EERHARTICLE RESEARCH DOI: 10.1002/adem.201180057

Structure and Mechanical Performance of a ‘‘Modern’’ **

By Deju Zhu, Cesar Fuentes Ortega, Ramak Motamedi, Lawrence Szewciw, Franck Vernerey and Francois Barthelat*

Protective materials and structures found in natural organisms may inspire new armors with improved resistance to penetration, flexibility, light weight, and other interesting properties such as transparency and breathability. All these attributes can be found in fish scales, which are the most common types of scales in modern fish species. In this work, we have studied the structure and mechanics of fish scales from striped bass (Morone saxatilis). This scale is about 200–300 mm thick and consists of a hard outer bony layer supported by a softer cross-ply of fibrils. Perforation tests with a sharp needle indicated that a single fish scale provides a high resistance to penetration which is superior to polystyrene and polycarbonate, two engineering polymers that are typically used for light transparent packaging or protective equipment. Under puncture, the scale undergoes a sequence of two distinct failure events: First, the outer bony layer cracks following a well defined cross-like pattern which generates four ‘‘flaps’’ of bony material. The deflection of the flaps by the needle is resisted by the collagen layer, which in biaxial tension acts as a retaining membrane. Remarkably this second stage of the penetration process is highly stable, so that an additional 50% penetration force is required to eventually puncture the collagen layer. The combination of a hard layer that can fail in a controlled fashion with a soft and extensible backing layer is the key to the resistance to penetration of individual scales.

Nature increasingly serves as a model and inspiration to past.[1–5] This type of scale displays interesting combinations scientists and engineers, and has the potential to of flexibility, strength, resistance to penetration, light weight, lead to novel engineering materials and systems with new and transparency. Fish scales exhibit large variations in shape, combinations of properties, multi-functionalities, adaptabil- size, and arrangement. The general classification includes ity, and environmental sustainability. In this work, we have cosmoid, ganoid, placoid, and elasmoid (cycloid and ctenoid) studied the structure and mechanics of modern teleost fish found in the modern teleost class of fishes.[6] The ‘‘primitive’’ scales, which have received relatively little attention in the cosmoid and ganoid scales are bulky, bony scales which offer very effective protective properties, through a multilayered [3] [*] Dr. D. Zhu, C. F. Ortega, R. Motamedi, L. Szewciw, structure capable of a variety of dissipative mechanisms. Dr. F. Barthelat However, over the course of the reduction of the Department of Mechanical Engineering, integumental skeleton has improved swimming perfor- [3,7] McGill University, Montreal, QC, (Canada) mance, and the ‘‘ancient’’ cosmoid and ganoid scales have [8] E-mail: [email protected] been replaced by the thinner, more flexible teleost scales. [9,10] Dr. F. Vernerey Teleost scales have excellent hydrodynamic properties [3,7,8] Department of Civil Engineering, and provide a protective layer resisting penetration. University of Colorado, Boulder, CO, (USA) Currey, in a review article on , noted that [**] The authors wish to acknowledge the support of the National some fish scales are so tough that they cannot be easily [11] Science Foundation under award CMMI 0927585 and of fractured even after immersion in liquid nitrogen. At larger Faculty of Engineering at McGill University. Atomic emission lengths, the arrangement of the scales provides a flexible spectroscopy tests were performed by Monique Riendeau, Dept. that allows for changes in shape. In fact, the scaled skin has of Mining & Materials Engineering, and Ranjan Roy and been shown to play a critical structural role in fish locomotion Andrew Golsztajn, Dept. of Chemical Engineering, McGill by regulating wave propagation[12–14] and by storing mechan- University. ical energy in order to make swimming more efficient.[15]

