- Email: [email protected]
All but diamonds – Biological materials are not forever
Available online at www.sciencedirect.com
Acta Materialia 61 (2013) 880–889 www.elsevier.com/locate/actamat
All but diamonds – Biological materials are not forever Richard Weinkamer a, John W.C. Dunlop a, Yves Bre´chet b, Peter Fratzl a,⇑ a
Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Science Park Potsdam-Golm, 14424 Potsdam, Germany b Grenoble-INP, SIMAP, BP75, 38402 Saint Martin d’He`res, France
Abstract Diamonds are known for their perfection and durability. Low flexibility and a lack of adaptation capability are the price to pay for such permanence. Over the course of evolution many different biological materials have appeared which adapt their physical properties to the environmental conditions. To allow for such flexibility biological materials such as bone, silk, shell, skin, plant stem and insect cuticle have complex, often hierarchical, structures. They contain defects, interfaces, structural and chemical gradients and are generally built to be either defect-tolerant in their behavior or to have the capability of self-repair. This complexity makes biological materials difficult to study and to understand. However, over the last hundred years materials engineers have developed metal alloys and other materials with increasing complexity, recognizing that imperfections are not always detrimental but can be useful to tune mechanical, electrical or optical properties. A wide range of models and concepts has been developed to understand the influence of microstructure and defects on the properties of engineering materials. This review reports a few examples where concepts borrowed from physical metallurgy were successful in describing the structure and (mostly mechanical) behavior of biological materials. Approaches of this kind, judiciously combined with biochemical and biological knowledge, may increasingly influence our thinking about tissues and organs. Conversely, the design principles learnt from nature may also help us to develop new types of materials with unexpected property combinations. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Biological materials science; Biomaterials; Mechanical properties; Phase transformations; Interface structure
1. Introduction Adaptation to an ever changing world is one of the major challenges of any living organism. This was recognized by Charles Darwin and his followers and led to the establishment of the laws of evolution and natural selection. By evolution, genetically similar organisms may develop certain traits adapted for example to their feeding habits or to other environmental constraints (see the special issues of Nature and Science commemorating the 200th birthday of Charles Darwin [1,2]). Imperfections during the replication of DNA drive evolution by creating the mutations upon which natural selection operates. This clearly shows the productive character of imperfections ⇑ Corresponding author.
E-mail address: [email protected] (P. Fratzl).
without which the development of new species would not be possible. Adaptation of natural organisms is a concept not only confined to the level of a species. Adaptation also occurs within an individual at the organ level. Muscles can be trained and augmented in the gym, and even bones increase or decrease their volume depending on the applied loads [3]. An example is adaptive growth in trees, where reaction wood (e.g. compression or tension wood) is formed in response to the applied loading, such as side winds and gravity [4]. Finally, the structural materials themselves that make up organs may respond in different ways to changing load levels, thus allowing some level of adaptation. This arises due to dynamic behavior, such as plastic or viscoelastic deformation, and may lead to self-healing after fracture. These different levels of adaptation are summarized in Fig. 1.
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.10.035
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
881
Fig. 1. Three levels of adaptation (outgoing arrows) to physical constraints (incoming arrows) in organisms. Whole species adapt to changes in their environment by evolution and natural selection. Individuals with similar genetic information can also adapt some of their organs (such as muscles, bones, plant stems, etc.) to a current physical stimulus. Finally, self-repair or healing of materials/organs can represent an adaptation at the material level to local functional burden.
The dynamic feedback between materials and the natural world requires that biological materials must cope with all kinds of imperfections or inhomogeneities, such as interfaces, microcracks, vascular channels, gradients, joints between dissimilar materials, and so on. Although imperfections may concentrate loads and lead to crack initiation, they might also be beneficial, like the microcracks appearing in bone. Indeed, microcracks are known to dissipate deformation energy around a large crack and thus improve the toughness of bone material [5–7]. It has been shown that a hierarchy of interfaces between components of various sizes (such as collagen fibrils, bone lamellae, and osteons which surround blood vessels) provides an interesting strategy for a progressive macroscopic response to loading, thus effectively retarding fracture [8,9]. Introducing sufficient interfaces in a material, essentially prefracturing the materials, has also proven to be an effective way to increase toughness in synthetic systems [10,11]. Unraveling the structure–property relations in biological materials requires not only a consideration of the biological constraints under which the material functions, but also knowledge of their complex architecture, including many types of imperfections. Studying structure–property relations of complex materials with many levels of microstructure and defects of various kinds is not an exceptional task for a physical metallurgist. In fact, progress in this area has been characterized by an increasing understanding of the role of vacancies, dislocations, grain boundaries, phase transformations and precipitates on the material behavior of metal alloys. In no other area have the models and framework of understanding of mechanical behavior been so much dependent on imperfections. This clearly sug-
gests that approaches and concepts developed for the description of alloys may be a valuable source of inspiration for materials scientists working on biological materials, despite the completely different context and the entirely different chemical nature of the material constituents. This short review attempts to offer a few examples where concepts borrowed from physical metallurgy have been successfully applied to describe the behavior of biological materials (i.e. the innermost cycle in Fig. 1). Section 2 will mention some of these concepts from the point of view of physical metallurgy. Section 3 then presents examples from biological materials, which nicely demonstrate how concepts from physical metallurgy can help in describing the material behavior of wood and bone and structural transformations in viruses, protein fibers and adhesive surfaces. The analogies are compelling, but it has to be emphasized that a proper understanding of any natural material is impossible without considering its biological function and the context that it derives from. 2. Imperfections and related concepts of physical metallurgy A classical and useful classification of imperfections in metals is possible according to their dimensionality. They can also be differentiated into “physical defects”, mostly associated with a localized change in structural periodicity, and “chemical defects”, depending on a local change in composition. Point defects (zero-dimensional imperfections) are crucial for diffusion transport in metals and alloys. They have an equilibrium concentration at a given temperature, something that is quite specific to crystalline materials. In poly-
882
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
mers, mass transport is governed by a reptation process of chains entangled with other chains. In many natural systems mass transport would be too slow by diffusion and fluid flow plays a key role, which is also the case in largescale solidification and vapor deposition. Line defects called dislocations (one-dimensional imperfections) are topological defects associated with a stress field. In contrast to point defects, they are fully out of equilibrium at any temperature. In essence they are physical defects, but they can also be associated with local variations in chemistry. They are crucial in understanding plasticity, but they can also be useful to describe departures from periodicity in an otherwise crystalline solid. Although the plasticity of metals and alloys is in many cases controlled by the multiplication, motion and interaction of dislocations (with other dislocations or with other microstructural features), one should keep in mind other deformation processes, such as twinning and kinking, which may have some relevance to biological systems, especially in fibrous systems [12]. Interfaces (two-dimensional imperfections) can be purely structural (such as grain boundaries or interfaces between two allotropic phases of a metal) or they can be purely chemical (such as the boundary of structurally coherent but chemically distinct precipitates), or they can be both structural and chemical, as in most of the interfaces between two phases of different compositions. These imperfections play a key role in phase transformations, in controlling both the morphology and the kinetics. Interfaces are quite different depending on whether they are obtained by a “top-down” process (such as co-laminates or metal matrix composites) or by a “bottom-up” process (such as in precipitation). The controlling factor for the shapes of precipitates embedded in a matrix is strongly dependent on the transformation conditions, depending on either the energetics or the mobility of the interfaces [13,14]. Heterophase inclusions (three-dimensional imperfections) can arise from either the liquid state (inclusions) or reaction in the solid state (dispersoids and precipitates). These imperfections are often both structural and chemical, and most often present elastic and plastic properties different from the mother phase. The topology and morphology can be extremely different from one system to another: precipitates embedded in a surrounding phase can be spherical, needle-like or plate-like in shape or have bipercolated structures from spinodal decomposition [14,15]. Their scale depends on the initiation stage (which is given by the ratio of the interface energy to the bulk thermodynamic driving force) and on the growth stage (in which the diffusion length often plays a key role). All these imperfections are of key importance for the basic processes governing transformations and response in metals and alloys. The above mentioned defects and microstructure in general have a major influence on the mechanical behavior of materials. The elasticity of metals (reversible deformation at small strains) is governed by the enthalpic term of the free energy of the material [13] (which is not the case in
