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CHAPTER 1 Compliant Structures and Materials in Animals

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CHAPTER 1 Compliant Structures and Materials in Animals CHAPTER 1 Compliant structures and materials in animals J.F.V. Vincent Centre for Biomimetic and Natural Technologies, University of Bath, UK Abstract The ability of plants and animals to run away from loads by being compliant saves much energy because the structures consume less energy in their production and require less energy for maintenance. However, as a model for engineering structures there are difficulties since compliant structures are commonly less stable, have less linear properties and are therefore more difficult to control and handle. 1 Introduction The materials from which the structures of animals are made have a gigantic range of stiffness. Ceramics (shell and bone) can be as stiff as 60 or 70 GPa [1] while gel-like materials, such as the extensible intersegmental membrane of many female locust species, can have a Young's modulus as low as 1 kPa [2]. Obviously ceramics cannot be classed as compliant materials, so where is the line to be drawn between "stiff” and "compliant"? In engineering terms compliance is more a term of function, indicating a material that is an effective shock absorber, has the equivalence of zero stiffness (by comparison with the other materials in the structure) or can extend so much that its properties cannot be modelled adequately by a normal linear model. So the functional definition is as much to do with context (and therefore comparative properties) as with mechanical properties. And the important mechanical property is probably ultimate strain rather than stiffness (table or food jellies are very soft but cannot be stretched very far before they fracture). Such soft tissues are remarkably widespread in the animal world and represent a useful, safe, cheap and efficient way of containing and organising other materials. Jim Gordon (author of the seminal The New Science of Strong Materials) once calculated that when one yawns, the strain energy density in the skin covering the cheek is about the same as that in a piece of mild steel just before fracture! The most commonly encountered compliant, high strain, material is the polyisoprenoid natural rubber, which is made from latex from the tree Hevea. Here, the resistance to deformation is provided by the tendency of the chain to revert to a random configuration whose driver is Brownian motion. The degree of randomness (or the number of allowed WIT Transactions on State of the Art in Science and Eng ineering, Vol 20, © 2005 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/978-1-85312-941-4/01 4 Compliant Structures in Nature and Engineering conformations of the molecule) is related to the freedom of rotation about the bonds along the main chain (double bonds provide stiffness), to the degree to which the side groups along the chain interfere with each other as they thresh around (steric hindrance) and to the lack of stabilising secondary structure. Natural rubber has both the freedom and the low degree of steric hindrance. However, single-phase elastomers such as natural rubber are rare, probably absent from living organisms. The side chains of proteins are frequently quite large and the rotation about the backbone bonds is not particularly free, so the number of conformations is limited, giving rise to a few repeating structures (alpha- and collagen-helices, beta sheet, etc.) most of which are intrinsically stable and therefore stiff. In hydrated conditions, water is attracted to charged sites and separates them. Since the water molecules bind and unbind at high speed (residency time of about 10–26 s) they also lubricate the movement of the polymer molecules and provide spatial freedom, so plasticising the material. This tendency is opposed by interactions between hydrophobic side groups that tend to associate in the presence of water. If the water content is reduced by the co-operative effect of these hydrophobic interactions, the charged side groups will also interact, further stabilising the polymer. Therefore materials with low stiffness and high extensibility are not inevitable in organisms; they are the result of specific chemistry and molecular structures. 