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(Figure mm 10 diameter about shape, in pentagonal irregular an with bass plate thin striped a adult is an from scale individual an level, mesoscale u ihmnrlzto okt rceigwl nothe into well proceeding layer. pockets collagen mineralization with layer, bony the but (‘‘basal’’ near layer mostly mineralized inner is the layer) ‘‘collagen’’ often whereas or and layer,’’ ‘‘bony mineralized as more to significantly referred is scale the of layer hc tfestesi nflexion. strongly, in more skin interact the scales stiffens the which stroke), swimming a the (at of curved highly end is fish the When compliance. flexural and penetration 1a,b). to (Figure barrier fish continuous the a provides of arrangement body This the of most are cover scales and the staggered level, macroscopic the At 1). (Figure scales distinct length several over built structure, hierarchical characteristic materials, B2 radial the ‘‘focus.’’ (circuli) the in rings called circular area grooves central form a of that around ridges consists and area (radii) direction anterior the while striped from scale fish (ctenoid) bass teleost single a of mechanics Skin Fish of Structure individ Hierarchical an (c) The scales, 1. multiple staggered (b) fish, Whole (a) saxatilis. fibrils. M. bass, collagen striped (f) from scale structure, fish collagen teleost a cross-ply of (e) structure hierarchical The 1. Fig. nti td ehv netgtdtesrcueand structure the investigated have we study this In h otro rao h cl ipasruhpatterns rough displays scale the of area posterior The ooesaxatilis Morone http://www.aem-journal.com [16–18] [7,23] h tutr ftlotfihsae ipasa displays scales fish teleost of structure the [10] nsrpdbs,bn n olgnlayers collagen and bony bass, striped In iemn te tutrlbiological structural other many Like . ees clsaecmoe fcollagen of composed are scales Teleost [19] ß h knte csa an as acts then skin The 01WLYVHVra mH&C.Ka,Wihi DACDEGNEIGMATERIALS ENGINEERING ADVANCED Weinheim KGaA, Co. & GmbH Verlag WILEY-VCH 2011 [21] [2,5,22–24] ai n circuli and Radii m ) sn AES Using m). .Teouter The ). [15,20] tthe At [9,10] ise htudromlixa tess(hl fsoft-shelled of (shell 1e). natural stresses turtles, (Figure in multiaxial next undergo found the that typically to tissues are ply structures one collagen from Cross-ply degrees 90 by rotated aie(3.17 patite olgnlyrt hl s cl ehnclproper- mechanical scale the fish of nature whole plywood to ties, the layer of collagen importance the discussed hsarneeti ossetwt h rwho individual of growth the with consistent 2). is (Figure arrangement scale the This of both focus layers), the around (‘‘C’’ organized layers) fibrils being layers (‘‘R’’ circumferential of fibrils made radial layers of achieved with is composed we cross-ply layers Interestingly, degree alternating 90 1f). the by (Figure bass striped scale in the that found of cross-section observed be a can on diameter, in nm 50–200 about individual fibrils, scales, collagen length smaller At directions. multiple along a ayfo pce ospecies. to species that from angles by vary layers across can rotated made fibrils being collagen ply parallel each of composites, layered cross-ply are layers on httebsllyri omdo 02 le about plies 20–25 of formed is layer basal 4–5 the that found ewe h oyadclae layers. collagen a and bony of the reports between mineralization with in difference consistent points percentage are 20–35% the general results than mineralized These more region. significantly gave lower upper is the scale that samples the confirming of fractions), lower region respectively volume 14%, in and 6% and and 50% upper (30% of contents The mass layer. off plies collagen few a dissecting the by samples we two into experiment, scale another a In separated 26%. as hydroxyapatite of fraction yrxaaiems rcino 6 o h hl scale. whole the (1.33 collagen for of 46% average density of an The fraction measured mass we hydroxyapatite spectroscopy), emission (atomic m [2,5,8,32–34] hc ah(iue1) hr h olgnfirl are fibrils collagen the where 1d), (Figure each thick m [30] ua nuu fibrosus annulus human 10 ngnrlb rvdn h cl ihstrength with scale the providing by general in 3 kg m .Zue l/ ‘oen’Fs Scale Fish ‘‘Modern’’ al./A et Zhu D. 3 ) [2] eeue oetmt h volume the estimate to used were 10 [25–29] 3 [31] a cl,()cosscino scale, a of cross-section (d) scale, ual kg .Svrlatoshave authors Several ). [25] m nsrpdbs,we bass, striped In oyadcollagen and Bony 3 n hydroxya- and ) 2011 , 13 o XX No. , ... RESEARCH ARTICLE 1 B3 s the [38] )upto 1 Assuming s 3 [38] 10 directions. 