Study of a compact energy absorber

129 Pages·2016·2.33 MB·English

by  Muhammad Ali

Iowa State University Capstones, Theses and
Retrospective Theses and Dissertations
Dissertations
2007
Study of a compact energy absorber
Muhammad Ali
Iowa State University
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Recommended Citation
Ali, Muhammad, "Study of a compact energy absorber" (2007).Retrospective Theses and Dissertations. 15760.
https://lib.dr.iastate.edu/rtd/15760
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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
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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
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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
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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
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F.1C38DR Element………………………………………………………….. 115
APPENDIXG………………………………………………………………………….. 100
G.1Young’s modulus of hexagonal honeycombs……………………………. 100
G.2Shearmodulus ofhexagonal honeycombs………………………………. 102
REFERENCES………………………………………………………………………… 105
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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
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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