1、Designation: F2514 08 (Reapproved 2014)Standard Guide forFinite Element Analysis (FEA) of Metallic Vascular StentsSubjected to Uniform Radial Loading1This standard is issued under the fixed designation F2514; the number immediately following the designation indicates the year oforiginal adoption or,
2、 in the case of 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
3、element analysistechniques 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 elementmode
4、ls used in the evaluation 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 the
5、finite element model(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
6、stents of the following 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 int
7、ended for both elasto-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 d
8、ifferent loadings 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 intende
9、d to include complete 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 ste
10、nt that is expandedat 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 intere
11、st composed ofmathematical models and equations representing that system.2.1.3 computational model, nimplementation of a concep-tual 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
12、 delivery device 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) a
13、bove its yieldpoint.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 Cardiovascu
14、lar Standards.Current edition approved March 1, 2014. Published April 2014. Originallyapproved in 2008. Last previous edition approved in 2008 as F2514 08. DOI:10.1520/F2514-08R14.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12.1.8
15、finite element analysis (FEA), n a general purposenumerical technique.2.1.8.1 DiscussionIn this guide, the structural continuumis discretized into regions known as elements, in which themechanical behavior is defined. Continuity is enforced at thevertices of the elements where node points are define
16、d. Themechanical behavior of the continuum is then defined accord-ing to mathematical expressions of physical laws at the nodepoints. This results in the definition of a set of simultaneousequations that are solved for state variables from which suchimportant quantities as displacements, stresses, a
17、nd strains canbe derived.2.1.9 geometrical nonlinearity, na type of nonlinearityrelated to structural deformation where 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
18、 proportional tothe corresponding strain it produces. Thus, linear elasticmaterials do not retain any stress or strain when 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 computationa
19、l model are checked or adjustedto create a model with the proper measure of accuracy.2.1.12 model validation, nthe process 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 comp
20、utational model and thereal world.2.1.13 model verification, nthe process of assessing thatthe implementation of the computational model accuratelyrepresents the engineers conceptual model and of the solutionto the model. It is an evaluation of the fidelity of the conceptualmodel and the computation
21、al model.2.1.14 nonlinear material, na material behavior in whichthe stress resulting from an applied external load is not directlyproportional to the induced strain.2.1.15 permanent deformation, nresidual or irrecoverablestrain and deformation in a structure after all loads andboundary conditions a
22、re removed.2.1.16 plasticity, nmaterial behavior characteristic wherepermanent or irrecoverable deformation remains when 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-expandin
23、g stent, na stent that expands at thetreatment site without mechanical assistance. The materialtypically used for the stent 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
24、of the relativechange in solution results caused by changing one or moreparameters in a computational model.2.1.20 stent, 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
25、purposes of this guide, a stent ismetallic and may be covered by a coating, synthetic textile, ortissue graft material.3. 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
26、 loading. The purposeof a structural analysis of the stent is to determine suchquantities as the displacements, stresses, and strains within adevice resulting from external loading. This includes stressesand strains potentially due, but not limited, to manufacturingprocesses, to delivery in the body
27、, and to pulsatile loading invivo.3.2 Current United States government guidelines (1)2rec-ommend structural analysis of 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
28、other techniques may be equallysuitable for the required analysis.3.3 Prior to the finalization of a device design, rigorousexperimental testing is recommended to complement the analy-ses performed. During these tests, care should be taken torepresent the loading and boundary support conditions cons
29、is-tent with those used not only in the finite element analysis andexperimental tests but also those expected in clinical 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 a
30、nd reliability.4. Significance and Use4.1 Finite element analysis is a valuable method for evalu-ating the performance of metallic stents and in quantifyingquantities such as internal stresses, internal strains, and defor-mation patterns due to applied external loads and boundaryconditions. Many tim
31、es an analysis is performed to correlate toand plan experimental tests. A finite element analysis isespecially valuable in determining quantities that cannot bereadily measured.5. Overall Technical Approach5.1 The application of finite element analysis is intended forthe development of a quantifiabl
32、e level of confidence in thestent design. The overall approach described in this guidefocuses on the development of a systematic 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
33、stent beingevaluated.5.1.2 The determination, quantification and validation of theimportant mechanical material properties.2The boldface numbers in parentheses refer to a list of references at the end ofthis standard.F2514 08 (2014)25.1.3 Selection of the appropriate finite element tools andprograms
34、 to ensure effective and reliable representations of thestent being evaluated.5.1.4 Selection and validation of the appropriate finiteelement model and type of element(s) used.5.1.5 Calibration, validation, and verification of modelinput, parameters for the numerical simulation, solution resultsand
35、comparison to experimental tests.5.1.6 Definition of all important loading steps.5.1.7 Selection and application of appropriate 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 inter
36、pretation of results to performan effective evaluation.5.1.10 Documentation of the analysis, including all support-ing citations and references, analysis methodology, andassumptions, results interpretation, and overall stent designevaluation.6. Input Data6.1 Finite element analysis is a numerical te
37、chnique use forsimulating the mechanical response of structures. A finiteelement structural analysis requires input to numerically 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 rep
38、resentation of materialproperties and the definition of load cases and boundaryconditions. These must reflect the entire process 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 th
39、e device. If all steps are notincluded, the reason for the omission should be described.6.1.1 Geometric Data:6.1.1.1 Finite 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 soli
40、d models, preliminary sketches, or anyother source consistent with defining the device model geom-etry.6.1.1.2 Finite element modeling is used extensively in thedesign phase of product development, many times before anyprototyping has occurred. As such, models are often based onpreliminary designs f
41、rom CAD drawings. Changes associatedwith the progress of the development of the design andmanufacturing processes should be 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
42、of stents that haveundergone all processing steps prior to insertion in the body.This processing may include, but is not limited to, cleaning,polishing, and crimping. Most evaluations use the nominaldimensions for the evaluation. It is also most appropriate toconsider the possible effects of variabi
43、lity in dimensions ordesign parameters within the finite element analysis, such thatthe manner in which the variability influence performance andsafety.6.1.2 Preliminary ModelsDuring the preliminary designphase, detailed geometric and/or material data may not bewarranted and/or readily available. In
44、 these cases, it is appro-priate to use initial design geometries and material data fromstandard engineering references. The 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 rigoro
45、us experimental testing of the materialthat has undergone all pertinent manufacturing processesincluding finishing, cleaning, and sterilization, if appropriate.The mechanical material properties for a finite element analysisare most often determined through tensile testing of thematerial. During the
46、 test, load and displacement data is to becollected to define the entire material curve. All relevanthysteresis and/or temperature 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-abl
47、e fixturing and appropriately calibrated devices for measur-ing both load and displacement.6.1.3.3 If warranted by the material, 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
48、 superelastic alloys. Differ-ences in the material behavior in tension and compressionshould also be considered along with any 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
49、values must beconverted into a format and form consistent with the finiteelement representation.6.1.4.2 Validation tests should 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 us
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