8 and to monitor failure [37] http://www.aem-journal.com ply laminate can be estimated at 500 MPa, 8 from the longitudinal direction (anteroposterior axis) of The samples were then mounted on a miniature loading The resulting stress–strain curves (Figure 3a) display an In order to assess the mechanical response of the collagen The stress–strain response (Figure 3a) displayed a linear 8 0.20 mm. Using this technique, samples90 were cut at 0, 45,the and fish. stage (Ernest F. Fullam Inc.,under Latham, NY), an which wasOlympus, placed upright, Markham, Canada) equipped reflected with(RETIGA a light CCD 2000R, camera Qimaging, microscopemonitor deformations and Surrey, failure (BX-51M, modes of Canada) thespecimens specimens. All were in loaded in order tension to at a rate of 0.005 mm (corresponding to a strain rate of 1.25 that the fibers do not carry anyto stress if the they are loading perpendicular carries direction, stress only in the halffibrils collagen of layer. have the Since individual a materialstrength collagen actually Young’s of modulus 200 MPa of and about a 1 GPa, strain at a failure tensile of 30%, complete failure. Images were taken throughout theevery entire test 10 s using themeasure CCD the camera. deformation Theusing and images were strain digital used values to image of correlation the samples modes such as debonding of thecollagen bony fibrils. layer All and pullout samples of were the keptduring in preparation hydrated conditions and testing. initial quasi-linear region,600–850 MPa with an range.reaching initial The a modulus material maximum inscale softens stress the orientation), after of slightly whichUsing 30–50 the MPa before optical stress (depending observation, dropsdecrease significantly. on we in could stress associate toSubsequently, the this the sudden collagen sudden layer cracking progressively ofthe detaches the from stiff bony bony layer. layer,other, yielding while step-like patterns collagen on the pliesto stress–strain curve total tear up failure one at after about 40% the strain. layer alone, we performedwith the additional bony layer tensile removed. The tests collagenpeeled on layer out was of scales carefully the scale which restedThe on a layered flat and hard structure surface. ‘‘delaminate’’ with of a the minimummaterial at of fish the force. separation site scale While might bepeeling the makes partially force damaged, collagen the was it deemed easythe insufficient collagen to to layer damage and the toties. rest alter The of its remaining overall 0.05 mechanical mmtested proper- thick in tension collagenous along material the was 0, 45, andregime 90 with aprogressive modulus failure after a of peak stress aboutstrain of 65 450 MPa. was MPa, The ultimate followed thebehavior by same of a withthe the and behavior of without collagen single bony collagen cross-ply layer. type I The is fibrils. consistent with modulus of the 90 its strength at 100 MPacompares well and with our its experimental results, strain showing thattensile at the behavior failure of at the 30%. collagenthe layer This stretching is of largely straight, controlled individual by collagen fibrils. 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ß ... , No. XX ) were acquired from a fish 13 , 2011 Morone saxatilis C until tested. Before the test, the scales were 8 [35,36] 20 In order to assess the mechanical response of individual ADVANCED ENGINEERING MATERIALS removed from the freezer5 and min put for in thawing, a andspecimens water then using bath cut a for into multi-tube about small rotarying dog-bone-shaped hole-punch scissors. The and resulting dissect- samples hada a gage gage length of width 4 mm, of 1.5 mm and an average thickness of about scales, we performed tensilesmall tests tensile in samples prepared hydrated from individual conditions scales.fresh on Whole, striped bass ( supplier (Nature’s Catch, Inc., Clarksdale, MS,on USA) and ice. kept Scales werefreezer plucked at using tweezers and stored in a scales, which occurs by deposition of collagenof at the the periphery scale. 