1、Designation: F 2514 08Standard Guide forFinite Element Analysis (FEA) of Metallic Vascular StentsSubjected to Uniform Radial Loading1This standard is issued under the fixed designation F 2514; the number immediately following the designation indicates the year oforiginal adoption or, in the case of
2、revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis guide establishes general requirements and considerations for using finite element analysis
3、techniques for the numerical simulation of metallic stents subjected to uniform radial loading. Thesestents are intended for use within the human vascular system.1. Scope1.1 PurposeThis guide establishes general requirementsand considerations for the development of finite elementmodels used in the e
4、valuation of the performance of a metallicvascular stent design under uniform radial loading. Suggestedcriteria are provided for evaluating the typical cases of metallicstents under uniform radially oriented and pulsatile loading.Recommended procedures for checking and validating thefinite element m
5、odel(s) are provided as a means to assess themodel and analysis results. Finally, the recommended contentof an engineering report covering the mechanical simulations ispresented.1.2 Limits:1.2.1 This guide is limited in discussion to the finite elementstructural analysis of metallic stents of the fo
6、llowing types:1.2.1.1 Plastically deformable metal stents.1.2.1.2 Self-expanding metal stents.1.2.1.3 Plastically deformable metal portions of coveredstents.1.2.1.4 Metal portions of self-expanding covered metalstents.1.2.2 The emphasis of the techniques described in this guideis intended for both e
7、lasto-plastic materials such as stainlesssteel, and superelastic materials such as nitinol. Unique con-cerns associated with stents designed for shape memorybehavior are not addressed within this guide.1.2.3 This guide does not consider changes to possible timevarying conditions or different loading
8、s related to vascularremodeling.1.2.4 This guide is restricted to cases that involve theapplication of uniform radially oriented loading.1.2.5 This guide does not provide guidance in the applica-tion or interpretation of FEA in determining fatigue life.1.2.6 This guide is not intended to include com
9、plete de-scriptions of the finite element method, nor its theoretical basisand formulation.1.3 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.2. Terminology2.1 Definitions:2.1.1 balloon expandable stent, na stent that is expan
10、dedat the treatment site by a balloon catheter. The purpose of theballoon is to plastically deform the stent material such that thestent remains expanded after the deflation of the balloon.2.1.2 conceptual model, nmodel produced by analyzingand observing the physical system of interest composed ofma
11、thematical models and equations representing that system.2.1.3 computational model, nimplementation of a con-ceptual model in software.2.1.4 crimp, vto secure the stent on a delivery system byradially compressing the stent into a delivery device such as acatheter or onto an expanding delivery device
12、 such as aballoon.2.1.5 delivery system, na mechanical system that is usedto deliver and deploy a stent at a target site.2.1.6 elasto-plastic material, na material behavioralmodel that exhibits elastic behavior (recoverable) up to itsyield point and plastic behavior (irrecoverable) above its yieldpo
13、int.2.1.7 endurance limit, nstress or strain level at which thematerial is considered to have “infinite” life.1This guide is under the jurisdiction of ASTM Committee F04 on Medical andSurgical Materials and Devices and is the direct responsibility of SubcommitteeF04.30 on Cardiovascular Standards.Cu
14、rrent edition approved July 15, 2008. Published August 2008.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.2.1.8 finite element analysis (FEA), na general purposenumerical technique.2.1.8.1 DiscussionIn this guide, the structural co
15、ntinuumis discretized into regions known as elements, in which themechanical behavior is defined. Continuity is enforced at thevertices of the elements where node points are defined. Themechanical behavior of the continuum is then defined accord-ing to mathematical expressions of physical laws at th
16、e nodepoints. This results in the definition of a set of simultaneousequations that are solved for state variables from which suchimportant quantities as displacements, stresses, and strains canbe derived.2.1.9 geometrical nonlinearity, na type of nonlinearityrelated to structural deformation where
17、the relation betweenstrain and displacement are not linearly proportional.2.1.10 linear elastic material, na material in which thestress resulting from an applied force is directly proportional tothe corresponding strain it produces. Thus, linear elasticmaterials do not retain any stress or strain w
