Overview Biological Materials Mechanics Structural ...meyersgroup.ucsd.edu/papers/journals/Meyers...

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Biological Materials MechanicsOverview

Table I. Principal Components of Common Structural Biological Composites

Mineral Organic

Biological Calcium HydroxylComposite Carbonate Calcium Silica Apatite Other Keratin Collagen Chitin Cellulose Other

Shells X XHorns X XBones X XTeeth X XBirdBeaks X XCrustacean X X X ExoskeletonInsectCuticle X XWoods XSpicules X X

Biologicalmaterialsarecomplexcom-positesthatarehierarchicallystructuredandmultifunctional.Theirmechanicalpropertiesareoftenoutstanding,consid-eringtheweakconstituentsfromwhichtheyareassembled.Theyareforthemostpartcomposedofbrittle(often,mineral)andductile(organic)components.Thesecomplex structures, which have risenfrommillionsofyearsofevolution,areinspiring materials scientists in thedesign of novel materials. This paperdiscussestheoveralldesignprinciplesinbiologicalstructuralcompositesandillustrates themforfiveexamples:seaspicules, the abalone shell, the conchshell, the toucan and hornbill beaks,andthesheepcrabexoskeleton.

IntrOductIOn

Many biological systems havemechanicalpropertiesthatarefarbeyondthose that can be achieved using thesame synthetic materials with presenttechnologies.1Thisisbecausebiologicalorganismsproducecompositesthatareorganizedintermsofcompositionandstructure,containingbothinorganicandorganiccomponentsincomplexstruc-tures.Theyarehierarchicallyorganizedat thenano-,micro-,andmeso-levels.Additionally,mostbiologicalmaterials

Structural Biological composites: An Overview*

MarcA.Meyers,AlbertY.M.Lin,YasuakiSeki,Po-YuChen,BimalK.Kad,andSaraBodde

are multifunctional2 (i.e., they accu-mulate functions). For example, boneprovidesstructuralsupportforthebodyplus blood cell formation; the chitin-basedexoskeletoninarthropodsoffersanattachmentformuscles,environmen-talprotection,andawaterbarrier;seaspicules offer light transmission plusstructuralsupport;androotsanchortreesplusprovidenutrienttransport.Athirddefiningcharacteristicofbiologicalsys-tems,incontrastwithcurrentsyntheticsystems,istheirself-healingability.Thisisnearlyuniversalinnature.Althoughbiologyisamaturescience, thestudyof biological materials and systemsby materials scientists and engineersis recent. It is intended, ultimately, toaccomplish two purposes. First, thisstudyprovidesthetoolsforthedevelop-mentofbiologicallyinspiredmaterials.Thisfield,alsocalledbiomimetics,3isattracting increasing attention and isone of the new frontiers in materialsresearch.Second,thestudyofbiologicalmaterials enhances the understandingoftheinteractionofsyntheticmaterialsandbiologicalstructureswiththegoalofenablingtheintroductionofnewandcomplex systems in the human body,leadingeventuallytoorgansupplemen-tation and substitution. These are the

so-calledbiomaterials. One of the defining features of therigidbiologicalsystemsthatcomprisea significant fraction of the structuralbiological materials is the existenceof two components: a mineral and anorganiccomponent.Theintercalationofthesecomponentscanoccuratthenano-,micro-, ormeso-scale andoften takesplaceatmorethanonedimensionalscale.TableIexemplifiesthisforanumberofsystems.Themineral componentpro-videsthestrengthwhereastheorganiccomponentcontributestotheductility.Thiscombinationofstrengthandductil-ityleadstohighenergyabsorptionpriorto failure. The most common mineralcomponents are calcium carbonate,calciumphosphate(hydroxyapatite),andamorphoussilica,althoughmorethan20minerals,withprincipalelementsbeingCa,Mg,Si,Fe,Mn,P,S,C,andthelightelementsHandO.Thesemineralsareembeddedinacomplexassemblageoforganicmacromolecules4thatarehier-archically organized. The best knownarekeratin,collagen,andchitin. The extent and complexity of thesubject are daunting and will requiremanyyearsofglobalresearchefforttobeelucidated.Thus,thefocushereisonfivesystemsthathaveattractedtheinterest

