits of the material

come at a cost. The complexity of its properties makes it difficult to process. Trial and error

techniques have been commonly employed in the past; it is, however, very time consuming; and in

today's market place, time is among the most valuable commodities. FEA can be employed to

hasten time to market of Nitinol products by greatly reducing the number of design iterations

required, hence expediting the design process. This article describes material models capable of

simulating the superelastic behavior of alloys such as Nitinol, and shows how they can be used to

simulate the fabrication and deployment of cardiovascular stents.

The purpose of FEA is to possibly expose and solve design flaws before a product is produced. It

does not normally preclude the manufacture of prototypes, but it should greatly reduce the number

of prototype iterations required, and in the best case, will reduce the number of prototypes to one.

In fact, in areas of high confidence of the materials and the model set-up, it is possible that

prototyping can be eliminated altogether.

Superelastic Alloy Material Behavior

While highly attractive for medical applications, Nitinol's behavior is complex, as can be seen in

the mechanical characterization provided in Figure 1. At rest, the material presents itself in an

austenite phase, which behaves linear elastically. Upon loading, this austenite phase transforms

into a martensite phase, which is also linear elastic; however, the elasticity of each phase has

different constants. The transformation produces a substantial amount of strain and is triggered by

stress, over a relatively narrow range. Upon unloading, the transformation is reversible.

However, the stress levels at which such reversible transformation occurs are smaller than the