18、hen all externalloads and boundary conditions are removed and all deforma-tions are recoverable.2.1.11 model calibration, nthe process through which theparameters of a computational model are checked or adjustedto create a model with the proper measure of accuracy.2.1.12 model validation, nthe proce
19、ss of determining thedegree to which a computational model accurately representsthe real world behavior it was intended to represent. It is anevaluation of the fidelity of the computational model and thereal world.2.1.13 model verification, nthe process of assessing thatthe implementation of the com
20、putational model accuratelyrepresents the engineers conceptual model and of the solutionto the model. It is an evaluation of the fidelity of the conceptualmodel and the computational model.2.1.14 nonlinear material, na material behavior in whichthe stress resulting from an applied external load is n
21、ot directlyproportional to the induced strain.2.1.15 permanent deformation, nresidual or irrecoverablestrain and deformation in a structure after all loads andboundary conditions are removed.2.1.16 plasticity, nmaterial behavior characteristic wherepermanent or irrecoverable deformation remains when
22、 theexternal loading is removed.2.1.17 pulsatile, adjrecurring alternate increase and de-crease of a quantity such as the pressure that would occur in anartery.2.1.18 self-expanding stent, na stent that expands at thetreatment site without mechanical assistance. The materialtypically used for the st
23、ent has the ability to return eitherpartially or fully to a previous size and shape and remainexpanded after the delivery system is removed.2.1.19 solution sensitivity, na measure of the relativechange in solution results caused by changing one or moreparameters in a computational model.2.1.20 stent
24、, na tubular structure that is permanentlyimplanted in the native or grafted vasculature and that isintended to provide mechanical radial support to enhancevessel patency. For the purposes of this guide, a stent ismetallic and may be covered by a coating, synthetic textile, ortissue graft material.3
25、. Summary of Practice3.1 This guide addresses the use of the finite elementmethod for structural analysis of metallic vascular stents undervarious types of simulated uniform radial loading. The purposeof a structural analysis of the stent is to determine suchquantities as the displacements, stresses
26、, and strains within adevice resulting from external loading. This includes stressesand strains potentially due, but not limited, to manufacturingprocesses, to delivery in the body, and to pulsatile loading invivo.3.2 Current United States government guidelines (1)2rec-ommend structural analysis of
27、a proposed device under physi-ologically appropriate loading. The analysis technique dis-cussed in this guide is restricted to the finite element analysistechnique (2-5), although other techniques may be equallysuitable for the required analysis.3.3 Prior to the finalization of a device design, rigo
28、rousexperimental testing is recommended to complement the analy-ses performed. During these tests, care should be taken torepresent the loading and boundary support conditions consis-tent with those used not only in the finite element analysis andexperimental tests but also those expected in clinica
29、l use.Experimental tests should be carefully monitored. Any behav-ior that was not captured by the numerical simulation should beidentified and evaluated for its effect on safety and reliability.4. Significance and Use4.1 Finite element analysis is a valuable method for evalu-ating the performance o
30、f metallic stents and in quantifyingquantities such as internal stresses, internal strains, and defor-mation patterns due to applied external loads and boundaryconditions. Many times an analysis is performed to correlate toand plan experimental tests. A finite element analysis isespecially valuable
31、in determining quantities that cannot bereadily measured.5. Overall Technical Approach5.1 The application of finite element analysis is intended forthe development of a quantifiable level of confidence in thestent design. The overall approach described in this guidefocuses on the development of a sy
32、stematic technical approachto using the finite element analysis technique to evaluate stentperformance. The basic process includes:5.1.1 Detailed definition of the geometry of the stent beingevaluated.5.1.2 The determination, quantification and validation of theimportant mechanical material properti
33、es.5.1.3 Selection of the appropriate finite element tools andprograms to ensure effective and reliable representations of thestent being evaluated.2The boldface numbers in parentheses refer to a list of references at the end ofthis standard.F25140825.1.4 Selection and validation of the appropriate
34、finiteelement model and type of element(s) used.5.1.5 Calibration, validation, and verification of model in-put, parameters for the numerical simulation, solution resultsand comparison to experimental tests.5.1.6 Definition of all important loading steps.5.1.7 Selection and application of appropriat
