Gong

2002 ABAQUS Users’ Conference 1

ABAQUS Analysis on Nitinol Medical Applications

Xiao-Yan Gong and Alan R. Pelton

Nitinol Devices and Components

A Johnson & Johnson Company

Fremont, CA, USA

Abstract: Nitinol, an alloy of about 50% Ni and 50% Ti, is a very unique material. At constant temperatureabove its Austenite finish (A f) temperature, under uniaxial tensile test, the material is highly nonlinear andcapable of large deformation to the ultimate strain on the order of 15%. This material behavior, known assuperelasticity, along with its excellent biocompatibility and corrosion resistance, makes Nitinol a perfectmaterial candidate for many medical device applications. However, the nonlinear material response alsorequires a specific material description to perform the stress analysis. The user developed materialsubroutine from HKS/West makes the simulation of the Nitinol devices possible. This article presents severalcase studies of the nonlinear finite element analysis using ABAQUS/Standard and the Nitinol UMAT. Theanalyses are found to agree well with the theoretical prediction and experimental measurement.

1. Introduction

Nitinol’s biocompatibility has made it a great material for many medical applications such asdentures, orthodontic arch wires, needles, guide wires, heart valve instruments, self-expandingstents, VenaCava filters, minimally invasive surgery instruments, and septal defect occlusionsystem, to name a few (Stoeckel, 2000, NDC web site, Stoeckel and Melzer, 1995, and Miyazaki,1999, etc). Many of these devices are implanted into the human body via minimally invasivesurgeries taking advantage of the unique superelastic behavior of Nitinol.

Figure 1 shows schematically the stress-strain relation for a superelastic Nitinol under uniaxialtensile test at a constant temperature above its A f. Initially, the material is in the Austenite phase.Upon loading, below a small strain, ε1, stress is linearly proportional to the strain. The slopedefines the Young’s Modulus of Nitinol in Austenite phase. When the strain reaches beyond ε1, asmall increase in stress induces a large amount of strain owing to the phase transition fromAustenite to Martensite. After completion of the phase transition, for strain larger than ε2, thestress and strain relation is linear, again with a different slope, which defines the Young’sModulus of Martensite phase. During unloading, Martensite remains until strain ε3, which is lessthan ε2. Below ε3, the Martensite reverts to Austenite and a large reverse strain is produced untilε4, which is smaller than ε1. After unloading below ε4, the material returns to be linear elastic.

This material behavior generates analysis difficulties due to its path-dependence and highly non-linearity. For such a complicated material behavior, a numerical solution using the finite elementmethod is nearly the only way for an accurate engineering analysis. This calls for an efficientconstitutive modeling because it is inevitable that numerical iteration is necessary during the

2 2002 ABAQUS Users’ Conference

analysis. A phenomenological approach is the most suitable solution for the simulation efficiency.Theory based on either the generalized plasticity theory, which focuses on the material response ata given temperature, or a free energy frame work, which focuses on the temperature dependenciesof the material, has been developed in the past years. Auricchio and Taylor (1996) and Auricchioet al (1997) provided detailed summary of the approach based on generalized plasticity theory.Qidwai and Lagoudas (1999) discussed the approach based on thermodynamic energy frameworkin detail. Schematically, both theories show the great potential to predict the material responsewell. Yet only HKS/West commercialized a user-defined material subroutine UMAT specific toNitinol based on the generalized plasticity theory. Rebelo et al (2001) and Rebelo and Perry(2000) demonstrated that the HKS/West’s UMAT is capable of predicting not only the uniaxialmaterial response at different temperatures, but also a Nitinol stent’s deformation. Rebelo et al(2001) also showed that the UMAT could provide the Austenite and Martensite composition atany material point in addition to the stress and strain fields.

Figure 1. Schematic uniaxial stress-strain relation of Nitinol at a given temperature

This article focuses on analyzing Nitinol’s medical applications in minimally invasive surgery.The analyses are divided into two categories from an analysis point of view. We choose arepresentative device from each category and discuss the analysis in detail. The first deviceanalyzed is a Nitinol needle/wire locator. The second device is a self-expanding stent. They arechosen with general indications on many other applications as listed in the section below. In bothcases, experimental data are used to compare with the analysis results. Theoretical estimations arealso provided to further confirm the analysis results.