2. Tensile Testing on Individual Scales Fig. 2. Arrangement ofwhole the scale collagen showing fibrils surface incollagen a features fibers striped in (optical bass the micrograph);circumferential scale. collagen (R–C) (b) (a) pattern layer; of Top bottom the (c) view collagen viewfrom removal fibrils; of showing (d) one of the locally, layer the the fibers to bony are the orthogonal layer next; reveals (e) the schematics radial– of the R–C pattern. D. Zhu et al./A ‘‘Modern’’ Fish Scale RESEARCH ARTICLE B4 90 and 45, 0, along scales deviations. fish standard for indicate curves bars stress–strain error Tensile (a) 3. Fig. opst.Snetetikeso h oyand is bony scale the the of modulus of strain the constant thickness similar, two-layer, is the layers a collagen Since like behaves scale composite. the whole regime, scale elastic the the In whole from results. test inferred tensile only were collagen and properties its testing, hl twsntpsil oioaetebn ae for layer bony the isolate to possible not was it While http://www.aem-journal.com ß 01WLYVHVra mH&C.Ka,Wihi DACDEGNEIGMATERIALS ENGINEERING ADVANCED Weinheim KGaA, Co. & GmbH Verlag WILEY-VCH 2011 8 rmtelniuia xso h s.Smayo eut o b on’ ouu;()srnt.The strength. (c) modulus; Young’s (b) for results of Summary fish. the of axis longitudinal the from aes epciey h ouu fbn ae a hnbe then can layer bony of modulus The respectively. layers, where E by: given S ¼ 2 1 E ðÞ E C C and þ E E B B r h on’ ouio olgnadbony and collagen of moduli Young’s the are .Zue l/ ‘oen’Fs Scale Fish ‘‘Modern’’ al./A et Zhu D. 2011 , 13 o XX No. , (1) ... RESEARCH ARTICLE B5 [3,7,8] The main function and polycarbonate are also [39] m). The needle was driven m http://www.aem-journal.com from completely penetrating the Juveniles striped bass are known while the force was recorded [40] [39] 1 s ) and cannibalism. m) was used to simulate a predator’s m 25 ¼ 1.8 MPa measured by spherical indentation) used to Pomatomus saltatrix E and, in particular, thesharp objects scale such as must teeth be capable of preventing to have( several sources of predation including bluefish pelagic fishes and . (Figure 4a). The load-deflectiontests curves were resulting highly from repeatablewith these throughout a all tested slightpenetration samples, force force of 3–3.5 drop Nalso (Figure performed at 4b). puncture For about tests comparison,polycarbonate we on (PC), 2 N which thin are polystyrene modern and engineeringtypically (PS) polymers used and a when maximum lighttranslucence, weight, stiffness, and strength, optical applications impact include CD resistanceas cases, petri are biomedical dishes, equipment and requiredsquash protective such goggles). gear For (their such proper as comparisondiameter safety we glasses prepared disks or 10 mm ofthickness so these the polymers,protective areal material) and of density the protective we (thefish layer scale, was adjusted mass then PC same and per the for significantly PS. unit higher Remarkably, resistance the area to fish puncture of high scale compared performance to provided these engineering a polymers (Figure 4b). of the scales is mechanical protection against predators skin and reachingtissues. A the sharp tooth softer concentrates the and bitingsmall force area over more on a the very fragile scale, whichWe underlying leads to have severe contact assessed stresses. striped bass the scales using an resistance experimentala setup to that simulates predator’s penetration bitedescribed of using above single in the the tensileradius same tests. A miniature sharp loading steel(bluefish, needle for stage example, (tip have teeth of aand shape similar to a a needle radius smallerthrough than a 250 ( scale restingsimulate the on soft and a tissuesspeed underlying silicone the scale, of at rubber a 0.005 