Material
Elastic
Modulus (GPa)
Tensile
Strength (GPa)
Compressive
strength (GPa)
       
Carbon nanotube
1300
14
 
Diamond
1200
   
Nickel-steel alloy
  1.4-1.6
 
Stainless steel
211
0.49-1.1
 
Malleable iron
200
0.345
 
Titanium
116
0.220
 
Copper
130
0.210
 
Gold
78
0.120
 
Hard rolled
aluminium-bronze
  0.26
 
Annealed aluminium
  0.059
 
Glass-fibre reinforced
concrete
15
  0.079
       
Bone
20
0.133
0.193
Collagen
2
0.1
 
Elastin
0.002
0.002
 
keratin (hair)
2.4
0.2
 
Silk
5-10
0.3-0.6
 
       
Rubber
0.01
0.017
 
Oak wood
11
0.109
0.043
Hornbeam wood
  0.153
0.054
Willow wood
  0.083
0.026
Ebony wood
    0.089
Balsa wood
  0.073
0.008

Elastic modulus (Young's modulus) is, despite the name, a measure of stiffness. A material with a very high
elastic modulus, like diamond, is a very stiff material - it is hard to pull or push it out of shape. A material like
rubber with a very low elastic modulus is easy to deform, but it is elastic and so easily springs back into shape.
For this reason rubber makes good bouncy balls! Natural rubber is produced by rubber trees.

What is GPa? A Pascal (Pa) is a unit of measure of pressure (as is millimetres of mercury or pounds per square
inch) equal to Newtons per square metre, where a Newton is a measure of force, similar to pound in pounds per
square inch (psi). If I were to stand on your back then my feet would exert a force of about 900 Newtons or a
pressure of about 25 000 Pa, which would feel uncomfortable. A gigapascal, GPa, is one thousand million
pascals. A typical elephant weighs 3.5 tonne (3500 kg) and exerts a force, due to its weight alone, of about 35
000 Newtons when stood still. If an elephant had two small feet like a human, then it would exert a pressure of
about 1 000 000 Pa or 1 MPa (a megapascal, MPa, is a million pascals) on the ground, and would promptly sink
whenever it rained! Fortunately, elephants have big splayed-out feet to spread this force over a wider area,
and thus lowering the pressure on the ground. The Eiffel Tower was built on similar principles. It splays out at
the bottom, spreading its weight out so much that it puts very little pressure on the floor. It could easily be held
up by enough people underneath it (allegedly, I seem to remember working it out once and agreeing). Similarly
a scorpion light battle tank can drive over a swamp in which a man would sink, even though the tanks weighs
several tonnes! Its tracks spread the weight out over a very large area.

The third column in the table shows us the
tensile strength of several materials in GPa and the fourth column
shows us
compressive strength in GPa. How would I measure the strength of say a piece of wood? There are
many ways in which to measure strength. I could try to pull the piece of wood apart (that is apply tension to it), I
could try to squeeze it in (apply compression to it) or I could try to twist it (apply torsion to it), I could bend it, or I
could hit it with something like a sharp steel axe (which is a measure of its hardness, because steel is harder
than wood, the axe cuts the wood) or I could measure how brittle it is by striking it hard with a hammer. All these
are useful measures of strength, but every material will fair better in one test than another. For example, I might
bend a steel bar, but I would be hard-pushed to pull it apart into a long wire, like a piece of blue-tac! Diamond is
much harder than steel and will cut steel, but diamond is more brittle and may shatter if struck hard.

The first thing to note is that no matter what measure I used, the strength will depend upon the amount of
material present! I might bend a steel wire easily, but a two metre cubic slab of iron, weighing some 60 tonnes,
would be difficult to bend! However, if I first used a machine to draw the slab out into a thin wire, then there is
no problem, even if the wire weighs the same as the slab did to start with. Thus, it is not so much the mass of
material that matters, but the cross-sectional area. If I cut across a one millimetre wire, then the surface area of
the cut face will be just under one square millimetre (the surface area of a circle = Pi times the square of the
radius,since Pi = 3.14, this gives 3.14 x (0.5 mm x 0.5 mm) = 0.79 square mm), so there wasn't much material
there to stop me bending it, but the cube of iron which was 2 metres by 2 metres by 2 metres, will have a
cross-sectional area 4 square metres (the area of a square = width x height, which gives us 2 m x 2 m = 4
square m) which explains why I could not bend it!

The bottom line is that when I measure the strength of a material I have to know:

1. What measure of strength I am using, e.g. tension or compression.        
2. How much material is present (cross-sectional area).
3. How much force was needed to break the material.

By 'break the material' I really mean to cause it to fail to maintain its structure well enough to do its job. A piece
of chewing-gum does not suddenly snap, but rather it starts to stretch first. The point at which it stretches
noticeably will be the point at which it has failed to resist the force. A lump of concrete, on the other hand, will
suddenly fracture and show very little stretching.