Strain

Str

ess

ε1

ε3ε4

ε2


2. FEA Analyses on Typical Nitinol Medical Applications

In the needle/wire locator application, we show that the UMAT is able to predict the uniaxialmaterial response at different Af by comparing with the experimental data. This opens doors forthe first order engineering approximation to optimize the Af to achieve the most suitable design.The stress analysis on the device is relatively easy and straightforward as the hook wire isconstrained very tightly inside the needle. Furthermore, the peak stress and strain values can beestimated from pure geometry change. Comparison shows that FEA agrees well with thetheoretical prediction.

In the stent application, the FEA results on a simplified unit cell of stent, i.e., a diamond shapedspecimen, are compared with the load-displacement results collected from the experiment. Atheoretical solution based on a piece-wise linear approximation in combination with thefundamental beam theory is generated on the loading portion of the specimen for comparison.Results show good agreement between FEA, theoretical prediction and the experimental data.

2.1. Needle/Wire Locator

Figures 2 shows the Homer Mammalok needle/wire locator. It is a two piece device that consistsof a Nitinol wire with a half circular shaped hook at one end, and a hollowed needle that the wiregoes into. The locator is originally withdrawn inside the needle cannula. During the application,the needle is inserted into the breast and adjusted until its tip is verified to be at the site of thetumor. The locator is then advanced and reforms back to the hook configuration. The position ofthe hook marks the correct location for the surgeon. If necessary, the locator can be withdrawninto the needle until the correct location is identified.

Figure 2. Homer Mammalok needle/wire locator

The design challenge is to have a strong hook so that it can be placed in position tightly, yet it isnot too hard to withdraw the hook into the needle. One of the possible design options, from amaterial application point, is to choose the right Af temperature. Pelton et al (2000) provideddetails on how to obtain the desired Af. Pelton et al (2001) also pointed out that the best way tooptimize both Af and the geometry is to perform a FEA without actually making and testing thedevice. This type of FEA normally involves a curved shaped wire being withdrawn into a straighttube. The analysis is very straightforward. One can mesh the wire with solid elements andsimplify the needle as a rigid cylinder. Use of symmetry can reduce the model to a half of itsactual size. Prescribed displacement condition can be used to pull the wire through the rigidcylinder. The outputs from FEA are the stress and strain fields and the contact pressure betweenthe wire and the needle (rigid surface). The wire diameter is 0.38mm and the hook radius is4.8mm in this study. The maximum tensile and compressive strains are theoretically estimatedfrom the curved beam theory to be approximately 4.1% and –3.8%.


Figure 3. Comparison of the uniaxial tensile tests with FEA prediction

Figure 4. Comparison of the uniaxial tensile tests on Af = 14 oC wires with FEAprediction from Af = 27 oC


Figure 5. Comparison of the uniaxial tensile tests on Af = -10 oC wires with FEAprediction from Af = 27 oC

Figure 6. Longitudinal stress contours in the same scale when different Af Nitinollocator is withdrawn inside the needle Indicates stress increases as Af decreases


A uniaxial tensile test is necessary to calibrate the UMAT for analysis. For comparison purposes,the tests were performed at three different A f temperatures, i.e., -10 o C, 14 oC and 27 o C. We usedthe highest A f, i.e., A f = 27oC, to calibrate the UMAT. We then run a single element test to predictthe stress-strain relations for the other two Af wires. Figure 3 shows the comparison of the FEAprediction and the experimental results of the highest Af wire. As one can tell, the calibratedmaterial response reproduces the experimental results very well. Figure 4 and 5 show thecomparison of the FEA prediction and the experimental results on the lower Af wires. Again, theresults agree, especially well in the range of application interests, i.e., up to 5%.

