Retrospective Theses and Dissertations 2007 Study of a compact energy absorber Muhammad Ali Iowa State University Follow this and additional works at:http://lib.dr.iastate.edu/rtd Part of theMechanical Engineering Commons Recommended Citation Ali, Muhammad, "Study of a compact energy absorber" (2007).Retrospective Theses and Dissertations. 15760. http://lib.dr.iastate.edu/rtd/15760 This Dissertation is brought to you for free and open access by Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please [email protected]. Study of a compact energy absorber by MuhammadAli Adissertationsubmittedtothegraduate faculty inpartial fulfillment oftherequirements forthedegreeof DOCTOR OFPHILOSOPHY Major: Mechanical Engineering Program ofStudyCommittee AbirQamhiyah,Co–majorProfessor DonaldFlugrad,Co–majorProfessor GregLuecke,Co–major Professor CarolynHeising GloriaStarns IowaStateUniversity Ames, Iowa 2007 Copyright ©Muhammad Ali,2007.All rights reserved. 3337371 Copyright 2008 by Ali, Muhammad All rights reserved 3337371 2009 ii DEDICATION Dedicatedtomyfather Muhammad Murtaza All Iknow andall Ihave Is bythemakingofhis hand TothememoryofmygrandfatherMuhammad Rasool TomyMother forherlovingguidanceandsacrifice and TomyFamilyfortheir endless loveand support iii TABLE OFCONTENTS LISTOF FIGURES …………………………………………………………………... vii LISTOFTABLES …………………………………………………………………… xii ACKNOWLEDGEMENTS ………………………………………………………….. xiii ABSTRACT ………………………………………………………………………….. xv CHAPTER 1 INTRODUCTION.…………………………………………………….... 1 1.1Characteristics ofan energyabsorber…………………………………….. 1 1.1.1 Irreversibleenergyconversion……………………………….. 1 1.1.2Restrictedandconstant reactive force………………………... 2 1.1.3 Longstroke…………………………………………………… 3 1.1.4Stableandrepeatabledeformationmode…………………….. 4 1.1.5 Light weight andhighspecificenergyabsorptioncapacity….. 4 1.1.6Cost effective andeasyinstallation…………………………... 5 1.2 Idealizedmaterial models………………………………………………… 5 1.3Effect oflargedeformation………………………………………………. 7 1.4Dynamiceffects…………………………………………………………... 7 1.4.1Stress wavepropagationandits effects onenergyabsorption.. 8 1.4.2Strainrateeffects……………………………………………... 12 CHAPTER 2HYPOTHESIS…………………………………………………………... 13 2.1Energyabsorbingissues andnature……………………………………... 13 2.2Bananacross-section……………………………………………………... 15 iv CHAPTER 3FINITEELEMENTANALYSIS………………………………………... 18 3.1Background...………………………………............................................... 18 3.2Modeling…………………………………………………………………. 19 3.3Analysis…………………………...……………………………………… 20 3.4Results……………………………………………………………………. 21 3.4.1Energy………………………………………………………... 26 3.4.2Simulations…………………………………………………… 27 CHAPTER 4THEORETICALANALYSIS………………..…………………………. 33 4.1Themechanics ofhoneycombs....………………………………………... 34 4.1.1Upperboundcollapsestress………………………………...... 36 4.1.2 Lowerboundcollapsestress………………………………….. 37 4.1.3 Lockingstrain………………………………………………... 38 4.2Finiteelement analysis ofGHS…...……………………………………… 40 4.2.1Modeling……………………………………………………... 40 4.2.2Results………………………………………………………... 41 CHAPTER 5STUDYOFGRADED HONEYCOMBSTRUCTURES (GHS) 44 UNDER IMPACT….………........................................................................................... 5.1Deformationmodes ofGHS underdynamicloading…………………….. 45 5.2Stress straincurve………………………….……………………………... 45 5.3GHS modes underhighloadingrates…………………………………….. 47 5.4Stress straincurves forhighimpact velocity……………………………... 50 5.5Mathematical model forhighvelocityimpact……………………………. 52 v 5.6EnergyabsorptionperformanceofGHS w.r.t regularhoneycombs……... 59 5.7Cell shape……………………………………………………………….... 65 CHAPTER 6CONCLUSIONS AND FUTUREWORK...…………………………… 67 6.2Conclusions………………………………………………………………. 67 6.1FutureWork ……………………………………………………………. 69 APPENDIXA………………………………….……………………………………… 70 A.1Classical theoryofplasticity……………………………………………. 