polymers above the glass transition temperature, for example). Elasticity being a global response to an external loading it is only mildly sensitive to the microstructure. In composites load transfer from the compliant phase to the stiff phase leads to an elastic modulus intermediate between those of the two phases. The equations governing elastic interactions do not generally depend on scale. Plastic deformation (permanent deformation at larger stains) is a localized response to an external load: defects (most often dislocations) move under an applied stress when a threshold value is reached. This, in contrast to elasticity, depends very strongly on microstructure, and on the absolute scale of the imperfections. Controlling the state of the microstructure is an efficient way of controlling plasticity. As plasticity proceeds metals usually become harder, either because there is greater interaction between them (isotropic hardening) or because the differences in plastic behavior leads to a build-up of directional internal stresses (kinematic hardening). As a result as deformation proceeds the rate of work hardening usually decreases. This occurs up until the point at which the work hardening rate equals the stress (the so-called Conside`re criterion) and deformation localization occurs. Some exceptions, associated with plasticity-induced phase transformations, can however show increasing work hardening (upward curvature in the stress–strain curve) due to increasing load transfer between two phases. It is in plastic deformation that imperfections play the most important role, particularly in metals and alloys. However, imperfections may also be at the origin of material failure. For instance, in a tensile test any imperfection on the surface will eventually develop into necking. Failure may also occur by damage accumulation: cavities nucleate and grow, most often from inclusions larger than 1 lm in size, until failure of the material. Hence the ductility of a material will also depend on the scale of the microstructure, such as the size and density of inclusions. The fracture toughness of a material is generally governed by intrinsic and extrinsic processes [16], which highlights the fact that imperfections are a double-edged sword. While they provide ductility (an intrinsic effect) to retard crack propagation, they may also enhance crack propagation in some cases, as just explained. Extrinsic effects retarding crack propagation are again due to other types of imperfections, such as interfaces causing the crack to deviate or uncracked ligaments bridging it [16]. This clearly shows the importance of microstructure and a proper distribution of imperfections at all scales to control the properties of a material, be it a metal alloy or even a biological material, as discussed below. 3. Concepts of physical metallurgy that help in understanding biological materials It cannot be expected, of course, that concepts from physical metallurgy can be directly applied to the problems encountered in biological materials research. Chemical
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
composition and structural complexity are really very distinct in natural materials. Many of the imperfections presented in the last section are connected to the crystalline lattice of metals. Biological materials are characterized by a hierarchical structure with a variety of structural motifs on different length scales [17,18]. However, while the nature of the defects may be quite different in the two worlds, their function can sometimes be similar. The first example presented below shows that plasticity in some natural materials is not provided by dislocations but by special properties of biomacromolecules. 3.1. Defects and plasticity In some biological materials an alternative mechanism to dislocation motion leads to plastic deformation. Evidence has accumulated that plasticity (e.g. in bone and wood) is controlled by biomacromolecules which fulfill the function of a reversible glue [19–21]. A key element is the presence of both weak and strong bonds coupling these molecules [22]. A schematic example is shown in Fig. 2. Covalently bound polymeric chains are connected to each other by a second weaker bonding based, for example, on hydrogen bonds, electrostatic interactions or metal coordination bonds. To describe the principle it is best to imagine these bonds either linking parts of the same molecule to each other (case a in Fig. 2) or two neighboring molecules (case b in Fig. 2). In the first example the weak bonds stabilize a fold in the molecular backbone. Upon stretching the weak bonds break, with the consequence that removal of the backbone loop results in notable extension in the length of the molecule. A suggestive terminology describes
883
this effect as “hidden length” (e.g. in the form of folds), which is freed by breaking the weak “sacrificial bonds” [21,23]. The presence of sacrificial bonds leads to somewhat unusual material behavior: Firstly, the breaking of these bonds dissipates a large amount of energy before the breaking of covalent bonds affects the structural integrity of the molecule [21]. Secondly, the sacrificial bonds can slowly reform after unloading, which leads to full restoration of the mechanical properties of the material, sometimes referred to as “self-healing”. A striking example for such behavior is seen in byssal threads. Mussels use these threads to fasten themselves to the rocky seashore, so as not to be washed away by wave motion [24,25]. The protein making up this fiber contains relatively stiff parts similar to collagen. Other parts are crosslinked with Zn–histidine bonds, which are weaker than covalent bonds and serve as sacrificial bonds in deformation. Hence the byssal threads show pronounced yielding due to breaking of the sacrificial bonds. After load release the threads are initially soft and stiffen only after the sacrificial bonds reform, in about 24 h [24,26]. In the scenario sketched in Fig. 2b the sacrificial bonds connect different adjacent molecules. When the sacrificial bonds break the molecules slip with respect to each other and the reversible character of these sacrificial bonds allows the bonds to reform (compare the two sketches in Fig. 2b). With such a stick–slip mechanism the material can undergo large permanent plastic deformations. In tendon [27], bone [21] and wood [28] it has been proposed that glue-like layers of macromolecules (proteoglycans, phosphorylated proteins and hemi-celluloses, respectively) connect stiff structural elements through sacrificial bonds. In
Fig. 2. The behavior of biological macromolecules under external load. (a) The backbone of the molecule shown as a dark grey line has a loop held together by weak bonds depicted as light grey connections. Upon loading these sacrificial bonds break, freeing the “hidden length” which extends. Upon unloading spontaneous refolding of the molecule (as is typical for proteins) allows reformation of the bonds. (b) Sacrificial bonds on two adjacent macromolecules allow large irreversible deformation by a stick–slip mechanism (adapted from Aichmayer and Fratzl [31]).
884
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
bone these stiff elements are mineralized collagen fibers and in wood cellulose fibrils, the strength of the material being controlled by the geometric arrangement and size of these elements [29]. Sacrificing the bonds in the glue layer before the stiff elements break allows plastic flow and energy dissipation that increases the toughness of the biological composite [17]. The importance of spatial order as a design principle of sacrificial bonds has been illustrated in a simple model [30]. Divalent cations between two plates carrying negative point charges were used to model ion-mediated sacrificial bonds. When the negative charges were arranged on an ordered triangular lattice the total bonding between the plates was strong but brittle. When they were randomly distributed shearing of the two plates allowed a 300 times larger strain and the energy dissipated before failure was increased by a factor of 20 [30].
roughly six orders of magnitude from the enamel as the outer coating of the tooth to the soft “cushion” material between the tooth and the jaw bone [32]. Gradients in the material properties are implemented in the enamel–dentine [40] and dentine–cementum junctions. iv. Interfaces that allow material movement. In plants, tissues can be found which swell with changes of humidity. When tissues with different rates of swelling are bonded together by a tight interface humidity changes result in shape changes of the overall organ [41]. A well-known example is found in the scales of the pine cone [42] (Fig. 3), which are bilayers of parallel and perpendicular oriented tissues. These layers shrink differently upon drying, resulting in bending and an opening of the cone, in a movement akin to that found in bimetallic strips.
3.2. The role of interfaces 3.3. Precipitation and nanocomposites Interfaces, seen as two-dimensional imperfections, influence the properties of biological materials in diverse ways which we are only beginning to be understood. Interfaces are used by nature as a powerful tool to control material function through the expenditure of only small amounts of material. If energy and other resources have to be invested interfaces are efficient places to expend them. In a recent article interfaces in biological materials were classified as follows according to their function [32]. i. Interfaces that enhance the fracture resistance of brittle materials by deviating or stopping cracks. One of the most studied biological materials of this type is nacre [33–36], which has a bricks and mortar structure with bricks made of stiff but brittle calcium carbonate and the mortar consisting of soft proteins (Fig. 3). Another example of this design principle is the glass sponge Euplectella [37], in which a small amount of proteinaceous material (less than 1% of the overall material) forming “glue layers” less than 10 nm thick is sufficient to improve the fracture resistance 2.5 times. ii. Interfaces that enable deformation. A possibility discussed in the previous section is providing plasticity via “Velcro-like” debonding and rebonding. An alternative design is realized in sutures [38], as found in, for example, the shell of the red-slider turtle [39]. The shell is essentially the rib cage in which the ribs have intergrown and interdigitate at the joint or suture. This suture is filled with a soft matrix which provides structural flexibility to the shell as long as the strains are small (Fig. 3). For larger deformations the bony elements interlock leading to a stiffening of the shell. iii. Interfaces joining materials with a high contrast in material properties. Fig. 3 shows schematically the example of a tooth, where the stiffness changes over
Biological materials that have to fulfill a mechanical function are virtually all composites [43], with the component dimensions typically in the nanometer range. In bone a staggered arrangement of stiff nanoscopic mineral platelets in a tough organic matrix results in a composite, combining the often conflicting properties of high stiffness and toughness [29]. A classical pathway used by nature to obtain nanocomposites is to nucleate and grow a mineral phase, often within a preformed matrix. Even for crystalline materials, in which there seems little space left for modification, the living world is forcing us to rethink our concepts. Biogenic single crystals may not be faceted as are geogenic ones, but display curved surfaces at different length scales [44]. The shapes of biogenic crystals seem without limitation, as demonstrated by the marvelous skeletal elements made from calcite in the brittle star [45]. The interaction with biomolecules not only controls the shape of crystals but also the size of, for example, iron oxide particles in magnetotactic bacteria [46]. Biogenic crystals usually contain many more impurities, and even macromolecules can be occluded within the crystals [47– 49]. As a result the degree of order is much lower in biogenic crystals. Taking the sea urchin spicule as an example, calcite has perfectly crystalline domains about 150 nm in size, compared with 1 mm in geogenic crystals [50]. This degree of imperfection has strong implications for the properties of the minerals. Most obvious are the different ways of fracture: instead of a fracture along cleavage planes, the fracture surface of the biogenic crystal is rough, which increases the mineral toughness. As demonstrated in bone, some nanoscale biogenic crystals can also be strained to a much higher degree before mechanical failure [51]. Not only the final product but also the crystallization pathway are significantly different in living organisms [44]. Firstly, crystallization occurs at ambient temperatures. Secondly, disordered precursor phases seem to be a
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
885
Fig. 3. Different functionalities of interfaces in biological materials. (i) The thin organic layer between mineral plates in nacre improves the fracture resistance. (ii) In the turtle shell the interdigitating bone structure and infilling of the suture with soft material allow small deformations but prevent larger ones. (iii) In teeth materials of different stiffness are bonded together as material gradients, with the stiffest, enamel (white), on the top, then dentin (light grey) and then cementum (dark gray layer covering the roots of the tooth). The tooth is anchored in the jaw by ligaments. (iv) The scales of the pine cone consist of layers with different swelling properties leading to opening and closing of the cone on changes in humidity.