Figure 6 shows stress contour on the deformed shape for different Af wires when they arewithdrawn into the needle. Clearly the different Af wire produces different stress values. Thelower the A f, the higher the stress it produces. Therefore, the lower the Af, the harder to withdrawthe wire into the needle. When the strain contours are plotted, there is less difference between thedifferent Af wires. This is because the deformation is bending dominant and the wire is soconfined in the needle that despite the material responses differ for different Af, the strain field, asin a same highly constrained environment, is less dependent of the material responses. Figure 7plots the comparison of strain distributions for different Af wires and the theoretical prediction.The results are almost identical. Notice these are the strain distributions in the body portion of thearc of the wire, at the locations where the wire changes from straight to arc the strain is slightlyhigher. This phenomenon, normally refers to as end effect, can only be predicted from the FEA.Figure 8 shows the strain distribution at this location with comparison to theoretical prediction.As one can tell, the strain is higher than the body portion of the curved wire. Therefore, eventheory and FEA agree extremely well to predict the strain in the body portion of the curved wire.FEA can also capture the end effect nicely and predict the strain more accurately.

This analysis technique also applies to other wire-shaped devices such as a duct-occlusion device,a radiofrequency interstitial tissue ablation device, and a hingeless grasper (Stoeckel, 2000).

Figure 7. Edge to edge longitudinal strain distribution when Nitinol locator iswithdrawn inside the needle


Figure 8. Edge to edge longitudinal strain distribution comparison at the end ofcurved wire when it is withdrawn inside the needle

2.2. Stent

A stent is a metal mesh made either from fine wires or from laser cutting the tubes into desiredpatterns set in place to hold a vessel open. Duerig et al (2000) discussed the key differencesbetween a balloon expandable stent and a self-expanding stent in addition to the key design issues.Among the key design issues, the most important ones are the fatigue life and stiffness of the stent.Figure 9 shows a Nitinol stent inside a latex tube.

Figure 9. A Nitinol stent inside a latex tube

An ideal self-expanding stent analysis would simulate the manufacture and deployment processes.This includes multiple step calculations and clearly requires more computation power and time.However, strong nonlinearity of Nitinol discourages such complicated analysis. Because a self-expanding stent at application is always compressed to smaller diameters than its manufacturedstrain-free diameter, Rebelo and Perry (2000) and Rebelo et al (2001) suggested that we use auser-defined rigid cylindrical surface to compress the stent to simplify the computation. Thismethod works well to predict the deformed stent shape and the locations of high strain are veryconsistent with the fracture locations in excessive fatigue test. Recent work also indicates that it


predicts the key performance parameters of a stent accurately (Gong et al, 2002). The analysistechnique applies to the devices that are used inside a circular shaped vessel. Another example ofthis type device is a Vena Cava filter as shown in Figure 10. It is implanted into the vein to trapthe blood clots (dark spots on the right of the figure) inside its basket to prevent them from furthermigrating.

Figure 10. Vena Cava filter and its schematic functionality

A simple and efficient way to study the mechanics of a stent is to analyze its individual struts.Tolomeo et al (2000) performed FEA on a single strut and compared the result with theexperiment on an “unzipped” stent. They also compared the linear elastic portion of the resultwith the analytical model. The results were found to be consistent with one another. Thisindicates that the stiffness of a stent can be predicted from FEA accurately.

The unzipped stent is not easy to handle experimentally especially in fatigue studies. We thereforebuilt a unit cell of a stent, i.e., a diamond shaped specimen, to overcome the handling difficulties(Figure 10). It is designed to be similar to the strut geometry from a Cordis SMART stent. Theends of diamond with small holes in the sample are for the ease of crimping. The samples areprocessed in the same manner as a stent so that it has the same Af and an electropolished surfacefinish. They are stretched and compressed before the actual fatigue test and the load anddisplacement are recorded to ensure the processing consistence in sample preparation.

Figure 11. Diamond specimen for fatigue study

side view top viewBaskets

Fixation hooks


FEA is used to calculate the strain field in the specimen and to interpret the fatigue results asstrain-life curve so that they can be used to guide the stent design (Gong and Pelton, 2002).Notice that when only the loading portion is concerned, one can simplify the stress-strain curve aspiece-wise linear. Under this simplification the beam theory can be used to estimate the maximumstrain inside the specimen and predict the load-displacement relation on the loading path toconfirm the FEA. Figure 11 shows the comparison of theoretical prediction, FEA and theexperimental data, the results agree well.