So why GPa? Well, pressure is force per unit area, e.g. pounds per square inch. In this case we are talking
about cross-sectional area. For example, according to the table, it takes as much as 1.1 GPa to pull a stainless
steel wire apart, but wait a minute, how thick is the wire? Well, 1.1 GPa means 1.1 thousand million Newtons per
square metre. Thus, it takes a force of about 1.1 thousand million Newtons (equivalent to about one hundred
million kilograms, dividing Newtons by 10 gives you kg approximately) to pull apart a wire one metre in
cross-section (area = Pi x radius squared, for a circular wire, giving the wire a radius of  56 cm, or a diameter of
112 cm) - that's a very thick wire! In practise engineers might measure this on a bar of steel one centimetre
thick, but to compare this to say a plank of wood 10 cm thick, they scale everything up into one square metre
and quote the result as GPa or MPa. (One MPa or megapascal = one million Pascals).

Example: a steel wire with a cross-sectional area of one square cm, that's 0.0001 square metres, since there
are 100 cm in one metre and 100 x 100 = 10000 square cm in one square m (this wire will have a diameter just
over 1 cm) requires (1.1 GPa x 0.0001m = 0.00011 Newtons = 0.11 N = 110 N = 110 000 N) 110 000 Newtons
of force to break it.
Dividing by ten, this means that such a wire could hold 11 000 kg dangling from it, that's
about three of our elephants!

Our elephants have just discovered that steel is very strong in tension! However, an elephant could easily bend
such a steel bar by standing on it, because steel is much weaker at resisting bending. In fact, steel is also
weaker in compression and so more easily squashed out of shape. An elephant would have no problem
squashing a steel frame on an old car!

So, steel ropes can support a lot of weight in tension, but steel structures tend to bend and buckle, and may
even do so under their own weight because steel is so heavy. We could build an Eiffel Tower like structure with
a minimum of weight (it is mostly empty space!) and arrange the steel rods so that they are under tension
rather than being squashed, but how would we build a large office block?

Let's think about concrete. Concrete is not very good under tension, it tends to crumble, but concrete has a
very high compressive strength. Indeed, most stony materials do, think about the marble columns that held up
those ancient Greek temples for so long. Stone doesn't resist bending very well, so they had to keep those
columns straight! Well, we could use concrete for our office block, so that it does not buckle under its own
weight like steel may, but that still leaves us with a problem. When our building sways in the wind it starts to feel
the pull and it will eventually crumble. The solution is steel reinforced concrete. We use a frame of steel rods
under tension embedded in a concrete matrix to resist compression, and now we have a strong building!

Wow! That was heavy! So what does all this have to do with biomaterials? Lots! A great big oak tree has to
support its heavy body and when its branches are covered by snow then it has a huge weight to support. In
gale force winds, the branches, especially if they have lots of leaves, start to feel the drag and the tree gets
bent about and put under tension too. Trees have to be enormously strong to survive. If they were made of
concrete they would crumble, if made of steel then they would bend out of shape. Nature has to be smarter
than this and her solution is a complex and elegant one which easily rivals modern engineering.

Here is part of the solution - choice of material. First, a tree has to be able to support its own weight. Look at
the wood for the hornbeam tree in the table. Hornbeams are so named because their wood is hard and
resilient, and has been used for the chopping boards that butchers use. You will see that its tensile strength is
comparable to that of a strong metal, whilst its compressive strength is similar to that of one of the strongest
concretes - glass-fibre reinforced concrete. Look at ebony wood; ebony trees are renown for the strength and
hardness of their wood. One can wear out many axes chopping down ebony trees! See how high its
compressive strength is. Nature uses what engineers call
high-performance materials, i.e. materials that are
very strong.

It should be noted than measurements of strength on natural materials are often underestimates, since these
materials lose strength when they are dead and dry. A dead and dry old bone is only about a tenth of its
strength when alive, so engineers have to be very careful to prepare fresh materials correctly. However, you
might have noticed that the strongest steels, which are enormously strong in tension, are still stronger than
wood. However, wood has a much greater advantage for trees...

Answer: it is very light! The density of a material is how much mass or weight it packs into a given volume.
Water has a density of one gram per cubic cm, so one ml of water, which is the same as one cubic cm of water,
weighs one gram (1g) and one litre of water (1L = 1000 ml) weighs 1000g or 1kg and one cubic metre of water
(one cubic metre = 100 x 100 x 100 = 1 000 000 ml) weighs 1000 kg or one tonne.