widely used strategy in biogenic crystallization [52]. These precursor minerals form within vesicles in cells. In some cases crystals remains within the cell, such as the guanine crystals responsible for iridescence in fish skin or spider cuticle [44]. When mineralization occurs outside the cell the amorphous phase may be transported within a vesicle to the site of crystallization. In the sea urchin larval spicules a preformed small crystal is used as a template for crystallization via secondary nucleation of the arriving mineral. However dissolution of the precursor phase and reprecipitation outside the cell are also possible [53]. Not only nucleation but also crystal growth are biologically controlled. Macromolecules play an important role in stopping crystal growth in specific crystal orientations [54,55]. Molecular scaffolds such as collagen fibrils are also important in the nucleation of mineral in bone [56]. In an in vitro experiment it was shown that a supersaturated solution of calcium phosphate together with an inhibitor of nucleation outside the collagen fibril is sufficient to obtain a mineralized collagen fibril with nanosized crystal particles [57]. In vitro experiments challenge the classical picture of nucleation as taking place in a supersaturated solution of ions by the stochastic formation of a critical nucleus. The size of the nucleus is given by the balance between the gain in bulk energy and the loss in surface energy. In contrast to the classical view it was demonstrated that even an undersaturated solution of calcium carbonate contains stable
pre-nucleation ion clusters. According to this view crystal growth takes place through coalescence of such clusters [58]. Diffusion and coalescence of nanosized inclusions has also been discussed as a possibility for the growth of precipitates in alloys [59,60] and indirectly shown experimentally [61]. Nature extends the idea of composites beyond a difference in chemical composition between matrix and inclusions. By manipulating the molecular bonding, even with the same chemistry, a contrast of properties between matrix and inclusions can be obtained. To protect against abrasion the cuticle of the byssal threads of mussels (already mentioned above) has to be hard, but should not compromise the high extensibility of the threads. Fig. 4 shows the microstructure of the cuticle, consisting of stiff granules in a soft matrix [62]. The granules consist of regions enriched in Fe3+-mediated crosslinks within the protein in the thread cuticle. Deformation localizes in the soft matrix between the granules upon stretching. The high abrasion resistance of the cuticle is thought to occur via granule–granule contacts resisting compression. 3.4. Phase transformations The concept of phase transformations, in particular diffusionless transformations, has been evoked in biological materials research. A remarkable example, in which even
886
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
Fig. 4. In the schematic a mussel attaches itself to a rock via several byssal threads. The scanning electron micrograph below shows the composite character of the thread cuticle with stiff granules embedded in a soft matrix (Image courtesy of M. Harrington). The contrast in properties is due to a difference in crosslinks via metal coordination bonds (right). On loading beyond a strain of 30% microcracks form in the matrix, while in the granules crosslink coordination bonds start to break. These sacrificial bonds in the granules can reform once the loading is reduced. The right-hand side of this figure is reprinted from Harrington et al. [62], reprinted with permission of the AAAS.
the matrix of lattice-distortive strains were reported [63,64], is the contraction of the tail sheath of bacteriophage. Bacteriophage T4 (Fig. 5) is a virus that attaches to and inserts its viral DNA into a bacterium. Its tail consists of two concentric cylinders, the smaller tail tube providing the channel for DNA transport, the larger tail sheath providing the force to penetrate the membrane of the bacterium. The force is generated by a dramatic shape change of the tail sheath. The sheath consists of a periodic arrangement of globular proteins forming a two-dimensional protein crystal (Fig. 5), which rolls up to form the cylindrical sheath. Sheath contraction is the result of shear-dominant lattice distortion (Fig. 5, right), which strikingly resembles a martensitic phase transformation [63]. As a result the sheath contracts irreversibly to roughly one-third of its original length and increases its diameter by a factor of two. The kinetics of the contraction process is well understood using a thermodynamic description from physical metallurgy. The protein crystal, originally grown on the so-called base plate of the virus, is in a metastable state in its extended form. Upon contact with a bacterium the base plate changes shape, thereby creating the necessary strains to induce nucleation of a new crystal phase in the sheath. Models have been proposed for how the interface between the extended and the contracted phase moves up the sheath under conservation of the coherency of the lattice [63,64]. In recent studies a phase transformation in a biopolymeric material used for encapsulation was investigated
[65,66]. Living in a wave swept marine environment, the whelk egg capsule has a protective function. A structural phase transition of the egg capsule tissue was observed upon stretching. This transition does not occur in a gradual way, but via the coexistence of a low strain phase (based on a helical conformation of the protein) and a high strain phase (corresponding to an extended conformation). In the coexisting phases the amount of the high strain phase gradually increases, in complete analogy to the Gibbs double tangent construction in classical phase transitions in solids, such as pseudoelastic metals, e.g. Ni–Ti (Fig. 6). In the strain region between the energy minima of the two phases the energy density is minimized by the double tangent, where the slope corresponds to the yield stress ry at which the transition occurs. As demonstrated in the schematic plot of molecular strain versus stress (Fig. 6, bottom), yield begins with the unfolding of discrete domains in the low strain phase due to breaking of the hydrogen bonding network. This transition occurs at constant stress (estimated as ry = 6.7 MPa), where with increasing strain the volume fraction of the extended high strain phase increases [65]. 3.5. Adhesion problems There is a remarkable range of tools that living systems use to attach themselves to different surfaces in both reversible and permanent ways. On the one hand, there are per-
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
Fig. 5. The two configurations of a virus in contact with a bacterium. The bacteriophage settles on the bacterium with its tail sheath in an uncontracted state. The two-dimensional lattice of proteins is shown below. Triggered by a configurational change in the lower part (the socalled base plate) a new contracted phase nucleates and extends over the whole sheath. In full contraction the length of the sheath is reduced to approximately one-third of the original length. The force generated by contraction is used to penetrate the bacterial membrane to channel the viral DNA into the bacterium (inspired by Olson and Hartman [63]).
887
manent adhesives, such as the chemical adhesives used in the plaque of the mussel byssus threads [68,69] and in the combined physical and chemical adhesion mechanisms used by the English ivy [70]. Of particular interest for bioinspired adhesives are the species that can attach themselves in a reversible manner to a substrate using appendages covered with many fine hairs or setae [67,71,72]. Although some species secrete fluids that improve adhesion via capillary action, species with “dry feet” use van der Waals-mediated adhesion, which seems to increase in strength with increasing setae density. One hypothesis, contact splitting, uses an extended Hertz theory to show that the pull-off force of a given set of setae scales with length, e.g. the contact radius, not the area, meaning that dividing a given adhesive area into many smaller parts should result in increased adhesive forces [67]. A subsequent interpretation of the scaling law is that pull-off forces increase with increasing peeling length, which in turn scales with setae density [73]. Despite the different modeling details, a consequence of both models is that it would be expected that larger animals would have higher setae densities [67,73]. Although such a general relation is indeed seen in the data (Fig. 7), a more detailed study, taking phylogenetic relationships between species into account, showed that there is no significant scaling within a given group of closely related taxa [74]. This highlights that although tools from materials science can be used to understand the material properties of biological systems and indeed inspire the development of novel reversible dry
Fig. 6. Schematic plots of the phase transition in the egg capsule biopolymeric material of whelks from the unstretched a-phase to the extended b-phase [65]. Yield occurs when domains in the a-phase start to unfold. The energy minimum is then giving by the common tangent to the energy density curves of the two phases. The tangent corresponds to the state of constant stress. At this stress both phases coexist. Only after full transformation to the b-phase does the stress again start to increase with strain.
888
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
Fig. 7. The area density of attachment pads as a function of body mass for a selection of different animal species, showing a trend of increasing density with size. Redrawn with permission from Arzt et al. [67], Ó 2003 National Academy of Sciences of the USA.