mm substrate (2) (3) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ß ... , No. XX 13 , 2011 C E S at which the bony layer fails is known. Just prior to s S S S B E s 2 E E ¼ ¼ The strength of bony layer can be evaluated with a similar This model assumes that both materials are in the linear Adult striped bass have a few natural predators, including B B ADVANCED ENGINEERING MATERIALS Fig. 4. (a) Experimental setup for the puncture test; (b) typical results for striped bass scales with and without bony layer. Results for polystyrene shown for comparison. E D. Zhu et al./A ‘‘Modern’’ Fish Scale estimated using: s failure the stress in the bony layer is then given by: various aquatic birds, marine , and potentially large 3. Resistance to SharpScales Penetration: Puncture of Individual approach. In theassumption, the linear stresses in regime,proportional the to bony their with stiffnesses. and From collagen the thestress whole layers scale uniform are test, the strain elastic range up toFigure 3a the shows failure that thetension, of probably scale due the to softens damage slightly accumulation bony in when the(collagen layer. behaves bony loaded linearly layer over In in this range reality of strain).therefore Equation 3 slightly overestimates the actuallayer. strength We of the used bony Equationsand (2) strength of and the (3) bony to layer.layer The estimate is results show about the that twice modulus the as bony stiffsame as tensile the strength collagen (Figure layer, 3b,c). withmore The about brittle, bony the failing layer at is, about however, 10%fails strain at while strains the in excess collagen of layer the 40%. Interestingly, we whole also found scale that only displays because in-plane of the anisotropic bony layer;planeintermsofbothmodulusandstrength.Thissetof properties, the but collagen layer is isotropicexperiments in highlights thenents: main the traits bony layer of is stiff,mineral the hard and scale’s content, brittle because compo- while ofsofter its and the high more underlying deformable, with larger collagen strains at cross-ply failure. is RESEARCH ARTICLE h atoeo h olgnsd eeotie ysann lcrnmcocp SM,wietefis oriae fteclae iewr ae ihan with taken were side collagen the of B6 images four first the while (SEM), microscopy electron imaging scanning (c) and by mechanisms; obtained associated (b) were stages; side distinct three collagen showing the curve Load–displacement of (a) one test. puncture last a the of sequence Detailed 5. Fig. ,tefredossihl,wihw soitdt the to layers associated collagen and we Bony layer. which bony is slightly, the of which drops cracking sudden force about region, of force the and a linear At damage N, layer. 2 by bony initial the and of scale surface the the entire of indentation the is of flexion I by dominated Stage 5). curve penetration the (Figure on points imaging different by at site of detail puncture in the across consist of investigated curves as we that penetration well stages The as distinct scale. three scale given to a on scale individual locations from that of repeatable mechanisms the of highly performance sequence was a with the followed scale synergy fish increase The in important scales. to an operating therefore layer system, is collagen layer the bony of The component force. resistance of puncture terms of in half was only layer providing collagen penetrated, isolated easily The removed. layer bony the with ial,w efre diinlpntr et nscales on tests puncture additional performed we Finally, http://www.aem-journal.com ß 01WLYVHVra mH&C.Ka,Wihi DACDEGNEIGMATERIALS ENGINEERING ADVANCED Weinheim KGaA, Co. & GmbH Verlag WILEY-VCH 2011 rcs tti on,teudryn olgnlyr while layer, ring-like a collagen over layer underlying bony the from the material detaches intact, point, bony remaining this of Upon At ‘‘flaps’’ circumferential directions. cracks. four generating specific downwards, layer, deflect along bony immediately the layer the of bony induces cracking therefore the layer of bony fibrils. failure collagen the underlying of local and microstructure the 5c) The (Figure of whose circuli orientation pattern, and the cross radii of