Experimental and Numerical Study of Ductile MetalAuxetic Tubular StructuresMuhammad AliThesis submitted to the faculty of Virginia Polytechnic Institute and State Universityin partial fulfillment of the requirements for the degree ofMaster of ScienceinCivil EngineeringEric JacquesMatthew R. EathertonIoannis KoutromanosMay 20, 2020Blacksburg, VirginiaKeywords: Auxetic, Ductile Metal, Tubular, Steel, Aluminum, Energy Dissipation,Energy AbsorptionCopyright 2020, Muhammad Ali
Experimental and Numerical Study of Ductile Metal AuxeticTubular StructuresMuhammad AliABSTRACTMethods to mitigate the risk posed by seismic and blast loads to structures are of highinterest to researchers. Auxetic structures are a new class of metamaterials that exhibitcounterintuitive negative Poisson’s ratio (NPR) behavior based on their geometric configuration.Cellular auxetics are light-weight and cost-effective materials that have the potential todemonstrate high strength and resilience under axial forces. Existing research on metallic auxeticsis scarce and based mostly on analytical studies. Apparent NPR behavior of auxetics has also beenlinked to enhanced energy absorbing potential. A pilot study was undertaken to investigate andunderstand auxetic behavior in tubes constructed using ductile metals commonly found instructural applications i.e. steel and aluminum. The main objective was to establish whetherperformance enhancements could be obtained through auxetic behavior in ductile metal tubes. Inaddition, any potential benefits to auxetic performance due to base material plasticity were studied.These objectives were fulfilled by conducting an experimental and analytical investigation, theresults of which are presented in this thesis.The experimental program consisted of establishing a design methodology, manufacturing,and laboratory testing for tubular metallic specimens. A total of eight specimens were designedand manufactured comprising five steel and three aluminum. For each base metal, three differentgeometric configurations of cells were designed: one with a rectangular array of circular voids andtwo with void geometries based on the collapsed shape of circular cells in a design tube underuniaxial compressive stress. A parameter called the Deformation Ratio (DR) was introduced toquantify cell geometry. Designed tubes were manufactured via a six-axis laser cutting process. Acustom-made test assembly was constructed and specimens were tested under reverse-cyclicuniaxial loading, with one exception. Digital Image Correlation (DIC) was used to acquireexperimental strain data. The performance of the auxetic and non-auxetic tubular structures was
evaluated based on the axial load-deformation characteristics, global deformations, and thespecific energy absorption of the test specimens.The experimental test results confirmed that ductile metal tubes with special collapsed cellgeometries were capable of demonstrating auxetic behavior under the applied elastic and inelasticuniaxial strains; both tensile and compressive. Base material plasticity was observed to have aninsignificant effect on the auxetic response. Experimental results suggested that the uniquedeformation mechanism precipitated by the auxetic cell geometries resulted in more stabledeformed shapes. Stability in global deformed shapes was observed to increase with an increasein DR value. In addition, the unique auxetic mechanism demonstrated an ability to distribute radialplastic strains uniformly over the height of the auxetic pattern. As a result, plastic strains wereexperienced by a greater fraction of auxetic tubes; this enhanced the energy-dissipating propertiesof auxetic specimens in comparison to the tested non-auxetic tubes. Tubes with cell geometriesassociated with higher DR values exhibited greater energy absorption relative to the non-auxeticspecimen. For the same base metal, auxetic specimens exhibited greater axial strength andeffective strain range, when compared to their non-auxetic counterparts. The increased strengthwas partially attributed to the increased cell wall thickness of the auxetic specimens. However, theincreased strain range was attributed to the rotation in unit cells induced by the unique auxeticgeometry.Experimental test data was used to validate the finite element (FE) and simplifiedmacromechanical modeling approaches. These methods were adopted to develop design toolscapable of replicating material performance and behavior as well as accurately predicting failureloads. Load-deformation response and effective Poisson’s ratio behavior was established using FEmodels of as-built specimens, while simplified macromechanical equations were derived based onthe equilibrium of forces to compute failure loads in tension. These equations relied on patterngeometry and measured experimental unit cell deformations. It was established that themanufacturing process had a detrimental effect on the properties of the aluminum specimens.Accordingly, empirical modifications were applied to the aluminum material model to capture thiseffect. FE models accurately replicated load-deformation behavior for both non-auxetic andauxetic specimens. Hence, the FE modeling approach was shown to be an effective tool forpredicting material properties and response in ductile metal tubes without the need for
experimental testing. The simplified strength equations also described material failure withreasonable accuracy, supporting their implementation as effective design tools to gauge tubestrength. It is recommended that FE models be refined further through the addition of failurecriteria and damage accumulation in material models.The result of this study established that auxetic behavior could be induced in ductile metaltubes through the introduction of unique cell geometry, thereby making them highly tunable andcapable of exhibiting variable mechanical properties. Owing to their deformation mechanism andNPR behavior, auxetic tubes demonstrated geometric stability at greater deformations, whichhighlighted their potential for use as structural elements in systems designed to deform whilebearing extreme loads e.g. earthquakes and blast events. Additionally, the capability of auxeticgeometries to distribute strains uniformly along their length was linked to the potentialdevelopment of energy-dissipating structural components. It was suggested that new knowledgeacquired in this study about auxetic behavior in ductile metals could support the development ofnew structural systems or methods of structural control based on NPR behavior. Finally,recommendations for future research were presented, based on the expansion of research to studythe effects of multiple loading regimes and parametric changes on auxeticity as well as additionalmechanical characteristics e.g. shear resistance.