adhesives [75], one needs to take note of the relatedness of species if conclusions about evolution are to be made. 4. Conclusions Some of the examples shown in this article demonstrate how ideas derived from physical metallurgy may contribute to an understanding of biological materials. Indeed, the roles of structural imperfections in tuning material properties were recognized early on by metallurgists and their description was transformed into a quantitative science. The idea that defects may be beneficial to the macroscopic properties of materials, providing plasticity and slowing down cracks, is a central theme of physical metallurgy. Approaches of this kind also turned out to be useful in describing some aspects of the structure and properties of natural materials. Of course, this viewpoint also has its limits. First, nature primarily uses polymers based on proteins or polysaccharides and several minerals to create composite materials chemically quite different to those common in engineering. Even more important, natural materials cannot be understood without their biological context, which defines the functions and requirements of these materials. Hence, research on biological materials is always first and foremost biological research, even if it takes its inspiration and methodologies from physics or materials science [76]. The successful description of structure–property relations in biological materials has become common in recent years, mainly because research teams with mixed backgrounds from biology to materials science have been put together in a number of universities and research institutions. This has gradually led to materials science concepts infiltrating the biological sciences, to the point that it has now became customary in the context of biological systems to talk about the elastic modulus, interface failure or fracture toughness. The examples in this article demonstrate
that ideas borrowed from physical metallurgy and materials science are more than just an analogy to phenomena observed in biomaterials research; they are gradually becoming part of the arsenal in the biological sciences. Conversely, there is much to learn from biological materials in the way exceptional properties may arise from a suitable combination of comparatively poor components. This is primarily due to the complex, often hierarchical structure of biological materials, assembled by growth following a recipe stored in the genes, rather than being fabricated according to an exact design [77]. Thus the study of structure–property relations in biological materials is increasingly seen as a source of inspiration for the development of new classes of materials with adaptive, self-healing or multifunctional properties [11,78,79]. In particular, the role of the geometry and architecture of hierarchical materials in the multifunctional behavior of composites has become a promising avenue for the development of new materials [80]. Indeed, the hierarchical structure of biological materials allows them to be adapted to their function at various length scales [77]. It must be highlighted, however, that bioinspired materials research is not conceivable without input from the biological sciences, since the function of any natural material cannot be known without taking into account the context of the living organism. Biological materials science is a new field developing in the area between the use of materials concepts in the description of biological organisms and the extraction of natural building principles for the benefit of the materials community. Biological materials may not have the perfection of diamonds, but they are gems worth being studied by biologists and by materials scientists and, at best, by the two together. Acknowledgements The authors are grateful to many colleagues and collaborators in particular, Barbara Aichmayer, Michaela Eder, Damien Faivre, Matthew Harrington, Yael Politi and Wolfgang Wagermaier. We acknowledge the Humboldt Foundation for supporting the visit of YB to Potsdam through the Gay-Lussac-Humboldt Award and support through the Leibniz prize of PF running under DFG contract number FR2190/4-1. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Gee H, Howlett R. Nature 2009;457:807. Sugden A, Ash C, Hanson B, Zahn L. Science 2009;323:727. Frost HM. Anat Rec 1987;219:1. Mattheck C. Design in nature: learning from trees. Berlin: SpringerVerlag; 1998. Taylor D, Hazenberg JG, Lee TC. Nat Mater 2007;6:263. Peterlik H, Roschger P, Klaushofer K, Fratzl P. Nat Mater 2005;5:52. Currey JD. Bones – structure and mechanics. Princeton, NJ: Princeton University Press; 2002. Koester KJ, Ager JW, Ritchie RO. Nat Mater 2008;7:672. Fratzl P. Nat Mater 2008;7:610.
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889 [10] Dyskin AV, Estrin Y, Kanel-Belov AJ, Pasternak E. Adv Eng Mater 2001;3:885. [11] Munch E, Launey ME, Alsem DH, Saiz E, Tomsia AP, Ritchie RO. Science 2008;322:1516. [12] Robinson W. Philos Trans R Soc Lond B 1921;210:49. [13] Haasen P. Physical metallurgy. Cambridge: Cambridge University Press; 1996. [14] Fratzl P, Penrose O, Lebowitz JL. J Stat Phys 1999;95:1429. [15] Kostorz G. Phase transformations in materials. Weinheim: WileyVCH; 2001. [16] Ritchie RO. Nat Mater 2011;10:817. [17] Fratzl P, Weinkamer R. Prog Mater Sci 2007;52:1263. [18] Meyers MA, Chen PY, Lin AYM, Seki Y. Prog Mater Sci 2008;53:1. [19] Currey J. Nature 2001;414:699. [20] Thompson JB, Kindt JH, Drake B, Hansma HG, Morse DE, Hansma PK. Nature 2001;414:773. [21] Fantner G, Hassenkam T, Kindt JH, Weaver JC, Birkedal H, Pechenik L, et al. Nat Mater 2005;4:612. [22] Keten S, Xu ZP, Ihle B, Buehler MJ. Nat Mater 2010;9:359. [23] Fantner GE, Oroudjev E, Schitter G, Golde LS, Thurner P, Finch MM, et al. Biophys J 2006;90:1411. [24] Harrington MJ, Gupta HS, Fratzl P, Waite JH. J Struct Biol 2009;167:47. [25] Vaccaro E, Waite JH. Biomacromolecules 2001;2:906. [26] Carrington E, Gosline JM. Am Malac Bull 2004;18:135. [27] Puxkandl R, Zizak I, Paris O, Keckes J, Tesch W, Bernstorff S, et al. Philos Trans R Soc Lond B 2002;357:191. [28] Keckes J, Burgert I, Fruhmann K, Muller M, Kolln K, Hamilton M, et al. Nat Mater 2003;2:810. [29] Gao HJ, Ji BH, Jager IL, Arzt E, Fratzl P. Proc Natl Acad Sci USA 2003;100:5597. [30] Hartmann MA, Fratzl P. Nano Lett 2009;9:3603. [31] Aichmayer B, Fratzl P. Phys J 2010;9:33. [32] Dunlop JWC, Weinkamer R, Fratzl P. Mater Today 2011;14:70. [33] Okumura K, de Gennes PG. Eur Phys J E 2001;4:121. [34] Barthelat F, Espinosa HD. Exp Mech 2007;47:311. [35] Wang RZ, Gupta HS. Annu Rev Mater Res 2011;41:41. [36] Jackson AP, Vincent JFV, Turner RM. Proc R Soc Lond B 1988;234:415. [37] Aizenberg J, Weaver JC, Thanawala MS, Sundar VC, Morse DE, Fratzl P. Science 2005;309:275. [38] Li YN, Ortiz C, Boyce MC. Phys Rev E 2011:84. [39] Krauss S, Monsonego-Ornan E, Zelzer E, Fratzl P, Shahar R. Adv Mater 2009;21:407. [40] Zaslansky P, Friesem AA, Weiner S. J Struct Biol 2006;153:188. [41] Burgert I, Fratzl P. Philos Trans R Soc A 2009;367:1541. [42] Dawson C, Vincent JFV, Rocca A-M. Nature 1997;390:668. [43] Dunlop JWC, Fratzl P. Annu Rev Mater Res 2010;40:1. [44] Weiner S, Addadi L. Annu Rev Mater Res 2011;41:21. [45] Aizenberg J, Tkachenko A, Weiner S, Addadi L, Hendler G. Nature 2001;412:819. [46] Faivre D, Schuler D. Chem Rev 2008;108:4875.
889
[47] Pokroy B, Quintana JP, Caspi EaN, Berner A, Zolotoyabko E. Nat Mater 2004;3:900. [48] Gilow C, Zolotoyabko E, Paris O, Fratzl P, Aichmayer B. Cryst Growth Des 2011;11:2054. [49] Weiner S, Addadi L. J Mater Chem 1997;7:689. [50] Berman A, Hanson J, Leiserowitz L, Koetzle TF, Weiner S, Addadi L. Science 1993;259:776. [51] Gupta HS, Seto J, Wagermaier W, Zaslansky P, Boesecke P, Fratzl P. Proc Natl Acad Sci USA 2006;103:17741. [52] Addadi L, Raz S, Weiner S. Adv Mater 2003;15:959. [53] Sone ED, Weiner S, Addadi L. J Struct Biol 2007;158:428. [54] Mann S. Biomineralization – principles and concepts in bioinorganic chemistry. Oxford: Oxford University Press; 2001. [55] Xu AW, Ma YR, Colfen H. J Mater Chem 2007;17:415. [56] Landis WJ, Silver FH, Freeman JW. J Mater Chem 2006;16: 1495. [57] Nudelman F, Pieterse K, George A, Bomans PHH, Friedrich H, Brylka LJ, et al. Nat Mater 2010;9:1004. [58] Gebauer D, Volkel A, Colfen H. Science 2008;322:1819. [59] Fratzl P, Penrose O. Phys Rev B 1997;55:R6101. [60] Weinkamer R, Fratzl P. Europhys Lett 2003;61:261. [61] Stadler LM, Sepiol B, Weinkamer R, Hartmann M, Fratzl P, Kantelhardt JW, et al. Phys Rev B 2003;68. [62] Harrington MJ, Masic A, Holten-Andersen N, Waite JH, Fratzl P. Science 2010;328:216. [63] Olson GB, Hartman H. J Phys 1982;43:855. [64] Falk W, James RD. Phys Rev E 2006:73. [65] Harrington MJ, Wasko SS, Masic A, Fischer FD, Gupta HS, Fratzl P. J R Soc Interface 2012;9:2911. [66] Miserez A, Wasko SS, Carpenter CF, Waite JH. Nat Mater 2009;8:910. [67] Arzt E, Gorb S, Spolenak R. Proc Natl Acad Sci USA 2003;100:10603. [68] Lin Q, Gourdon D, Sun CJ, Holten-Andersen N, Anderson TH, Waite JH, et al. Proc Natl Acad Sci USA 2007;104:3782. [69] Lee H, Scherer NF, Messersmith PB. Proc Natl Acad Sci USA 2006;103:12999. [70] Melzer B, Steinbrecher T, Seidel R, Kraft O, Schwaiger R, Speck T. J Roy Soc Int 2010;7:1383. [71] Kwak MK, Pang C, Jeong HE, Kim HN, Yoon H, Jung HS, et al. Adv Funct Mater 2011;21:3606. [72] Meyers MA, Chen PY, Lopez MI, Seki Y, Lin AYM. J Mech Behav Biomed Mater 2011;4:626. [73] Varenberg M, Pugno NM, Gorb SN. Soft Matter 2010;6:3269. [74] Peattie AM, Full RJ. Proc Natl Acad Sci USA 2007;104:18595. [75] Kwak MK, Jeong HE, Suh KY. Adv Mater 2011;23:3949. [76] Fratzl P, Barth FG. Nature 2009;462:442. [77] Fratzl P. J Roy Soc Int 2007;4:637. [78] Hager MD, Greil P, Leyens C, van der Zwaag S, Schubert US. Adv Mater 2010;22:5424. [79] Ortiz C, Boyce MC. Science 2008;319:1053. [80] Ashby MF, Brechet YJM. Acta Mater 2003;51:5801.