2006 July • JOM 37

oftheauthors.Thesilicaspiculeshavebeenstudiedandextensivelydescribedby Mayer and coworkers.5,6 The fourother systems have been investigatedby the authors: abalone,7–9 conch,9,10toucan,11,12andcrabexoskeleton.13

HIerArcHIcAl OrgAnIzAtIOn Of

Structure

Itcouldbearguedthatallmaterialsarehierarchicallystructured,sincethechangesindimensionalscalebringaboutdifferent mechanisms of deformationand damage. However, in biologicalmaterialsthishierarchicalorganizationisinherenttothedesign.Thedesignofthematerialandstructureareintimatelyconnectedinbiologicalsystems,whereasinsyntheticmaterialsthereisadisciplin-aryseparation,basedlargelyontradition,betweenmaterials(materialsengineers)andstructures(mechanicalengineers).ThisisillustratedbythreeexamplesinFigure1(bone),Figure2(abaloneshell),andFigure3(crabexoskeleton). Inbone(Figure1),thebuildingblockoftheorganiccomponentisthecollagen,whichisatriplehelixwithadiameterofapproximately1.5nm.Thesetropocol-lagenmoleculesareintercalatedwiththemineralphase(hydoxyapatite,acalciumphosphate)formingfibrilsthat,ontheirturn, curl into helicoids of alternatingdirections.Theseosteonsarethebasicbuilding blocks of bones. The weightfractiondistributionbetweentheorganicand mineral phase is approximately60/40, making bone unquestionably acomplexhierarchicallystructuredbio-logicalcomposite. Similarly, the abalone shell (Figure2) owes its extraordinary mechanicalproperties(muchsuperiortomonolithicCaCO

3) to a hierarchically organized

structure,startingatthenano-level,withanorganiclayerhavingathicknessof20–30nm,proceedingwithsinglecrystalsofthearagonitepolymorphofCaCO

3,

consistingof“bricks”withdimensionsof0.5µmvs.10µm(microstructure),andfinishingwithlayersapproximately0.3mm(mesostructure). Crabsarearthropodswhosecarapacecomprises a mineralized hard compo-nent,whichexhibitsbrittlefracture,anda softer, organic component, which isprimarilychitin.Thesetwocomponentsare shown in the scanning-electron

Figure 1. The hierarchical organization of bone.

Figure 2. The hierarchy of abalone structure. Clockwise from top left: entire shell; mesostructure with mesolayers; microstructure with aragonite tiles; nanostructure showing organic interlayer comprising 5 wt.% of overall shell.

Figure 3. The hierarchy of spider crab structure.

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havingadiametersimilartoapencil,intoafullcircle.Thisdeformationwasfullyreversible.Additionally,theserodsaremultifunctionalandcarrylight.Theopti-calpropertieswerestudiedbyAizenbergetal.15Figure4showsafracturedhexac-tinellidspicule(muchsmallerthantheonestudiedbyLevietal.14)thatrevealsits structure. This spicule, which hasbeenstudiedbyMayerandSarikaya,16isacylindricalamorphoussilicarodandhasanonion-skintypestructurewhicheffectivelyarrestscracksandprovidesanincreasedflexuralstrength.Figure4bshowstheflexuralstressasafunctionofstrain.Thespiculeresponseiscomparedwiththatofasyntheticmonolithicsilicarod.Thebreakingstressofthespiculeisfourtimeshigherthanthemonolithicsilica.Additionally,animportantdiffer-ence exists between the two: whereasthemonolithicsilicabreaksinasinglecatastrophic event, the spicule breaksgracefullywithprogressiveloaddrops.Thisisthedirectresultofthearrestofthefractureat theonionlayers.Theseintersilica layers contain an organiccomponentwhichhasbeenidentifiedbyCha,Morse,andcoworkers17assilicatein(meaningasilica-basedprotein).