70 APPENDIXB…………………………………………………………………………... 75 B.1Propagationvelocity……………………………………………………... 75 B.2Particlevelocity………………………………………………………….. 77 APPENDIXC...………………………………………………………………………… 78 C.1Effect ofsizeonstiffness………………………………………………… 78 C.2MATLABCode………………………………………………………….. 80 APPENDIXD………………………………………………………………………….. 91 D.1Explicit method………………………………………………………….. 91 D.2Central differencemethod……………………………………………….. 91 APPENDIXE…………………………………………………………………………... 94 E.1Contact pair………………………………………………………………. 94 E.2Constraint enforcement method………………………………………….. 95 E.2.1Kinematiccontact constraints………………………………... 95 E.2.2Penaltycontact constraints…………………………………… 96 APPENDIXF…………………………………………………………………............... 98 vi F.1C38DR Element………………………………………………………….. 115 APPENDIXG………………………………………………………………………….. 100 G.1Young’s modulus of hexagonal honeycombs……………………………. 100 G.2Shearmodulus ofhexagonal honeycombs………………………………. 102 REFERENCES………………………………………………………………………… 105 vii LIST OFFIGURES Figure1.1 Uniaxial truestress-straincurve…...……………………………………. 3 Figure1.2 Impact responseofanobject from twodifferent materials...…………… 4 Figure1.3 Idealizedstress-strain curves ofelasticmaterials undertension...……... 6 Figure1.4 Idealizedstress-strain curves ofrigidmaterials undertension……….… 6 Figure1.5 Stress waves indecreasinglystrainhardeningmaterials ……...………... 9 Figure1.6 Stress waves inincreasinglystrainhardeningmaterials ………………... 9 Figure2.1 Thecellularstructurein ahumanfemur.……………………………...... 13 Figure2.2 Thecompressive responseofcellularstructurein humanfemur……... 14 Figure2.3 Thestress-strain curves ofwoodunder compression…………….…… 14 Figure2.4 Thecompressivebehaviorofplasticandelastomerichoneycombs ...….. 15 Figure2.5 Cross sectionofabanana peel…………..………………………………. 16 Figure3.1 Rigid platehittingthesolidaluminum plate……………..……….……... 19 Figure3.2 Replicationofcell shape from abananapeel ………………………...… 20 Figure3.3 Aluminum withdifferent cell packing…………………………………... 21 Figure3.4 DynamicForce-Displacement curveofahoneycombstructure………... 22 Figure3.5 Force-Displacement curves at 3m/s impact velocity…………………… 22 Figure3.6 Energy-Displacement curves at 3m/s impact velocity…………………. 23 Figure3.7 Deformedsolidplate at theendofthestroke..………………………..... 29 Figure3.8 Deformedplatecontainingonelayerofcells,at theendofthestroke.. 29 Figure3.9 Deformedplatecontainingtwolayers of cells,at theendofthestroke. 29 viii Figure3.10 Deformedplatecontainingtwo gradedlayers of cells,at theendofthe stroke……………………………………………………………………. 30 Figure3.11 Deformedplatecontainingthreelayers ofcells,at theendofthestroke.. 30 Figure3.12 Deformedplatecontainingthree gradedlayers ofcells,at theendofthe stroke……………………………………………………………..... 30 Figure3.13 Deformedplatecontainingmodifieddesign1structure,at theendofthe stroke…………………………………………………………………….. 31 Figure3.14 Deformedplatecontainingmodifieddesign2structure,at theendofthe stroke…………………………………………………………………….. 31 Figure3.15 Deformedplatecontainingmodifieddesign3structure,at theendofthe stroke…………………………………………………………………….. 31 Figure3.16 Deformedplatecontainingmodifieddesign4structure,at theendofthe stroke……………………………………………………………………. 32 Figure3.17 Model containingcells filledwithcrushablefoam....…………………… 32 Figure3.18 Compositegradedsection……………………………………………….. 32 Figure4.1 Theregulartwodimensional honeycombstructure...…………………... 33 Figure4.2 Aunit cell ofaregularhoneycomb……………………………………… 35 Figure4.3 Plasticcollapseofinclinedwalls intheYdirection…………………...... 37 Figure4.4 Internal and external bendingmoment ontheinclinedwall…………...... 38 Figure4.5 Themodifiedpeel structure……………………………………………... 39 Figure4.6 Thetheoretical response oftheGHS intheYdirectionusingequation 4.10.……………………………………………………………………… 40