Acta Materialia 61 (2013) 880–889 www.elsevier.com/locate/actamat
All but diamonds – Biological materials are not forever Richard Weinkamer a, John W.C. Dunlop a, Yves Bre´chet b, Peter Fratzl a,⇑ a
Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, Science Park Potsdam-Golm, 14424 Potsdam, Germany b Grenoble-INP, SIMAP, BP75, 38402 Saint Martin d’He`res, France
Abstract Diamonds are known for their perfection and durability. Low flexibility and a lack of adaptation capability are the price to pay for such permanence. Over the course of evolution many different biological materials have appeared which adapt their physical properties to the environmental conditions. To allow for such flexibility biological materials such as bone, silk, shell, skin, plant stem and insect cuticle have complex, often hierarchical, structures. They contain defects, interfaces, structural and chemical gradients and are generally built to be either defect-tolerant in their behavior or to have the capability of self-repair. This complexity makes biological materials difficult to study and to understand. However, over the last hundred years materials engineers have developed metal alloys and other materials with increasing complexity, recognizing that imperfections are not always detrimental but can be useful to tune mechanical, electrical or optical properties. A wide range of models and concepts has been developed to understand the influence of microstructure and defects on the properties of engineering materials. This review reports a few examples where concepts borrowed from physical metallurgy were successful in describing the structure and (mostly mechanical) behavior of biological materials. Approaches of this kind, judiciously combined with biochemical and biological knowledge, may increasingly influence our thinking about tissues and organs. Conversely, the design principles learnt from nature may also help us to develop new types of materials with unexpected property combinations. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Biological materials science; Biomaterials; Mechanical properties; Phase transformations; Interface structure
1. Introduction Adaptation to an ever changing world is one of the major challenges of any living organism. This was recognized by Charles Darwin and his followers and led to the establishment of the laws of evolution and natural selection. By evolution, genetically similar organisms may develop certain traits adapted for example to their feeding habits or to other environmental constraints (see the special issues of Nature and Science commemorating the 200th birthday of Charles Darwin [1,2]). Imperfections during the replication of DNA drive evolution by creating the mutations upon which natural selection operates. This clearly shows the productive character of imperfections ⇑ Corresponding author.
E-mail address: [email protected] (P. Fratzl).
without which the development of new species would not be possible. Adaptation of natural organisms is a concept not only confined to the level of a species. Adaptation also occurs within an individual at the organ level. Muscles can be trained and augmented in the gym, and even bones increase or decrease their volume depending on the applied loads [3]. An example is adaptive growth in trees, where reaction wood (e.g. compression or tension wood) is formed in response to the applied loading, such as side winds and gravity [4]. Finally, the structural materials themselves that make up organs may respond in different ways to changing load levels, thus allowing some level of adaptation. This arises due to dynamic behavior, such as plastic or viscoelastic deformation, and may lead to self-healing after fracture. These different levels of adaptation are summarized in Fig. 1.
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.10.035
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
881
Fig. 1. Three levels of adaptation (outgoing arrows) to physical constraints (incoming arrows) in organisms. Whole species adapt to changes in their environment by evolution and natural selection. Individuals with similar genetic information can also adapt some of their organs (such as muscles, bones, plant stems, etc.) to a current physical stimulus. Finally, self-repair or healing of materials/organs can represent an adaptation at the material level to local functional burden.
The dynamic feedback between materials and the natural world requires that biological materials must cope with all kinds of imperfections or inhomogeneities, such as interfaces, microcracks, vascular channels, gradients, joints between dissimilar materials, and so on. Although imperfections may concentrate loads and lead to crack initiation, they might also be beneficial, like the microcracks appearing in bone. Indeed, microcracks are known to dissipate deformation energy around a large crack and thus improve the toughness of bone material [5–7]. It has been shown that a hierarchy of interfaces between components of various sizes (such as collagen fibrils, bone lamellae, and osteons which surround blood vessels) provides an interesting strategy for a progressive macroscopic response to loading, thus effectively retarding fracture [8,9]. Introducing sufficient interfaces in a material, essentially prefracturing the materials, has also proven to be an effective way to increase toughness in synthetic systems [10,11]. Unraveling the structure–property relations in biological materials requires not only a consideration of the biological constraints under which the material functions, but also knowledge of their complex architecture, including many types of imperfections. Studying structure–property relations of complex materials with many levels of microstructure and defects of various kinds is not an exceptional task for a physical metallurgist. In fact, progress in this area has been characterized by an increasing understanding of the role of vacancies, dislocations, grain boundaries, phase transformations and precipitates on the material behavior of metal alloys. In no other area have the models and framework of understanding of mechanical behavior been so much dependent on imperfections. This clearly sug-
gests that approaches and concepts developed for the description of alloys may be a valuable source of inspiration for materials scientists working on biological materials, despite the completely different context and the entirely different chemical nature of the material constituents. This short review attempts to offer a few examples where concepts borrowed from physical metallurgy have been successfully applied to describe the behavior of biological materials (i.e. the innermost cycle in Fig. 1). Section 2 will mention some of these concepts from the point of view of physical metallurgy. Section 3 then presents examples from biological materials, which nicely demonstrate how concepts from physical metallurgy can help in describing the material behavior of wood and bone and structural transformations in viruses, protein fibers and adhesive surfaces. The analogies are compelling, but it has to be emphasized that a proper understanding of any natural material is impossible without considering its biological function and the context that it derives from. 2. Imperfections and related concepts of physical metallurgy A classical and useful classification of imperfections in metals is possible according to their dimensionality. They can also be differentiated into “physical defects”, mostly associated with a localized change in structural periodicity, and “chemical defects”, depending on a local change in composition. Point defects (zero-dimensional imperfections) are crucial for diffusion transport in metals and alloys. They have an equilibrium concentration at a given temperature, something that is quite specific to crystalline materials. In poly-
882
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
mers, mass transport is governed by a reptation process of chains entangled with other chains. In many natural systems mass transport would be too slow by diffusion and fluid flow plays a key role, which is also the case in largescale solidification and vapor deposition. Line defects called dislocations (one-dimensional imperfections) are topological defects associated with a stress field. In contrast to point defects, they are fully out of equilibrium at any temperature. In essence they are physical defects, but they can also be associated with local variations in chemistry. They are crucial in understanding plasticity, but they can also be useful to describe departures from periodicity in an otherwise crystalline solid. Although the plasticity of metals and alloys is in many cases controlled by the multiplication, motion and interaction of dislocations (with other dislocations or with other microstructural features), one should keep in mind other deformation processes, such as twinning and kinking, which may have some relevance to biological systems, especially in fibrous systems [12]. Interfaces (two-dimensional imperfections) can be purely structural (such as grain boundaries or interfaces between two allotropic phases of a metal) or they can be purely chemical (such as the boundary of structurally coherent but chemically distinct precipitates), or they can be both structural and chemical, as in most of the interfaces between two phases of different compositions. These imperfections play a key role in phase transformations, in controlling both the morphology and the kinetics. Interfaces are quite different depending on whether they are obtained by a “top-down” process (such as co-laminates or metal matrix composites) or by a “bottom-up” process (such as in precipitation). The controlling factor for the shapes of precipitates embedded in a matrix is strongly dependent on the transformation conditions, depending on either the energetics or the mobility of the interfaces [13,14]. Heterophase inclusions (three-dimensional imperfections) can arise from either the liquid state (inclusions) or reaction in the solid state (dispersoids and precipitates). These imperfections are often both structural and chemical, and most often present elastic and plastic properties different from the mother phase. The topology and morphology can be extremely different from one system to another: precipitates embedded in a surrounding phase can be spherical, needle-like or plate-like in shape or have bipercolated structures from spinodal decomposition [14,15]. Their scale depends on the initiation stage (which is given by the ratio of the interface energy to the bulk thermodynamic driving force) and on the growth stage (in which the diffusion length often plays a key role). All these imperfections are of key importance for the basic processes governing transformations and response in metals and alloys. The above mentioned defects and microstructure in general have a major influence on the mechanical behavior of materials. The elasticity of metals (reversible deformation at small strains) is governed by the enthalpic term of the free energy of the material [13] (which is not the case in