nAcreOuS SHellS

The growth and self-assembly ofaragoniticcalciumcarbonate found inmany shells is a fascinating and stillnotcompletelyunderstoodprocess.Thedepositionofaproteinlayerofapproxi-mately 20–30 nm is intercalated witharagoniteplatelets,whichareremarkablyconstantindimensionforeachanimal.Inthecaseoftheabaloneshell,themineralphasecorrespondstoapproximately95%of the total volume. This platelet sizewas found to be constant for abaloneshells with varying diameters of 10mm,50mm,and200mm.8However,therearedifferencesbetween species:thethicknessofthetilesintheabaloneshellsisapproximately0.5µm,asseeninFigure5a,whileitisaround1.5µmforabivalveshellfoundintheAraguaiaRiver(Brazil),thousandsofmilesfromtheocean(Figure5b).Periodicgrowtharrests create mesolayers that play acritical role in themechanicalproper-tiesandarepowerfulcrackdeflectors.These mesolayers are separated by athicker viscoelastic organic layer thatisinterspersedwiththemineralphase.

Figure 6. The growth of nacreous tiles by terraced cone mechanism. (a) A schematic of growth mecha-nism showing intercalation of mineral and organic layers; (b) SEM of arrested growth showing partially grown tiles (arrow A) and organic layer (arrow B).

b

a

Figure 5. Nacreous tile structures; (a) abalone (Haliotis rufescens) from Southern California; (b) bivalve shell from Araguaia River, Brazil.

a b

Figure 4. (a) A fractured spicule on sea sponge; (b) flexural stress vs. strain for monolithic (synthetic) and for sea spicule (Courtesy of G. Mayer, University of Washington).

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micrograph (SEM) of Figure 3. Thebrittlecomponentisarrangedinaheli-calpatterncalledaBouligandstructure.Therearecanalslinkingtheinsidetotheoutsideoftheshell;theyareboundbytubulesshowninthemicrographandinaschematicfashion.Thehardmineral-izedcomponenthasdarkerspotsseenin

theSEM.Athighermagnification,thisconsistsofachitin-proteinmixture.

SpOnge SpIculeS

Seaspongeshaveoftenlongrodsthatprotrudeout.TheiroutstandingflexuraltoughnesswasfirstdiscoveredbyLevietal.,14whowereabletobenda1mrod,

2006 July • JOM 39

The growth of the aragonite com-ponentofthecompositeoccursbythesuccessivearrestofgrowthbymeansofaprotein-mediatedmechanism; this isfollowedbythereinitiationofgrowth.This takesplace in theChristmas-treepattern and is represented in Figure6a. The calcium and carbonate ionscanpenetratethroughtheorganiclayerdepositedbytheepithelium.Thegrowthofthenacreouslayers(aragonite)wasobservedbyLinandMeyers8insertingglassplatesintheextrapalliallayerfordifferenttimeperiods,removingthem,andobservingthembySEM.Detailsofthegrowthsequencewererevealed. Quasi-static and dynamic compres-sion and three-point bending testswerecarriedoutbyMenigetal.7ThemechanicalresponsewasfoundtovarysignificantlyfromspecimentospecimenandrequiredtheapplicationofWeibullstatistics in order to be quantitativelyevaluated. The abalone exhibited ori-entationdependenceofstrengthaswellassignificantstrain-ratesensitivity;thefailurestrengthat loadingratesof104