followed a patterns invariably followed the always orientation Interestingly, towards cracks layer. flexural bony propagate the reach the the at rapidly stresses of initiate surface cracks these and the layer, Once bony interface layer. the collagen/bone of bony a strength As the tensile the layer. the of in bony stresses side the tensile within lower generate lies deformations scale flexural the result, the stiffer, of is layer plane bony the neutral since but thickness, same the have .Zue l/ ‘oen’Fs Scale Fish ‘‘Modern’’ al./A et Zhu D. h mgso h oysd and side bony the of images The . pia microscope. optical 2011 , 13 o XX No. , ... RESEARCH ARTICLE B7 he forces generated by the http://www.aem-journal.com 60 MPa (evaluated from our tensile test). In order to ¼ Y s The bending moment transmitted at the ligament was Figure 6a,b. Each ofand the fours flaps hinged wasinterface. assumed along to The be a rigid forceevenly straight distributed from between line the themechanical tips needle loads at resist of the the was deflection the of 4 thethe assumed flaps. flaps force by bone/collagen Only from balancing to the two needle: be i)through the the bending remaining moment ligament transmitted ofintact the collagen bony layer, layer, and which ii)for acts the the as flaps. a Interestingly, ‘‘retaininglayer in membrane’’ is this in configuration a state the ofthe collagen biaxial purpose tension and at advantage the of penetration itsevident. site, cross-ply and structure becomes evaluated by assumingwith perfect plasticity in the bony layer balance this moment,estimated the force at applied 1.2 Nwhich by is (see the actually needle Appendixfractures. below was for the This calculation force valuesince at represents details), in which reality an the the upper bonyplastic bony layer bound state probably layer cracks estimate, can beforestage be the II, full reached. there is This noflaps, prediction bending moment shows and transmitted that at that the in the bony flaps can be assumed to rotate about 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ß ... , No. XX 13 , 2011 We further investigated the mechanisms operating at stage ADVANCED ENGINEERING MATERIALS Fig. 6. (a) Top view of the idealized puncture configuration; (b) three-dimensional view of single bony flaps. The force applied by the needle (F/4) and t tension in the collagen layer are shown. (c) Effect of collagen layer thickness and (d) collagen resilience on the normalized penetration force. D. Zhu et al./A ‘‘Modern’’ Fish Scale area observable with anopaque optical microscope to (the scale, electrons,cracking while of is the transparent bonydominated by layer to further marks flexion of visible the thecracks scale, beginning opening light). as of of the the The stage four cross ‘‘flaps’’the II, collagen of layer, bony radial material propagation arefurther of bent the cross towards delamination cracks, and betweenEventually collagen the andsufficient deflection to bony and let layers. completely opening puncture the of it needlecollagen (stage the reach layer III). flaps indicates The thesharp the initial are collagen drop beginning failure in layer of of force stagerapid, the and at III, this possibly and point suggestsThroughout the because that the the the rest failurethe is of collagen needle, stage layer the III,layers is the delamination propagates scale between stretched. morecontinue is collagen extensively, to deflected grow. and and by the bony radial cracks II, since they are powerful enoughthe to scale increase by the an resistance additional of 1 Nof (representing an the additional 50% loadexamined at the failure controlled of deflectionusing the of the an bony four layer). idealized ‘‘bony In flaps’’ three-dimensional particular, geometry we shown in RESEARCH ARTICLE olgnfirl n lwo raiaini h collagen thicker the in of organization substantiates benefits plywood finding layer. and mechanical This fibrils flaps. on collagen stiff discussions form previous to material bony required of minimum collagen is a although thick beneficial, A also 6c,d). is (Figure layer bites stronger and for teeth penetration larger to resistance