polymers above the glass transition temperature, for example). Elasticity being a global response to an external loading it is only mildly sensitive to the microstructure. In composites load transfer from the compliant phase to the stiff phase leads to an elastic modulus intermediate between those of the two phases. The equations governing elastic interactions do not generally depend on scale. Plastic deformation (permanent deformation at larger stains) is a localized response to an external load: defects (most often dislocations) move under an applied stress when a threshold value is reached. This, in contrast to elasticity, depends very strongly on microstructure, and on the absolute scale of the imperfections. Controlling the state of the microstructure is an efficient way of controlling plasticity. As plasticity proceeds metals usually become harder, either because there is greater interaction between them (isotropic hardening) or because the differences in plastic behavior leads to a build-up of directional internal stresses (kinematic hardening). As a result as deformation proceeds the rate of work hardening usually decreases. This occurs up until the point at which the work hardening rate equals the stress (the so-called Conside`re criterion) and deformation localization occurs. Some exceptions, associated with plasticity-induced phase transformations, can however show increasing work hardening (upward curvature in the stress–strain curve) due to increasing load transfer between two phases. It is in plastic deformation that imperfections play the most important role, particularly in metals and alloys. However, imperfections may also be at the origin of material failure. For instance, in a tensile test any imperfection on the surface will eventually develop into necking. Failure may also occur by damage accumulation: cavities nucleate and grow, most often from inclusions larger than 1 lm in size, until failure of the material. Hence the ductility of a material will also depend on the scale of the microstructure, such as the size and density of inclusions. The fracture toughness of a material is generally governed by intrinsic and extrinsic processes [16], which highlights the fact that imperfections are a double-edged sword. While they provide ductility (an intrinsic effect) to retard crack propagation, they may also enhance crack propagation in some cases, as just explained. Extrinsic effects retarding crack propagation are again due to other types of imperfections, such as interfaces causing the crack to deviate or uncracked ligaments bridging it [16]. This clearly shows the importance of microstructure and a proper distribution of imperfections at all scales to control the properties of a material, be it a metal alloy or even a biological material, as discussed below. 3. Concepts of physical metallurgy that help in understanding biological materials It cannot be expected, of course, that concepts from physical metallurgy can be directly applied to the problems encountered in biological materials research. Chemical
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
composition and structural complexity are really very distinct in natural materials. Many of the imperfections presented in the last section are connected to the crystalline lattice of metals. Biological materials are characterized by a hierarchical structure with a variety of structural motifs on different length scales [17,18]. However, while the nature of the defects may be quite different in the two worlds, their function can sometimes be similar. The first example presented below shows that plasticity in some natural materials is not provided by dislocations but by special properties of biomacromolecules. 3.1. Defects and plasticity In some biological materials an alternative mechanism to dislocation motion leads to plastic deformation. Evidence has accumulated that plasticity (e.g. in bone and wood) is controlled by biomacromolecules which fulfill the function of a reversible glue [19–21]. A key element is the presence of both weak and strong bonds coupling these molecules [22]. A schematic example is shown in Fig. 2. Covalently bound polymeric chains are connected to each other by a second weaker bonding based, for example, on hydrogen bonds, electrostatic interactions or metal coordination bonds. To describe the principle it is best to imagine these bonds either linking parts of the same molecule to each other (case a in Fig. 2) or two neighboring molecules (case b in Fig. 2). In the first example the weak bonds stabilize a fold in the molecular backbone. Upon stretching the weak bonds break, with the consequence that removal of the backbone loop results in notable extension in the length of the molecule. A suggestive terminology describes
883
this effect as “hidden length” (e.g. in the form of folds), which is freed by breaking the weak “sacrificial bonds” [21,23]. The presence of sacrificial bonds leads to somewhat unusual material behavior: Firstly, the breaking of these bonds dissipates a large amount of energy before the breaking of covalent bonds affects the structural integrity of the molecule [21]. Secondly, the sacrificial bonds can slowly reform after unloading, which leads to full restoration of the mechanical properties of the material, sometimes referred to as “self-healing”. A striking example for such behavior is seen in byssal threads. Mussels use these threads to fasten themselves to the rocky seashore, so as not to be washed away by wave motion [24,25]. The protein making up this fiber contains relatively stiff parts similar to collagen. Other parts are crosslinked with Zn–histidine bonds, which are weaker than covalent bonds and serve as sacrificial bonds in deformation. Hence the byssal threads show pronounced yielding due to breaking of the sacrificial bonds. After load release the threads are initially soft and stiffen only after the sacrificial bonds reform, in about 24 h [24,26]. In the scenario sketched in Fig. 2b the sacrificial bonds connect different adjacent molecules. When the sacrificial bonds break the molecules slip with respect to each other and the reversible character of these sacrificial bonds allows the bonds to reform (compare the two sketches in Fig. 2b). With such a stick–slip mechanism the material can undergo large permanent plastic deformations. In tendon [27], bone [21] and wood [28] it has been proposed that glue-like layers of macromolecules (proteoglycans, phosphorylated proteins and hemi-celluloses, respectively) connect stiff structural elements through sacrificial bonds. In
Fig. 2. The behavior of biological macromolecules under external load. (a) The backbone of the molecule shown as a dark grey line has a loop held together by weak bonds depicted as light grey connections. Upon loading these sacrificial bonds break, freeing the “hidden length” which extends. Upon unloading spontaneous refolding of the molecule (as is typical for proteins) allows reformation of the bonds. (b) Sacrificial bonds on two adjacent macromolecules allow large irreversible deformation by a stick–slip mechanism (adapted from Aichmayer and Fratzl [31]).
884
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
bone these stiff elements are mineralized collagen fibers and in wood cellulose fibrils, the strength of the material being controlled by the geometric arrangement and size of these elements [29]. Sacrificing the bonds in the glue layer before the stiff elements break allows plastic flow and energy dissipation that increases the toughness of the biological composite [17]. The importance of spatial order as a design principle of sacrificial bonds has been illustrated in a simple model [30]. Divalent cations between two plates carrying negative point charges were used to model ion-mediated sacrificial bonds. When the negative charges were arranged on an ordered triangular lattice the total bonding between the plates was strong but brittle. When they were randomly distributed shearing of the two plates allowed a 300 times larger strain and the energy dissipated before failure was increased by a factor of 20 [30].
roughly six orders of magnitude from the enamel as the outer coating of the tooth to the soft “cushion” material between the tooth and the jaw bone [32]. Gradients in the material properties are implemented in the enamel–dentine [40] and dentine–cementum junctions. iv. Interfaces that allow material movement. In plants, tissues can be found which swell with changes of humidity. When tissues with different rates of swelling are bonded together by a tight interface humidity changes result in shape changes of the overall organ [41]. A well-known example is found in the scales of the pine cone [42] (Fig. 3), which are bilayers of parallel and perpendicular oriented tissues. These layers shrink differently upon drying, resulting in bending and an opening of the cone, in a movement akin to that found in bimetallic strips.
3.2. The role of interfaces 3.3. Precipitation and nanocomposites Interfaces, seen as two-dimensional imperfections, influence the properties of biological materials in diverse ways which we are only beginning to be understood. Interfaces are used by nature as a powerful tool to control material function through the expenditure of only small amounts of material. If energy and other resources have to be invested interfaces are efficient places to expend them. In a recent article interfaces in biological materials were classified as follows according to their function [32]. i. Interfaces that enhance the fracture resistance of brittle materials by deviating or stopping cracks. One of the most studied biological materials of this type is nacre [33–36], which has a bricks and mortar structure with bricks made of stiff but brittle calcium carbonate and the mortar consisting of soft proteins (Fig. 3). Another example of this design principle is the glass sponge Euplectella [37], in which a small amount of proteinaceous material (less than 1% of the overall material) forming “glue layers” less than 10 nm thick is sufficient to improve the fracture resistance 2.5 times. ii. Interfaces that enable deformation. A possibility discussed in the previous section is providing plasticity via “Velcro-like” debonding and rebonding. An alternative design is realized in sutures [38], as found in, for example, the shell of the red-slider turtle [39]. The shell is essentially the rib cage in which the ribs have intergrown and interdigitate at the joint or suture. This suture is filled with a soft matrix which provides structural flexibility to the shell as long as the strains are small (Fig. 3). For larger deformations the bony elements interlock leading to a stiffening of the shell. iii. Interfaces joining materials with a high contrast in material properties. Fig. 3 shows schematically the example of a tooth, where the stiffness changes over
Biological materials that have to fulfill a mechanical function are virtually all composites [43], with the component dimensions typically in the nanometer range. In bone a staggered arrangement of stiff nanoscopic mineral platelets in a tough organic matrix results in a composite, combining the often conflicting properties of high stiffness and toughness [29]. A classical pathway used by nature to obtain nanocomposites is to nucleate and grow a mineral phase, often within a preformed matrix. Even for crystalline materials, in which there seems little space left for modification, the living world is forcing us to rethink our concepts. Biogenic single crystals may not be faceted as are geogenic ones, but display curved surfaces at different length scales [44]. The shapes of biogenic crystals seem without limitation, as demonstrated by the marvelous skeletal elements made from calcite in the brittle star [45]. The interaction with biomolecules not only controls the shape of crystals but also the size of, for example, iron oxide particles in magnetotactic bacteria [46]. Biogenic crystals usually contain many more impurities, and even macromolecules can be occluded within the crystals [47– 49]. As a result the degree of order is much lower in biogenic crystals. Taking the sea urchin spicule as an example, calcite has perfectly crystalline domains about 150 nm in size, compared with 1 mm in geogenic crystals [50]. This degree of imperfection has strong implications for the properties of the minerals. Most obvious are the different ways of fracture: instead of a fracture along cleavage planes, the fracture surface of the biogenic crystal is rough, which increases the mineral toughness. As demonstrated in bone, some nanoscale biogenic crystals can also be strained to a much higher degree before mechanical failure [51]. Not only the final product but also the crystallization pathway are significantly different in living organisms [44]. Firstly, crystallization occurs at ambient temperatures. Secondly, disordered precursor phases seem to be a
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
885
Fig. 3. Different functionalities of interfaces in biological materials. (i) The thin organic layer between mineral plates in nacre improves the fracture resistance. (ii) In the turtle shell the interdigitating bone structure and infilling of the suture with soft material allow small deformations but prevent larger ones. (iii) In teeth materials of different stiffness are bonded together as material gradients, with the stiffest, enamel (white), on the top, then dentin (light grey) and then cementum (dark gray layer covering the roots of the tooth). The tooth is anchored in the jaw by ligaments. (iv) The scales of the pine cone consist of layers with different swelling properties leading to opening and closing of the cone on changes in humidity.