Figure 12. Comparison of FEA, theoretical prediction, and experimental data ofload-displacement relation on diamond-shaped specimen

3. Conclusion

ABAQUS, with user-defined material subroutine specific for Nitinol developed by HKS/West, hasopened the door for Nitinol engineering evaluations. Experimental data and theoretical estimationagree well with the FEA on two different Nitinol medical device applications that were presented.The analysis techniques are general and apply to many other types of Nitinol medical devices orimplants. The use of FEA helps learn the device functionality and the fatigue properties of theNitinol. They combine can guide the device design to improve its service life and optimize thedevice functionality.

Load-Displacement

-3

-2

-1

0

1

2

3

4

-7 -5 -3 -1 1 3 5 7

Displacement (mm)

FEA

Experiment

Theory


4. References

1. Auricchio, F. and Taylor, R. L., “Shape-Memory Alloys: Modeling and NumericalSimulations of the Finite-Strain Superelastic Behavior”, Comput. Methods Appl. Mech.Engrg. 143:175-194, 1996.

2. Auricchio, F., Taylor, R. L. and Lubliner, J., “Shape-Memory Alloys: Macromodeling andNumerical Simulations of the Superelastic Behavior”, Comput. Methods Appl. Mech. Engrg.146:281-312, 1997.

3. Duerig, T. W., Tolomeo, D. E., and Wholey, W., “An Overview of Superelastic StentDesign”, Min, Invas. Ther. & Allied Technol., Vol. 9, No. 3/4, pp 235-246, 2000.

4. Gong, X-Y, Pelton, A. R., “Fatigue Testing of NiTi on Diamond-Shaped Specimens”, to bepresented at the SEM Annual Conference on Experimental and Applied Mechanics,Biologically Inspired and Multi-Functional Materials and Systems in Milwaukee, WI, in June2002.

5. Gong, X-Y, Pelton, A. R., Duerig, T. W., Rebelo, N, and Perry, K. E., “Finite ElementAnalysis and Experimental Study on Superelastic Nitinol Stent”, to be presented at the 14th

U.S. National Congress on Theoretical and Applied Mechanics in Blacksburg, VA, in June2002.

6. Miyazaki, S., “Medical and Dental Applications of Shape Memory Alloys”, Shape MemoryMaterials, edited by Otsuka K. and Wayman C.M., Cambridge University Press, pp267-281,1999.

7. NDC web site, www.nitinol.com.

8. Pelton, A. R., Dicello, J. and Miyazaki, S., “Optimization of Processing and Properties ofMedical Grade Nitinol Wire”, Min, Invas. Ther. & Allied Technol., Vol. 9, No. 2, pp 107-118, 2000.

9. Pelton, A. R., Duerig, T.W. and Stoeckel, D, “Design with Nitinol” Presented at SMST 2001,in Kunming, China, Sept. 2001.

10. Qidwai, M. A., and Lagoudas, D. C., “Numerical Implementation of a Shape Memory AlloyThermomechanical Constitutive Model Using Return Mapping Algorithms”, Int. J. Numer.Meth. Engrg, 43:1123-1168, 2000.

11. Rebelo N. and Perry M., “Finite Element Analysis for the Design of Nitinol MedicalDevices”, Min, Invas. Ther. & Allied Technol., Vol. 9, No. 2, pp 75-80, 2000.

12. Rebelo N., Walker, N. and Fodian, H., “Simulation of Implantable Nitinol Stent”, ABAQUSUser’s Conference, pp. 421 – 434, 2001.

13. Stoeckel, D., “Nitinol Medical Devices and Implants,” Min, Invas. Ther. & Allied Technol.,Vol. 9, No. 2, pp 81-88, 2000.

14. Stoeckel D. and Melzer A, “The use of NiTi Alloys for Surgical Instruments”, Materials inClinical Applications, edited by Vincenzini, P., Techna Srl, pp 791-798, 1995.

15. Tolomeo, D., Slater, T., and Wu, P., “Predictive Modeling of Radial Force for SuperelasticStents”, Proceedings of SMST 2000, to be published.

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