GPa/s was approximately 50% higherthanthequasi-staticstrength.Theaba-lonecompressivestrengthwhenloadedperpendicular to theshell surfacewasapproximately50%higherthanparallelto theshellsurface.Quasi-staticcom-pressivefailureinbothshellsoccurredgradually,ingracefulfailure.Theshearstrengthoftheorganic/ceramicinterfacesofHaliotisrufescenswasdeterminedbymeansofasheartestandwasfoundtobeapproximately30MPa.Considerableinelastic deformation of these layers(up to a shear strain of 0.4) precededfailure.Crackdeflection,delocalizationofdamage,plasticmicrobuckling(kink-ing),andviscoplasticdeformationoftheorganic layers are the most importantmechanismscontributingtotheuniquemechanical properties of these shells.Figure7ashowsthetensilefailurealongthe direction of the tiles. The tensilestrengthofthetilesissuchthattheydonotingeneralbreak,butslide.Thetilesliding represented in Figure 7b. Thisis accomplished by the viscoplasticdeformationoftheorganiclayerand/orbytheshearingofthemineralligamentstraversing the organic phase. Uponcompressionperpendiculartotheplaneofthetiles,aninterestingphenomenonobservedpreviouslyincompositeswas

Figure 9. The tesselated bricks on Brunelleschi’s Duomo (Florence, Italy) and equivalent structure of conch shell.

a bFigure 8. A conch shell: (a) overall view and (b) structure.

a

b

c

Figure 7. The mechanisms of damage accumulation in nacreous region of abalone. (a, b) Pullout of tiles; (c) plastic microbuckling.

JOM • July 200640

seen:plasticmicrobuckling.Thismodeofdamageinvolvestheformationofaregionofslidingandofaknee.Figure7cshowsaplasticmicrobucklingevent.The5wt.%oforganicphase,thetensilesignificantly increased the strength,providingtoughnesstotheshell. Thecompressivestrengthofabaloneis 1.5–3 times the tensile strength (asdetermined from flexural tests), incontrastwithmonolithicceramics,forwhichthecompressivestrengthistypi-callyanorderofmagnitudegreaterthanthe tensile strength. The compressivestrength,however,isnotgreatlyaltered

a

b

Figure 10. Fracture patterns in a conch shell; (a) crack delocalizaiton shown in polished section and (b) scanning-electron micrograph of fracture surface showing cross lamellar structure.

Figure 11. A schematic of the (a) toucan and (b) hornbill beaks.

a bFigure 12. A scanning-electron micrograph of exterior structure the beak keratin: (a) fracture region and (b) external surface.

bytheintroduction

StrOMBuS SHell

The Strombus shells, which have aspiralconfiguration,haveastructurethatisquitedifferentfromtheabalonenacre.Figure8ashowstheoverallpictureofthe well known Strombus gigas (pinkconch)shell.Incontrastwiththeabaloneshell,whichischaracterizedbyparallellayersoftiles,thestructureoftheconchconsistsofthreemacrolayerswhicharethemselves organized into first-orderlamellae,whichareintheirturn,com-prisedofsecond-orderlamellae.These

aremadeupoftilesinsuchamannerthatsuccessivelayersarearrangedinates-sellated(tweed)pattern.Thethree-tieredstructureisshowninFigure8b.Thispat-tern,calledcross-lamellar,isreminiscentofplywoodorcrossed-plycompositesand has been studied extensively byHeuerandcoworkers.18–20AninterestinganalogywithalargedomestructureisshowninFigure9.TheFlorencedome,builtbythearchitectBruneleschi,usesatessellatedarrayoflongbrickswithadimensional proportion similar to thetilesinconch.Thisarrangementprovidesthe dome with structural integrity notpossiblebeforethattime. Inconch,thefractionoforganicmate-rialislowerthaninabalone:~1wt.%vs.5wt.%.Thestrategyoftougheningthatisusedintheconchshellistodelocalizecracking by distributing damage. AnexampleofhowacrackisdeflectedbythealternativelayersisshowninFigure10a. The fracture surface viewed bySEMshowsthecross-lamellarstructure(Figure10b)inaclearfashion.Thelinesseen in thedamagedsurfaceofconchshowninFigure9indicateslidingoftheindividual,tiles.Theabsenceofaclearcrackleadstoanincreaseinthefractureenergyof10,0000incomparisonwithmonolithiccalciumcarbonate.Theworkoffractureisashighas13kJm.18