widely used strategy in biogenic crystallization [52]. These precursor minerals form within vesicles in cells. In some cases crystals remains within the cell, such as the guanine crystals responsible for iridescence in fish skin or spider cuticle [44]. When mineralization occurs outside the cell the amorphous phase may be transported within a vesicle to the site of crystallization. In the sea urchin larval spicules a preformed small crystal is used as a template for crystallization via secondary nucleation of the arriving mineral. However dissolution of the precursor phase and reprecipitation outside the cell are also possible [53]. Not only nucleation but also crystal growth are biologically controlled. Macromolecules play an important role in stopping crystal growth in specific crystal orientations [54,55]. Molecular scaffolds such as collagen fibrils are also important in the nucleation of mineral in bone [56]. In an in vitro experiment it was shown that a supersaturated solution of calcium phosphate together with an inhibitor of nucleation outside the collagen fibril is sufficient to obtain a mineralized collagen fibril with nanosized crystal particles [57]. In vitro experiments challenge the classical picture of nucleation as taking place in a supersaturated solution of ions by the stochastic formation of a critical nucleus. The size of the nucleus is given by the balance between the gain in bulk energy and the loss in surface energy. In contrast to the classical view it was demonstrated that even an undersaturated solution of calcium carbonate contains stable
pre-nucleation ion clusters. According to this view crystal growth takes place through coalescence of such clusters [58]. Diffusion and coalescence of nanosized inclusions has also been discussed as a possibility for the growth of precipitates in alloys [59,60] and indirectly shown experimentally [61]. Nature extends the idea of composites beyond a difference in chemical composition between matrix and inclusions. By manipulating the molecular bonding, even with the same chemistry, a contrast of properties between matrix and inclusions can be obtained. To protect against abrasion the cuticle of the byssal threads of mussels (already mentioned above) has to be hard, but should not compromise the high extensibility of the threads. Fig. 4 shows the microstructure of the cuticle, consisting of stiff granules in a soft matrix [62]. The granules consist of regions enriched in Fe3+-mediated crosslinks within the protein in the thread cuticle. Deformation localizes in the soft matrix between the granules upon stretching. The high abrasion resistance of the cuticle is thought to occur via granule–granule contacts resisting compression. 3.4. Phase transformations The concept of phase transformations, in particular diffusionless transformations, has been evoked in biological materials research. A remarkable example, in which even
886
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
Fig. 4. In the schematic a mussel attaches itself to a rock via several byssal threads. The scanning electron micrograph below shows the composite character of the thread cuticle with stiff granules embedded in a soft matrix (Image courtesy of M. Harrington). The contrast in properties is due to a difference in crosslinks via metal coordination bonds (right). On loading beyond a strain of 30% microcracks form in the matrix, while in the granules crosslink coordination bonds start to break. These sacrificial bonds in the granules can reform once the loading is reduced. The right-hand side of this figure is reprinted from Harrington et al. [62], reprinted with permission of the AAAS.
the matrix of lattice-distortive strains were reported [63,64], is the contraction of the tail sheath of bacteriophage. Bacteriophage T4 (Fig. 5) is a virus that attaches to and inserts its viral DNA into a bacterium. Its tail consists of two concentric cylinders, the smaller tail tube providing the channel for DNA transport, the larger tail sheath providing the force to penetrate the membrane of the bacterium. The force is generated by a dramatic shape change of the tail sheath. The sheath consists of a periodic arrangement of globular proteins forming a two-dimensional protein crystal (Fig. 5), which rolls up to form the cylindrical sheath. Sheath contraction is the result of shear-dominant lattice distortion (Fig. 5, right), which strikingly resembles a martensitic phase transformation [63]. As a result the sheath contracts irreversibly to roughly one-third of its original length and increases its diameter by a factor of two. The kinetics of the contraction process is well understood using a thermodynamic description from physical metallurgy. The protein crystal, originally grown on the so-called base plate of the virus, is in a metastable state in its extended form. Upon contact with a bacterium the base plate changes shape, thereby creating the necessary strains to induce nucleation of a new crystal phase in the sheath. Models have been proposed for how the interface between the extended and the contracted phase moves up the sheath under conservation of the coherency of the lattice [63,64]. In recent studies a phase transformation in a biopolymeric material used for encapsulation was investigated
[65,66]. Living in a wave swept marine environment, the whelk egg capsule has a protective function. A structural phase transition of the egg capsule tissue was observed upon stretching. This transition does not occur in a gradual way, but via the coexistence of a low strain phase (based on a helical conformation of the protein) and a high strain phase (corresponding to an extended conformation). In the coexisting phases the amount of the high strain phase gradually increases, in complete analogy to the Gibbs double tangent construction in classical phase transitions in solids, such as pseudoelastic metals, e.g. Ni–Ti (Fig. 6). In the strain region between the energy minima of the two phases the energy density is minimized by the double tangent, where the slope corresponds to the yield stress ry at which the transition occurs. As demonstrated in the schematic plot of molecular strain versus stress (Fig. 6, bottom), yield begins with the unfolding of discrete domains in the low strain phase due to breaking of the hydrogen bonding network. This transition occurs at constant stress (estimated as ry = 6.7 MPa), where with increasing strain the volume fraction of the extended high strain phase increases [65]. 3.5. Adhesion problems There is a remarkable range of tools that living systems use to attach themselves to different surfaces in both reversible and permanent ways. On the one hand, there are per-
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
Fig. 5. The two configurations of a virus in contact with a bacterium. The bacteriophage settles on the bacterium with its tail sheath in an uncontracted state. The two-dimensional lattice of proteins is shown below. Triggered by a configurational change in the lower part (the socalled base plate) a new contracted phase nucleates and extends over the whole sheath. In full contraction the length of the sheath is reduced to approximately one-third of the original length. The force generated by contraction is used to penetrate the bacterial membrane to channel the viral DNA into the bacterium (inspired by Olson and Hartman [63]).
887
manent adhesives, such as the chemical adhesives used in the plaque of the mussel byssus threads [68,69] and in the combined physical and chemical adhesion mechanisms used by the English ivy [70]. Of particular interest for bioinspired adhesives are the species that can attach themselves in a reversible manner to a substrate using appendages covered with many fine hairs or setae [67,71,72]. Although some species secrete fluids that improve adhesion via capillary action, species with “dry feet” use van der Waals-mediated adhesion, which seems to increase in strength with increasing setae density. One hypothesis, contact splitting, uses an extended Hertz theory to show that the pull-off force of a given set of setae scales with length, e.g. the contact radius, not the area, meaning that dividing a given adhesive area into many smaller parts should result in increased adhesive forces [67]. A subsequent interpretation of the scaling law is that pull-off forces increase with increasing peeling length, which in turn scales with setae density [73]. Despite the different modeling details, a consequence of both models is that it would be expected that larger animals would have higher setae densities [67,73]. Although such a general relation is indeed seen in the data (Fig. 7), a more detailed study, taking phylogenetic relationships between species into account, showed that there is no significant scaling within a given group of closely related taxa [74]. This highlights that although tools from materials science can be used to understand the material properties of biological systems and indeed inspire the development of novel reversible dry
Fig. 6. Schematic plots of the phase transition in the egg capsule biopolymeric material of whelks from the unstretched a-phase to the extended b-phase [65]. Yield occurs when domains in the a-phase start to unfold. The energy minimum is then giving by the common tangent to the energy density curves of the two phases. The tangent corresponds to the state of constant stress. At this stress both phases coexist. Only after full transformation to the b-phase does the stress again start to increase with strain.
888
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889
Fig. 7. The area density of attachment pads as a function of body mass for a selection of different animal species, showing a trend of increasing density with size. Redrawn with permission from Arzt et al. [67], Ó 2003 National Academy of Sciences of the USA.
adhesives [75], one needs to take note of the relatedness of species if conclusions about evolution are to be made. 4. Conclusions Some of the examples shown in this article demonstrate how ideas derived from physical metallurgy may contribute to an understanding of biological materials. Indeed, the roles of structural imperfections in tuning material properties were recognized early on by metallurgists and their description was transformed into a quantitative science. The idea that defects may be beneficial to the macroscopic properties of materials, providing plasticity and slowing down cracks, is a central theme of physical metallurgy. Approaches of this kind also turned out to be useful in describing some aspects of the structure and properties of natural materials. Of course, this viewpoint also has its limits. First, nature primarily uses polymers based on proteins or polysaccharides and several minerals to create composite materials chemically quite different to those common in engineering. Even more important, natural materials cannot be understood without their biological context, which defines the functions and requirements of these materials. Hence, research on biological materials is always first and foremost biological research, even if it takes its inspiration and methodologies from physics or materials science [76]. The successful description of structure–property relations in biological materials has become common in recent years, mainly because research teams with mixed backgrounds from biology to materials science have been put together in a number of universities and research institutions. This has gradually led to materials science concepts infiltrating the biological sciences, to the point that it has now became customary in the context of biological systems to talk about the elastic modulus, interface failure or fracture toughness. The examples in this article demonstrate
that ideas borrowed from physical metallurgy and materials science are more than just an analogy to phenomena observed in biomaterials research; they are gradually becoming part of the arsenal in the biological sciences. Conversely, there is much to learn from biological materials in the way exceptional properties may arise from a suitable combination of comparatively poor components. This is primarily due to the complex, often hierarchical structure of biological materials, assembled by growth following a recipe stored in the genes, rather than being fabricated according to an exact design [77]. Thus the study of structure–property relations in biological materials is increasingly seen as a source of inspiration for the development of new classes of materials with adaptive, self-healing or multifunctional properties [11,78,79]. In particular, the role of the geometry and architecture of hierarchical materials in the multifunctional behavior of composites has become a promising avenue for the development of new materials [80]. Indeed, the hierarchical structure of biological materials allows them to be adapted to their function at various length scales [77]. It must be highlighted, however, that bioinspired materials research is not conceivable without input from the biological sciences, since the function of any natural material cannot be known without taking into account the context of the living organism. Biological materials science is a new field developing in the area between the use of materials concepts in the description of biological organisms and the extraction of natural building principles for the benefit of the materials community. Biological materials may not have the perfection of diamonds, but they are gems worth being studied by biologists and by materials scientists and, at best, by the two together. Acknowledgements The authors are grateful to many colleagues and collaborators in particular, Barbara Aichmayer, Michaela Eder, Damien Faivre, Matthew Harrington, Yael Politi and Wolfgang Wagermaier. We acknowledge the Humboldt Foundation for supporting the visit of YB to Potsdam through the Gay-Lussac-Humboldt Award and support through the Leibniz prize of PF running under DFG contract number FR2190/4-1. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Gee H, Howlett R. Nature 2009;457:807. Sugden A, Ash C, Hanson B, Zahn L. Science 2009;323:727. Frost HM. Anat Rec 1987;219:1. Mattheck C. Design in nature: learning from trees. Berlin: SpringerVerlag; 1998. Taylor D, Hazenberg JG, Lee TC. Nat Mater 2007;6:263. Peterlik H, Roschger P, Klaushofer K, Fratzl P. Nat Mater 2005;5:52. Currey JD. Bones – structure and mechanics. Princeton, NJ: Princeton University Press; 2002. Koester KJ, Ager JW, Ritchie RO. Nat Mater 2008;7:672. Fratzl P. Nat Mater 2008;7:610.