greater a provides scale the forces, since and desirable, scale. and the II of stage resistance penetration dominates ultimate effect the membrane controls retaining demonstrates the which that experimentally, measured we force tion L n tegh( strength and s ‘mlfig’tepoete a eni te ls of in class scale other the in of seen architecture (as and materials properties biological structure the the ‘‘amplifying’’ important of the highlights role than which weaker and polymers, softer both engineering are these that are materials of scales set fish a of to Remarkably, made applications. resistance protective typically for polymers offering used engineering modern systems, to superior protective puncture natural mance by Conclusions layer 4. collagen softer area. large the the a mitigate over to them onto and redistributing needle, transmitted the from layer of collagen tip stresses the the protect with to contact is the direct layer bony damage function harder the and the function, may of this for ideal that therefore is collagen deflection of cross-ply A penetration. layer needle excessive before even backing tissues to underlying soft too lead a may although penetration, to resistance ae ntepoete fteclae ae ( layer collagen of the force of penetration properties the a on tensile predicted based our to model according MPa Our collagen 65 of the tests). stress when a reached (at be tension to in assumed failed was II stage of end stersl fafieblneo tutr n material and an structure and layer, inner of the of the strength balance of and stiffness softness the and fine layer, hardness outer the a particular in of and properties, result the is B8 collagen and bony of function a ( thickness as layer force expression simple penetration a to the led hinge for the balance about flap moment bony the single a geometry, of idealized the on dominant the acts Based as then stress. tension layer biaxial collagen with membrane, The retaining II. observa- a stage as experimental of the end with the consistent of towards tions is surface which overlying layer, the bony from delaminated flaps. the completely for membrane the retaining with a as associated acts was which examined collagen, hinge. bony mechanism the no second though or The little transmitted that be confirming can hinges, moment circumferential the bending of show region the experiments in cracks The hinges. frictionless C ¼ niiultlotfihsae r hrfr ihperfor- high therefore are scales fish teleost Individual ¼ ntrso ein h oe htlne asare flaps longer that reveals model the design, of terms In ntemdl h olgnlyrwsasmdt have to assumed was layer collagen the model, the In 200 5Ma n pia bevto ( observation optical and MPa) 65 [8,32,33,41] m http://www.aem-journal.com ) hspeito srmral ls openetra- to close remarkably is prediction This m). s ial,asf n togmtra increases material strong and soft a Finally, C t fteclae ae.Fl eerto tthe at penetration Full layer. collagen the of ) B , t [42–44] C ,lnt fteflp ( flaps the of length ), L slre o agr‘teh’adhigher and ‘‘teeth’’ larger for larger is .Tehg efrac ftescales the of performance high The ). ß 01WLYVHVra mH&C.Ka,Wihi DACDEGNEIGMATERIALS ENGINEERING ADVANCED Weinheim KGaA, Co. & GmbH Verlag WILEY-VCH 2011 L ,adsifes( stiffness and ), t B ¼ E C t C ¼ ¼ 0 MPa, 500 100 F ¼ m 3N E m, C ) olna to collinear tani h olgni nfr n qa to: " equal and uniform is tensile collagen the the that assumption in the strain to leads which area, puncture uigsaa rdc oproject to product scalar (using nfr ntepntr ie nweg fsri nthe in from found strain ( modulus tests of the tensile using the Knowledge stress, to site. leads and layer puncture equi-biaxial collagen is the layer collagen in the in uniform strain the that such is oD,s htisdslcmn etrcnb rte,i the in written, be can vector displacement of system its section Cartesian moves that D the so point flap of D’, the centroid to of deflection the Upon D). in (point point collagen the of displacement Strain A.1. retaining layer the collagen and underlying A.1). the flaps (Figure by four provided effect the membrane of deflection progressive Model Flaps’’ ‘‘Four Analytical Appendix: a properties. yield