Experimental and Numerical Study of Ductile Metal AuxeticTubular StructuresMuhammad AliGENERAL AUDIENCE ABSTRACTSpecial structures known as Auxetics have been studied that exhibit counterintuitive behaviorbased on their geometric configuration. The novel shapes and architecture of these structures allowthem to deform such that they expand laterally in tension and contract laterally in compression; aproperty known as negative Poisson’s ratio (NPR) which is rarely observed in naturally-occurringmaterials. Auxetic materials demonstrate mechanical properties such as high resilience,indentation resistance, and energy-absorption. An experimental and analytical study wasundertaken to explore the beneficial properties of auxetic behavior, along with the effect ofinelastic deformations in ductile metal auxetics. To this end, tubular test specimens, made withsteel and aluminum, were designed and manufactured. To achieve auxetic behavior, a unique arrayof collapsed cells was cut out from metal tubes using a laser cutting process. Subsequently,specimens were tested in the laboratory under cyclic and monotonic loads. Experimental resultsindicate that tubes with auxetic geometries exhibited NPR behavior and a unique deformationmechanism based on the rotation of the unit cells. Owing to this mechanism, auxetic specimenspossessed greater geometric stability under applied axial deformations, when compared to thetested non-auxetic specimens. The deformation mechanism was also responsible for a uniformdistribution of strains along the length of the auxetic geometry which was linked to relatively betterenergy absorbing capacity than the non-auxetic tubes. Developed finite element (FE) modelscaptured the response and behavior of all specimens with good accuracy. Derived simplifiedstrength equations were also able to calculate the ultimate tensile failure loads for all specimensaccurately. Both numerical methods demonstrated the potential to be utilized as design andevaluation tools for predicting material properties. Finally, recommendations to expand research,based on metal auxetic structures, were presented to further our understanding of auxetic behaviorin ductile metals and to explore its benefits under varying loading regimes. Results from thisresearch can be used to support the design of new structural systems or methods to control existingstructures by exploiting NPR properties of ductile metal auxetics. Furthermore, energy-dissipating
properties of metal auxetic materials may prove to be beneficial for structural applications underextreme loading conditions such as earthquakes and blasts.
AcknowledgmentsI extend my deepest gratitude to my advisor Dr. Eric Jacques for his guidance, patienceand constructive criticism throughout the course of this research. Using his invaluable experienceand knowledge, he has helped me become a better thinker, writer and researcher.To all my teachers at the University, I owe great thanks for imparting their knowledge tome. Special thanks to the wonderful staff at Patton Hall who made this experience so enjoyable.I wish to thank the staff at the Murray Structures Lab for their help with experimentaltesting. I also extend my gratitude to Samuel Sherry for his continuous help and guidance with theuse of the Digital Image Correlation (DIC) equipment.I am deeply grateful to the Advanced Research Computing (ARC) division of VirginiaTech. for their help in conducting simulations.Finally, I would like to thank my parents for their undying love, encouragement andsupport. This would not have been possible without their patience and sacrifice. To them, I dedicatethis thesis.vii
Table of ContentsAcknowledgments . viiTable of Contents . viiiList of Figures . xList of Tables . xivNotations and Symbols . xvIntroduction . 1General . 1Research Objectives . 22.214.171.124.2Experimental Program. 5Analytical Modeling. 5Thesis Organization . 5Literature Review . 126.96.36.199.21.4.3Naturally Occurring Auxetics . 8Mechanical Models for Auxetic Materials . 10Auxetic Materials and Properties . 19Conclusions from Literature Review . 40Potential Applications for Metal Auxetics . 42Experimental Program . 47General . 47Auxetic Unit Cell Design . 47Description of Tubular Specimens . 53Material Properties . 55Test Setup . 5188.8.131.52.184.108.40.206.4Test Assembly . 57Loading Protocol . 58Instrumentation . 61Procedure. 63Experimental Results . 65General . 65Summary of Results .