2 Compliant molecules 2.1 Proteins and polysaccharides There are several materials found in animals that can extend by more than 10% (which is rather more than the breaking strain of collagens), even up to 100% (e.g. elastin, found in vertebrate animals). By analogy with rubbers derived from plants and polymer chemistry, these are often classed as rubbery materials even though a piece of Hevea rubber can extend to 5 or 6 times its original length. However, this is an oversimplification, since it implies that high extensibility is due to a single mechanism. The commonality is that a polymeric molecule whose normal state is to be folded back on itself, whether the folding is orderly or random, will be capable of high extensions if the chains do not link together and are free to move and straighten out. The mechanisms by which they can return to their unextended length (i.e. recover elastically) can in principle be various. In fact it is likely that purely rubbery elasticity is rare in nature. We are becoming more aware that the mechanism of elastic recoil suggested by Urry for elastin (see below) is general [3]; it has been found in gluten, a plant protein, and probably occurs in resilin and abductin, rubbery proteins found in bivalve molluscs and insects, respectively. However, there are other components. The skin of the sea cucumber (an animal related to sea urchins and starfish), a material that can change from stiff to nearly liquid as part of the animal’s defence-and-escape behaviour, has a network of “microfibrils” which may provide a link between the collagen fibrils, causing them to form more stable bundles with fixed topological relationships. The problem then is how can a highly extensible material of very low stiffness (implying only weak crosslinks) return to its original shape after such extreme deformation? The microfibrils in the sea cucumber are chemically very similar to the mammalian protein fibrillin (a protein rich in cysteine), which serves as a scaffolding for the deposition of elastin; similar filaments are found in sea anemones and jelly-fish. So perhaps microfibrils are a common feature in connective tissues, forming a more structured matrix. They were isolated [4] by dissolving unbonded protein and polysaccharides in guanidine hydrochloride (which breaks H bonds) and then dissolving the collagen with a collagenase. In the electron microscope the microfibrils, from which the collagen had been removed, were still clumped together with spaces between which corresponded to the size of the collagen fibrils; WIT Transactions on State of the Art in Science and Eng ineering, Vol 20, © 2005 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) Compliant structures and materials in animals 5 so presumably they were not much changed. Breaking the sulfur bonds and then adding NH2 groups allowed the skin to swell and the microfibrils were seen to be more widely spaced. They are 10–14 nm in diameter with 13-nm diameter beads spaced about 45 nm apart along their length (Fig. 1). Mechanical testing of the extracted skin (in sea water) showed the feltwork of microfibrils to be able to stretch to a strain of 2.75 (engineering strain) before breaking (Fig. 2). By comparison with titin (q.v.) the beads might be areas of hydrophobicity that unravel when the molecule is stretched. Figure 1: Microfibres from the skin of a sea cucumber, isolated using guanidine-HCl, a breaker of H bonds. Figure 2: Stress–strain curve of microfibrils form skin of a sea cucumber, extracted with guanidine-HCl and collagenase, then tested in sea water. WIT Transactions on State of the Art in Science and Eng ineering, Vol 20, © 2005 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) 6 Compliant Structures in Nature and Engineering The fibrillin microfibrils in the filaments of the bovine ocular zonule (a network of fibres that suspends the lens from the ciliary body in the eye) are more orientated than those in the skin of the sea cucumber, and typically show a maximum strain of about 75%, nearer 25% in vivo, where they are permanently prestrained [5]. 2.2 High strain 2.2.1 Titin Titin (also known as connectin) is a giant filamentous protein that stretches between the Z- and M-lines of the vertebrate muscle sarcomere. It probably maintains the structural integrity of the sarcomere and generates the passive force of muscle. The molecule is an entropic (rubbery) spring that unfolds as it is stretched (> 400 pN) and refolds upon release. Unfolding of the molecule is characterized by the disappearance of mechanical hysteresis at high forces; refolding results in hysteresis at low forces. The various globular domains in titin require different unfolding forces due to differences in the activation energies for their unfolding [6]. The resulting force–deflection curve is an elaborate and lengthy saw-tooth profile. 2.2.2 Nacre matrix When mother-of-pearl fractures, the matrix is spun into fibres or ligaments across the gaps between the platelets (Fig. 3). Their action contributes at least half of the toughness of nacre [7], a mechanism that can be mimicked, to a limited extent, by low modulus non-setting glue between the platelets of a model material [8]. These ligaments have been stretched in an atomic force microscope, when they elongate in a stepwise manner suggesting that the process involves folded domains or loops being pulled open. Figure 3: Ligaments (silk-like) bridging the gap between layers of nacre as part of the fracture process. The steps occur with forces of a few hundred pN, smaller than the force (more than a nanonewton) that would be required to break the main chain peptide bonds [9].
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