35、e boundaryconditions, such as symmetry.5.1.8 Effective and proper application of the finite elementanalysis program for the intended evaluation.5.1.9 The generation and interpretation of results to performan effective evaluation.5.1.10 Documentation of the analysis, including all support-ing citatio
36、ns and references, analysis methodology, and as-sumptions, results interpretation, and overall stent designevaluation.6. Input Data6.1 Finite element analysis is a numerical technique use forsimulating the mechanical response of structures. A finiteelement structural analysis requires input to numer
37、ically rep-resent geometric and material information, as well as mechani-cal support and loading conditions. Two important parts of anyfinite element analysis is the proper representation of materialproperties and the definition of load cases and boundaryconditions. These must reflect the entire pro
38、cess and perfor-mance history and environment of the device. The load historyshould include all relevant manufacturing loads and all steps ofthe intended clinical end use of the device. If all steps are notincluded, the reason for the omission should be described.6.1.1 Geometric Data:6.1.1.1 Finite
39、element models are based on a geometricrepresentation of the device being studied. The source of thedetails of the geometry can be drawings, computer aideddesign (CAD) and solid models, preliminary sketches, or anyother source consistent with defining the device model geom-etry.6.1.1.2 Finite elemen
40、t modeling is used extensively in thedesign phase of product development, many times before anyprototyping has occurred. As such, models are often based onpreliminary designs from CAD drawings. Changes associatedwith the progress of the development of the design andmanufacturing processes should be
41、addressed in the finiteelement model to accurately represent actual stent geometry.6.1.1.3 Stent geometry is often determined by measuringand inspecting representative samples of stents that haveundergone all processing steps prior to insertion in the body.This processing may include, but is not lim
42、ited to, cleaning,polishing, and crimping. Most evaluations use the nominaldimensions for the evaluation. It is also most appropriate toconsider the possible effects of variability in dimensions ordesign parameters within the finite element analysis, such thatthe manner in which the variability infl
43、uence performance andsafety.6.1.2 Preliminary ModelsDuring the preliminary designphase, detailed geometric and/or material data may not bewarranted and/or readily available. In these cases, it is appro-priate to use initial design geometries and material data fromstandard engineering references. The
44、 results of such simula-tions will be considered preliminary results.6.1.3 Material Property Tests:6.1.3.1 Mechanical properties of the material should bedetermined from rigorous experimental testing of the materialthat has undergone all pertinent manufacturing processesincluding finishing, cleaning
45、, and sterilization, if appropriate.The mechanical material properties for a finite element analysisare most often determined through tensile testing of thematerial. During the test, load and displacement data is to becollected to define the entire material curve. All relevanthysteresis and/or tempe
46、rature effects on the material responsemust be included.6.1.3.2 When testing for material properties, extreme careshould be taken to ensure accurate measurements using suit-able fixturing and appropriately calibrated devices for measur-ing both load and displacement.6.1.3.3 If warranted by the mater
47、ial, the material curve(s)should be measured at the appropriate temperature(s) of theintended use. The effects of temperature on the materialresponse are extremely critical for superelastic alloys. Differ-ences in the material behavior in tension and compressionshould also be considered along with a
48、ny load history depen-dent tension/compression asymmetry phenomena or workhardening of the material.6.1.4 Material Property Validation:6.1.4.1 The material mechanical property values must beconverted into a format and form consistent with the finiteelement representation.6.1.4.2 Validation tests sho
49、uld be performed to validate thematerial model used in the analysis. The effects of the testspecimen size or shape (tube, wire, sheet) must be consideredin applying the material model to the validation model.6.1.4.3 A material validation test could include the determi-nation of the load-displacement behavior of a finite elementmodel of a simple tensile test. For example, a model is firstcreated of a simple geometric specimen of material using theelement type for which the validation is being performed. Thegeometry and number of elements in the validation modelshou
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