Asinabalone,theratioofthetensilestrengthtocompressivestrengthislargein comparison to ceramics, providingincreasedtoughness.

tOucAn And HOrnBIll BeAkS

Beaksarefascinatingstructuresthathavereceivedonlyscantattentionfrommaterials scientists. An exception isthe study of the European starling byBonser.21,22Theuniquenessofthetoucanbeakledtoarecentstudy(Sekietal.11),theresultsofwhicharesummarizedasfollows. Beaks are usually short andthickorlongandthin.Thetoucanbeakisanexception;itisbothlongandthick.Itcomprisesonethirdofthelengthofthetoucanandyetonlyabout1/20thofitsmass,whilemaintainingoutstandingstiffness.ThestructureofaTocotoucanandhornbillbeak,shownschematicallyinFigure11,wasfoundtobeasandwichcomposite with an exterior of keratinand a fibrous network of closed cellsmade of calcium-rich proteins. The

a b

2006 July • JOM 41

keratinlayeriscomprisedofsuperposedhexagonalscales(50µmdiameterand1µmthickness)gluedtogether.ThisisshowninFigure12.Theinteriorofthebeakiscomprisedofacellularstructure.Itsdensityisontheorderof0.04forthetoucanand0.14forthehornbill.Figure13showsthisfoamattwomagnifications.Itisclearthatitiscomprisedofwebsand membranes and can therefore beconsideredaclosed-cellfoamasdefinedbyGibsonandAshby.23Thus,theoveralldensityofthebeakisapproximately0.1forthetoucanand0.3forthehornbill. Thetensilestrengthofthekeratinisabout50MPaandYoung’smodulusis1.4GPa(Figure14a).Thekeratinshellexhibitsastrain-ratesensitivitywithatransition from slippage of the scales(duetoreleaseoftheorganicglue)atalowstrainrate(5×10–5s–1)tofractureofthescalesatahigherstrainrate(1.5×10–3

s–1).Theclosed-cellfoamiscomprisedoffibershavingaYoung’smodulustwicethat of the keratin shells due to theirhighercalciumcontent.Thecompressiveresponseofthefoam,whichisshowninFigure14b,wassuccessfullymodeledbytheGibson-Ashbyconstitutiveequationforclosed-cellfoam.Thehornbillfoam,whichhasadensitythreetimeshigherthanthetoucanbeak,hasastrengththatis correspondingly higher. There is asynergisticeffectbetweenfoamandshellevidencedbyexperimentsandanalysisestablishing the separate responses ofshell,foam,andfoam+shell.Thestabil-ity analysis developed by Karam andGibson,24assuminganidealizedcircularcrosssection,wasappliedtothebeak.It shows that the foam stabilizes thedeformation of the beak by providinganelasticfoundationwhichincreasesitsBrazierandbucklingloadunderflexureloading.

crAB exOSkeletOn

Theexoskeletonofarthropodscon-sistsmainlyofchitin.Inthecaseofthelobsterandcrab,thereisahighdegreeofmineralization.Thestructureofthesheepcrab(Loxorhynchusgrandis)clawisbeingstudiedintheauthors’laborato-ries.ItissimilartothestructureofthelobsterclawthatwasstudiedbyRaabeetal.25,26andconsistsofacomplexnet-workofhighlymineralizedchitinrodsinaBouligand27patterninterwovenwithflexible fibers that stitch the structure

a

b

Figure 13. Scanning-electron micrographs of cellular interior structure of (a) toucan beak and (b) hornbill beak.

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a bFigure 14. The mechanical properties of (a) keratin shell (tension) and (b) cellular bone interior (compression).