attractive to a with macroscale with system the protective at combined hierarchical scales be the of therefore the arrangement at could clever design level biomimetic scale A individual desirable armors. personal highly for scales two the properties overlapping breathability, of and addition, reminiscent compliance In arrangement ensures glass. an bulletproof in of alternates layers design system soft multilayer and resulting or The hard 3 with scales. covered of is that body layers the counted 4 of we surface the bass, on striped point given for any number and, large a scales with covered overlapping course of of is fish the The of scale. skin the actual of capability also dissipation energy effects the viscoplastic to and contribute viscoelastic that likely viscous is consider it not on effects, does study scale first fish this of While mechanics puncture flaps. the collagen bony the the under allow stretch and to layer delaminate to enough weak interface D 4 6 6 6 6 2 C D ~ h tan nteclae eedtrie ytakn the tracking by determined were collagen the in strains The the capture to derived was model analytical simplified A ¼ 2 h olgni eahdfo h oylyri the in layer bony the from detached is collagen The n brcosn h rcswl xedb distance a by extend will cracks the crossing fiber Any neetnl,tegoer n ieaisfrtesystem the for kinematics and geometry the Interestingly, 0 2 p L ¼ p 2 1 L 2 ffiffiffi ðÞþ 2 ffiffiffi

ðÞ 1 cos sin 2 2 p cos L u p u L T 2 ffiffiffi 0 2 ffiffiffi ): u ðÞ 1 t cos sin 2 C ðÞ E u u cos xyz L t 2 ¼ C t 0 p C 1 sin t 0 MPa). 500 u .Zue l/ ‘oen’Fs Scale Fish ‘‘Modern’’ al./A et Zhu D. 2 2 ffiffiffi C Fgr A.1): (Figure sin ðÞ u 1 cos t 2 C 5 7 7 7 7 3 u sin : u 4 6 6 6 6 6 2 u 1 p 0 1 p 2 ffiffiffi 1 2 ffiffiffi 5 7 7 7 7 7 3 D ¼ D ~ L 0 4 ðÞþ nteui vector unit the on 1 cos u 2011 , 2 13 t p C o XX No. , 2 ffiffiffi (A.2) (A.1) (A.3) sin ... u RESEARCH ARTICLE B9 (A.8) (A.7) (A.9) (A.10) (A.11) and the t http://www.aem-journal.com : C 1 C A s u C L t 1 C A u 2 C L tan t B þ 2 L t tan u ffiffiffi 2 B þ L t u p ffiffiffi 2 tan ffiffiffi 2 þ p B tan p 1 s ffiffiffi 2 þ 2 0 B @ p 1 B C B t s 2 0 B @ t t 2 C  t L s M L B 2 2 C t ffiffiffi 2 ¼ Lt  ¼ p 2 8 4 F 2 Normalized by the square of the scale thickness Combining Equations (A.9) and (A.10), we get the force The force applied by the needle is balanced by this t ¼ Assuming that the entire thickness of the bony layer ffiffiffi 2 ¼ ¼ F C L p s get the force retained by the collagen layer as follows: F A.4. Force Generated by Flexural Stresses at theundergoes Hinges plasticity, thecalculated as bending follows: moment transmitted is M generated by flexural stresses at the hinges: F moment: tensile strength of collagen (A.6) (A.4) (A.5) , then we ~ F 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim is equivalent ß ~ T and 0 ~ C and O 0 ~ D O ... /4, the rigid bony flap , No. XX F 13 , 2011 1 u 3 7 7 7 7 7 7 7 7 5 ffiffiffi 2 ffiffiffi 2 u sin 0 T T B p p t cos 2 6 6 6 6 6 6 6 6 4 1 ðÞ B t ¼ u 1 axis and the loading location changes from 0 ~ T þ y u u cos ðÞ B sin t cos ðÞþ 3 7 5 ffiffiffi 2 L ffiffiffi 2 u 4 p L = p 0 0 F sin

: ffiffiffi 2 0 L ~ 2 6 4 C ¼ p 0 As the cross product of the vectors The deflection at the loading point is then the z component Similarly, point C at the upper tip of the flaps moves to C’ Under the concentrated force C ¼ ~ ¼ C ~ to half of the cross product of the vectors ADVANCED ENGINEERING MATERIALS C upon deflection, and A.2. Deflection of the Flaps Fig. A.1. Schematic diagram of the deformation and force in the four flaps model. D. Zhu et al./A ‘‘Modern’’ Fish Scale d of A.3. Force F rotates along the C to C’. Thelayers force are: vectors acting on the bony and collagen RESEARCH ARTICLE 1]M .Myr,A .M i,Y ei .Y hn .K Kad, K. B. Chen, Y. P. Seki, Y. Lin, M. Y. A. Meyers, A. M. [16] 1]M .Hbak .H Hebrank, H. J. Hebrank, R. M. [15] Westneat, W. M. F McHenry, J. M. Hale, E. M. Long, H. J. [13] Currey, D. J. [11] 1]J .Ln,T .Ko,K rig .Cmi,V Engel, V. Combie, K. Irving, K. Koob, J. T. Long, H. J. [14] Root, G. R. Adcock, B. Long, H. J. [12] 1]J .Sire, Y. J. 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