R. Weinkamer et al. / Acta Materialia 61 (2013) 880–889 [10] Dyskin AV, Estrin Y, Kanel-Belov AJ, Pasternak E. Adv Eng Mater 2001;3:885. [11] Munch E, Launey ME, Alsem DH, Saiz E, Tomsia AP, Ritchie RO. Science 2008;322:1516. [12] Robinson W. Philos Trans R Soc Lond B 1921;210:49. [13] Haasen P. Physical metallurgy. Cambridge: Cambridge University Press; 1996. [14] Fratzl P, Penrose O, Lebowitz JL. J Stat Phys 1999;95:1429. [15] Kostorz G. Phase transformations in materials. Weinheim: WileyVCH; 2001. [16] Ritchie RO. Nat Mater 2011;10:817. [17] Fratzl P, Weinkamer R. Prog Mater Sci 2007;52:1263. [18] Meyers MA, Chen PY, Lin AYM, Seki Y. Prog Mater Sci 2008;53:1. [19] Currey J. Nature 2001;414:699. [20] Thompson JB, Kindt JH, Drake B, Hansma HG, Morse DE, Hansma PK. Nature 2001;414:773. [21] Fantner G, Hassenkam T, Kindt JH, Weaver JC, Birkedal H, Pechenik L, et al. Nat Mater 2005;4:612. [22] Keten S, Xu ZP, Ihle B, Buehler MJ. Nat Mater 2010;9:359. [23] Fantner GE, Oroudjev E, Schitter G, Golde LS, Thurner P, Finch MM, et al. Biophys J 2006;90:1411. [24] Harrington MJ, Gupta HS, Fratzl P, Waite JH. J Struct Biol 2009;167:47. [25] Vaccaro E, Waite JH. Biomacromolecules 2001;2:906. [26] Carrington E, Gosline JM. Am Malac Bull 2004;18:135. [27] Puxkandl R, Zizak I, Paris O, Keckes J, Tesch W, Bernstorff S, et al. Philos Trans R Soc Lond B 2002;357:191. [28] Keckes J, Burgert I, Fruhmann K, Muller M, Kolln K, Hamilton M, et al. Nat Mater 2003;2:810. [29] Gao HJ, Ji BH, Jager IL, Arzt E, Fratzl P. Proc Natl Acad Sci USA 2003;100:5597. [30] Hartmann MA, Fratzl P. Nano Lett 2009;9:3603. [31] Aichmayer B, Fratzl P. Phys J 2010;9:33. [32] Dunlop JWC, Weinkamer R, Fratzl P. Mater Today 2011;14:70. [33] Okumura K, de Gennes PG. Eur Phys J E 2001;4:121. [34] Barthelat F, Espinosa HD. Exp Mech 2007;47:311. [35] Wang RZ, Gupta HS. Annu Rev Mater Res 2011;41:41. [36] Jackson AP, Vincent JFV, Turner RM. Proc R Soc Lond B 1988;234:415. [37] Aizenberg J, Weaver JC, Thanawala MS, Sundar VC, Morse DE, Fratzl P. Science 2005;309:275. [38] Li YN, Ortiz C, Boyce MC. Phys Rev E 2011:84. [39] Krauss S, Monsonego-Ornan E, Zelzer E, Fratzl P, Shahar R. Adv Mater 2009;21:407. [40] Zaslansky P, Friesem AA, Weiner S. J Struct Biol 2006;153:188. [41] Burgert I, Fratzl P. Philos Trans R Soc A 2009;367:1541. [42] Dawson C, Vincent JFV, Rocca A-M. Nature 1997;390:668. [43] Dunlop JWC, Fratzl P. Annu Rev Mater Res 2010;40:1. [44] Weiner S, Addadi L. Annu Rev Mater Res 2011;41:21. [45] Aizenberg J, Tkachenko A, Weiner S, Addadi L, Hendler G. Nature 2001;412:819. [46] Faivre D, Schuler D. Chem Rev 2008;108:4875.
889
[47] Pokroy B, Quintana JP, Caspi EaN, Berner A, Zolotoyabko E. Nat Mater 2004;3:900. [48] Gilow C, Zolotoyabko E, Paris O, Fratzl P, Aichmayer B. Cryst Growth Des 2011;11:2054. [49] Weiner S, Addadi L. J Mater Chem 1997;7:689. [50] Berman A, Hanson J, Leiserowitz L, Koetzle TF, Weiner S, Addadi L. Science 1993;259:776. [51] Gupta HS, Seto J, Wagermaier W, Zaslansky P, Boesecke P, Fratzl P. Proc Natl Acad Sci USA 2006;103:17741. [52] Addadi L, Raz S, Weiner S. Adv Mater 2003;15:959. [53] Sone ED, Weiner S, Addadi L. J Struct Biol 2007;158:428. [54] Mann S. Biomineralization – principles and concepts in bioinorganic chemistry. Oxford: Oxford University Press; 2001. [55] Xu AW, Ma YR, Colfen H. J Mater Chem 2007;17:415. [56] Landis WJ, Silver FH, Freeman JW. J Mater Chem 2006;16: 1495. [57] Nudelman F, Pieterse K, George A, Bomans PHH, Friedrich H, Brylka LJ, et al. Nat Mater 2010;9:1004. [58] Gebauer D, Volkel A, Colfen H. Science 2008;322:1819. [59] Fratzl P, Penrose O. Phys Rev B 1997;55:R6101. [60] Weinkamer R, Fratzl P. Europhys Lett 2003;61:261. [61] Stadler LM, Sepiol B, Weinkamer R, Hartmann M, Fratzl P, Kantelhardt JW, et al. Phys Rev B 2003;68. [62] Harrington MJ, Masic A, Holten-Andersen N, Waite JH, Fratzl P. Science 2010;328:216. [63] Olson GB, Hartman H. J Phys 1982;43:855. [64] Falk W, James RD. Phys Rev E 2006:73. [65] Harrington MJ, Wasko SS, Masic A, Fischer FD, Gupta HS, Fratzl P. J R Soc Interface 2012;9:2911. [66] Miserez A, Wasko SS, Carpenter CF, Waite JH. Nat Mater 2009;8:910. [67] Arzt E, Gorb S, Spolenak R. Proc Natl Acad Sci USA 2003;100:10603. [68] Lin Q, Gourdon D, Sun CJ, Holten-Andersen N, Anderson TH, Waite JH, et al. Proc Natl Acad Sci USA 2007;104:3782. [69] Lee H, Scherer NF, Messersmith PB. Proc Natl Acad Sci USA 2006;103:12999. [70] Melzer B, Steinbrecher T, Seidel R, Kraft O, Schwaiger R, Speck T. J Roy Soc Int 2010;7:1383. [71] Kwak MK, Pang C, Jeong HE, Kim HN, Yoon H, Jung HS, et al. Adv Funct Mater 2011;21:3606. [72] Meyers MA, Chen PY, Lopez MI, Seki Y, Lin AYM. J Mech Behav Biomed Mater 2011;4:626. [73] Varenberg M, Pugno NM, Gorb SN. Soft Matter 2010;6:3269. [74] Peattie AM, Full RJ. Proc Natl Acad Sci USA 2007;104:18595. [75] Kwak MK, Jeong HE, Suh KY. Adv Mater 2011;23:3949. [76] Fratzl P, Barth FG. Nature 2009;462:442. [77] Fratzl P. J Roy Soc Int 2007;4:637. [78] Hager MD, Greil P, Leyens C, van der Zwaag S, Schubert US. Adv Mater 2010;22:5424. [79] Ortiz C, Boyce MC. Science 2008;319:1053. [80] Ashby MF, Brechet YJM. Acta Mater 2003;51:5801.