Exocuticle

Endocuticle

xy

z10~15 µm

3~5 µm

Figure 15. The paral-lel lines on fracture surface of crab exo-skeleton evidencing periodic 180 degree rotations in Bouligand pattern.

together.ThehierarchyshowninFigure3isdesignedsuchthatthestructurehasexcellentmechanicalproperties.Figure15showsthelamellarstructureinwhicheachunitcorrespondstoa180degreerotationofthehelix.Acoordinatesystem

isshownontheside.Thespacingintheexternallayerofexoskeleton(exocuticle)isapproximately3–5µm,increasingto10–15µmintheinsidelayers(endocu-ticle).TheBouligand(helicalstacking)arrangementprovidesstructuralstrength

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thatisin-planeisotropic(planeXY)inspite of the anisotropic nature of theindividualbundles The fracture is brittle as is evidentfromtheflatsurfacesinFigure16.Thereisaregularspacingofdarkspotswithdiametersofapproximately50nm.TheyareseenathighermagnificationinFigure17.Thesecorrespondtoorganicfibers,from which the mineral componentgrows. The spacing of these organicfibersisapproximately100nm. Canals enveloped in tubules areformed along the Z direction. Thesetubulesarehollowandhaveaflattenedconfiguration that twists in a helicalfashion. A region where separationwas introduced by tensile tractions isshowninFigure18(a).Thehighdensityof these tubules (also schematicallyshown inFigure3) is clearly evident.Thesetubulesfailinaductilemodeasshown in Figure 18b. The neck crosssectionisreducedtoasmallfractionofthe original thickness (approximately0.5–1µm).ItisthoughtthatthisductilecomponenthelpstostitchtogetherthebrittlebundlesarrangedintheBouligand

pattern and provides the toughness tothestructure.Italsoundoubtedlyplaysaroleinkeepingtheexoskeletoninplaceevenwhenitisfractured,allowingforselfhealing.Theseaspectsarecurrentlyunderinvestigation.

cOncluSIOnS

Structural biological materials arecomplexcompositesthathavestructuresthatarebeingextensivelyinvestigatedbymaterialsscientistsandengineerswiththeultimategoalofmimickingtheminsyntheticsystems.Thisisindeedanewfrontierinmaterialsscienceandisafer-tilegroundforinnovativeandfar-reach-ing work. Although these compositeshavestructuresandconstituentmaterialsthatvarywidely,thereisacommonalityofarchitectureandproperties: • Synergismbetweenbrittleandduc-

tilecomponentsinthestructure • Hierarchicalorganization • Multifunctionality • Ambient temperature processing;

selfassemblyisoneoftheprincipalaspectsofthisprocess.28

• Poorhigh-temperatureperformance

• Inherently weak (in comparisonwith synthetic materials) constit-uents.Thiscanbeclearly seen ifone analyzes themechanical per-formancemapsdevelopedbyAsh-byandWegst29forbiologicalma-terials.

AcknOwledgeMentS

ThisresearchisfundedbytheNationalScienceFoundationDivisionofMate-rials Research, Ceramics Program(Grant DMR 0510138). We gratefullyacknowledgesupportfromDr.LynnetteD.Madsen,programdirector.ThehelpprovidedbyDr.ChrisOrme,LawrenceLivermore National Laboratory, isgreatlyappreciated.Theinspirationpro-videdbyDr.GeorgeMayer,Universityof Washington, is deeply appreciated,aswellastheuseofthenanoindenta-tion facilitybyProfessorFrankTalke,UniversityofCaliforniaatSanDiego.Dr.M.Mace,CuratorofBirdsattheSanDiegoZoo’sWildAnimalPark,kindlyprovided us with hornbill beaks. Mr.JerryJenkins,ownerofEmeraldForestBirdGardens,hashelpedusimmenselywiththetoucanbeaks.

