Über die Autorin bzw. den Autor

Julian Vincent, a biologist with a long-standing interest in engineering, is Honorary Professor of Biomimetics in the Department of Mechanical Engineering at Bath University and Special Professor in the Faculty of the Built Environment at Nottingham University.

Von der hinteren Coverseite

"With this revision, this book should continue its thirty-year role as a unique resource. No other so squarely faces the mechanical interrelationships between structure and the functions of the materials of which we--and all other life--are made. The new edition adds a much-enriched set of references and an uncommonly sensible chapter on biomimetics."--Steven Vogel, professor emeritus, Duke University

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Structural Biomaterials

PRINCETON UNIVERSITY PRESS

Contents

Preface....................................................................viiCHAPTER ONE Basic Elasticity and Viscoelasticity..........................1CHAPTER TWO Proteins......................................................29CHAPTER THREE Sugars and Fillers..........................................61CHAPTER FOUR Soggy Skeletons and Shock Absorbers..........................84CHAPTER FIVE Stiff Materials from Polymers................................116CHAPTER SIX Biological Ceramics...........................................143CHAPTER SEVEN Implementing Ideas Gleaned from Biology.....................178References.................................................................205Index......................................................................223

Chapter One

In the physically stressful environment there are three ways in which a material can respond to external forces. It can add the load directly onto the forces that hold the constituent atoms or molecules together, as occurs in simple crystalline (including polymeric crystalline) and ceramic materials—such materials are typically very rigid; or it can feed the energy into large changes in shape (the main mechanism in noncrystalline polymers) and flow away from the force to deform either semipermanently (as with viscoelastic materials) or permanently (as with plastic materials).

1.1 Hookean Materials and Short-Range Forces

The first class of materials is exemplified among biological materials by bone and shell (chapter 6), by the cellulose of plant cell walls (chapter 3), by the cell walls of diatoms, by the crystalline parts of a silk thread (chapter 2), and by the chitin of arthropod skeletons (chapter 5). All these materials have a well-ordered and tightly bonded structure and so broadly fall into the same class of material as metals and glasses. What happens when such materials are loaded, as when a muscle pulls on a bone, or when a shark crunches its way through its victim's leg?

In a material at equilibrium, in the unloaded state, the distance between adjacent atoms is 0.1 to 0.2 nm. At this interatomic distance the forces of repulsion between two adjacent atoms balance the forces of attraction. When the material is stretched or compressed the atoms are forced out of their equilibrium positions and are either parted or brought together until the forces generated between them, either of attraction or repulsion, respectively, balance the external force (figure 1.1). Note that the line is nearly straight for a fair distance on either side of the origin and that it eventually curves on the compression side (the repulsion forces obey an inverse square law) and on the extension side. With most stiff materials the extension or compression is limited by other factors (see section 1.6) to less than 10% of the bond length, frequently less, so that the relationship between force and distance is essentially linear. When the load is removed, the interatomic forces restore the atoms to their original equilibrium positions.

It is a fairly simple exercise to extend this relationship to a material such as a crystal of hydroxyapatite in a bone. This crystal consists of a large number of atoms held together by bonds. The behavior of the entire crystal in response to the force is the summed responses of the individual bonds. Thus one arrives at the phenomenon described by Hooke as ut tensio, sic vis, "as the extension, so the force." In other words, extension and force are directly and simply proportional to each other, and this relationship is a direct outcome of the behavior of the interatomic bond. However, when one is dealing with a piece of material it is obvious that measurements cannot conveniently be made of the interatomic distance (though they have been made using X-ray diffraction, which confirms the following). What is actually measured is the increase in length of the whole sample or a part of the sample (making the verifiable assumption that in a homogeneous material one part will deform as much as the next). This difference is then expressed as a function of the starting length called the strain, ε. Strain can be expressed in a number of ways, each offering certain advantages and insights into the processes of deformation. The most commonly encountered form is conventional, nominal, engineering, or Cauchy strain, which is the increase in length per unit starting length:

ε_ITLITL = Δl/L₀ [Eq. 1.1]

This estimate of extension works well if the material is extended by no more than a tenth of its starting length. Strain is expressed either (as in this text) as a number (e.g., 0.005) or as a percentage (e.g., 0.5%).

The force acting on each bond is a function of the number of bonds available to share the load. Thus if the area over which the force acts is doubled, then the load carried by each bond will be halved. It is therefore important, if one is to bring the data to the (notionally) irreducible level of the atomic bond, to express the force as a function of the number of bonds that are responding to it. In practice this means expressing the force as force divided by the area across which the force is acting, which is called the stress, σ:

σ = f/A₀ [Eq. 1.2]

However, just as with strain, this simple equation is suitable only for small extensions.

In SI units, the force is expressed in newtons (a function of mass and the acceleration due to gravity: one newton is approximately the force due to 100 g, which can be produced by an average apple falling under the influence of gravity), the area in square meters. One newton acting over an area of one square meter is a pascal (Pa). Other units are in use in many parts of the world. For instance, in the United States the unit of force is the dyne (the force exerted by one gram under the influence of gravity), and the unit of area is the square centimeter. One dyne per square centimeter is one hundred-thousandth (10^-5) of a pascal. Traditional engineers in Britain often use pounds and square inches as their measures of "force" and area.

The slope of the straight, or Hookean, part of the curve in figure 1.1 is characteristic of the bond type and is a function of the energy of the bond. For the same reason, the ratio of stress to strain is a characteristic of a material. This ratio is the stiffness or Young's modulus, E:

E = σ/ε. [Eq. 1.3]

The units of E are the same as for stress, since strain is a pure number. Graphs showing the relationship between stress and strain are conveniently plotted with the strain axis horizontal and the stress axis vertical, irrespective of whether the relationship was determined by stretching the test piece in a machine and recording the developed forces or by hanging masses onto the test piece and recording the extension. Do not be surprised if it takes a long time for the mental distinctions between stress and strain to become totally clear. Not only are the concepts surprisingly difficult to disentangle, but the confusion is compounded by their uncritical use in everyday speech.

One other characteristic of Hookean materials is that they are elastic. That is to say, they can be deformed (within limits) and will return to their original shape almost immediately after the force is removed...