references 1. J.F.V. Vincent, Structural Biomaterials (Princeton, NJ: Princeton University Press, 1991).2. A.V. Srinivasan et al., Appl. Mech. Rev., 44 (1991), p. 463.3. M. Sarikaya, Microscopy Research and Technique, 27 (1994), p. 360. 4. S. Mann, Biomineralization (Oxford, U.K.: Oxford University Press, 2001). 5. G. Mayer, Science, 310 (2005), p. 1144. 6. G. Mayer et al., MRS Symposium Proceedings, v. 844: Mechanical Properties of Bioinspired and Biological Materials, ed. C. Viney et al. (Warrendale, PA: Materials Research Society, 2005), p. 79. 7. R. Menig et al., Acta Mater., 48 (2000), p. 2383. 8. A. Lin and M.A. Meyers, Mater. Sci. and Eng. A, 390 (2005), p. 27. 9. A. Lin et al., Mater. Sci. and Eng. �Sci. and Eng. � (in press). 10. R. Menig et al., Mater. Sci. and Eng. A,Sci. and Eng. A, 297 (2001), p. 203. 11. Y. Seki et al., Acta Mater., 53 (2005), p. 5281. 12. Y. Seki et al., Mater. Sci. and Eng. �Sci. and Eng. � (in press). 13. P.-Y. Chen, A. Lin, and M.A. Meyers, unpublished results (2006). 14. C. Levi et al., J. Mater. Sci. �ett.,Sci. �ett., 8 (1989), p. 337. 15. J. Aizenberg et al., Science, 309 (2005), p. 275. 16. G. Mayer and M. Sarikaya, Exper. Mech.,Mech., 42 (2002), p. 395. 17. J.N. Cha et al., Proc. �atl. Acad. Sci. �SA,�atl. Acad. Sci. �SA, 96 (1999), p. 361. 18. L.F. Kuhn-Spearing et al., J. Mater. Sci.,Sci., 31 (1996), p. 6583. 19. J.V. Laraia and A.H. Heuer, J. Am. �eram. Soc., 72 (1989), p. 2177. 20. A.H. Heuer et al., Science, 255 (1992), p. 1098. 21. R.H.C. Bonser, J. Mater. Sci. �ett., 19 (2000), pp. 1039–1040.22. J. Mater. Sci. �ett., 21 (2002), p. 1563.

Fig 16. An SEM micrograph of fracture surface showing the twisted plywood (Bou-ligand) structure of crab exoskeleton.

Figure 17. A detailed view of fracture section of brittle Bouligand component showing organic fibrils.

a bFigure 18. An SEM micrograph of fracture surface showing the tubules in the Z-direction in crab exoskeleton: (a) extended configuration and (b) necked configuration in tensile extension.

2006 July • JOM 43

23. L. Gibson and M.F. Ashby, �ellular Solids: Structure and Properties, 2nd ed. (New York: Cambridge University Press, 1997). 24. G.N. Karam and L.J. Gibson, Int. J. Solids Structures, 32 (1995), pp. 1259, 1285. 25. D. Raabe et al., Acta Mater., 53 (2005), p. 4281. 26. D. Raabe et al., Mater. Sci. and Eng. ASci. and Eng. A (in press).27. Y.J. Bouligand, Tissue and �ell, 4 (1972), p. 189. 28. G. Whitesides, Mater. Res. Bulletin (January 2002), p. 56. [couldn’t find this listed in Jan. 2002 online to get volume or issue number.]29. M.F. Ashby and U.G.K. Wegst, Phil. Mag., 84 (2004), p. 2167.

Marc A. Meyers, Albert Y.M. Lin, YasuakiSeki, Po-Yu Chen, Bimal K. Kad, andSaraBoddearewiththe MaterialsScienceandEngineering Program in the Department ofMechanical and Aerospace Engineering at theUniversityofCalifornia,SanDiego.

For more information, contact Marc A. Meyers, University of California, San Diego, Materials Science and Engineering Program, Department of Mechanical and Aerospace Engineering, La Jolla, CA 92093; (858) 534-4719; fax (858) 534-5698; e-mail mameyers@ucsd.edu.