We shall refer to the densities of materials relative to water, so iron, which has a density of 7.87 g per cubic
centimetre, has a relative density of 7.87, that is iron is almost eight times as dense as water, so that the same
volume of iron weighs eight times more than water. The (relative) density of oak wood varies between 0.32 and
0.93. So it is that one cubic metre of wood weighs less than one cubic metre of water and much less than one
cubic metre of iron. Perfect! That means that our tree can be huge without having to worry about holding up its
own weight!

What about willow trees? The biomaterials table above gives values of tensile strength (0.083 GPa) and
compressive strength (0.026 GPa) that were only about half those of hornbeam wood (0.153 GPa and 0.054
GPa respectively). Why is willow wood weaker than oak wood? Is it because willow trees are less well made?
No, not at all. Willow trees prefer to grow by water, streams and ponds and such. Now water is a useful form of
transport. Willows tend to break off twigs and branches, and these fall into the water and carried further
downstream. This is not a loss to the tree, however, because detached willow branches and twigs have a very
high ability to grow roots! Stick a stick of willow in the ground and it will take root and grow into a new tree! (It
doesn't take a miracle as such, just a miracle of Nature). So, the twigs and branches get swept downstream,
enter some calm bit of water and maybe get deposited on the river banks, and so they take root and grow into
new willow trees. The
crack willow (Salix fragilis) takes this strategy to extremes and in old age the whole tree
may split open into fragments because its wood is so brittle that it falls apart under its own weight! The tree is
unhurt, however, it just keeps on growing! So, sometimes it pays to be fragile! Incidentally, the young green
wood of most willow trees tends to be very springy and not brittle at all, as is the old wood of the crack willow,
and this enable it to bend in the wind rather than breaking. Even so, these trees seem to shed a lot of twigs,
probably 'intentionally'.

What about balsa trees? You may have seen balsa wood used in model aeroplanes or in floats or as insulation.
Balsa wood is also called corkwood and it is very light and spongy, but as a consequence it is not very strong
compared to the wood of other trees (though it has an easier time supporting its own weight) as you can see in
the biomaterials table. The balsa tree (
Ochroma pyramidale) grows in Central and South American rain forests
where there is plenty of moisture and its tissue contains about five times as much water as most trees. In fact it
is this water which 'inflates' the tree and keeps it strong, so the balsa has found a different way to support itself,
but one which is only suitable where there is lots of water. The other advantage of having such light wood is
that balsa trees can grow very quickly. This enables them to exploit gaps in the canopy by springing up and
filling them before other trees can.

What materials are animals made from? The biggest contributor to the animal body is muscle tissue, but this is
a very special tissue that will be talked about elsewhere. Muscles attach to bones via tendons. Tendons are
very strong, you may be able to feel tendons as hard as bone in your thigh just behind the knee. Muscles are
also encased in tough sheaths as are all the internal organs. Ligaments are tough structures joining adjacent
bones together.  All these tough connecting tissues that hold the body together contain two important proteins
in varying amounts: collagen and elastin. If you look at the biomaterials table, then you will see that
collagen is
similar in tensile strength to the tougher metals and metal alloys. Indeed, collagen has the same role that steel
rods have in steel-reinforced concrete - the collagen is wound into rope-like fibres that are held under tension.

However, you will see in the biomaterials table that
elastin is weak in tension, so what's it for? Well, notice that
elastin has a very low elastic modulus (0.002 GPa), remember that elastic modulus is a measure of stiffness, so
elastin is not at all stiff, in fact, as its name suggests, it is very elastic. Elastin functions like a spring by making
tissues springy. A ligament that allows two bones, that it holds together, to move apart, will spring them back
into place again. Such a ligament will be rich in elastin. A tendon that has a lot of force to bear, but which can
not afford to stretch too much, will have less elastin and more collagen. Elasticity is very important, for example,
when you sprint about one third of the force that moves you along comes from the elastic recoil of your joints
and other body parts -
you literally bounce along!

So what about bones? Bones have a lot of work to do. First of all they have to form a skeletal framework for
your muscles, otherwise you would look very saggy! They act as levers, they are what muscles pull against
(muscles never push, they always pull) to move you about. Bones are also protective, indeed the densest bone
in the human body is the skull, which has the vital role of protecting your brain. (Bones also have a few other
functions, like the manufacture of blood cells and immunity to infection). What most people do not realise is how
strong muscles are - imagine a heavy steel bar about as long as you are tall: you can lift it easier from the
middle, but lie it on the floor and try to lift it from one end with one hand, whilst keeping the bar level with the
floor; tricky isn't it? This is what we call leverage, lifting the bar from the middle gave you good leverage, whilst
lifting it from the end gave you bad leverage. Unfortunately, muscles have to work with bad leverage; the
muscle (biceps) that flexes your arm is situated close to the elbow, and yet it lifts your arm with your hand on
the far end of your forearm - it's like lifting the bar from one end. To do this muscles have to be very strong.
When a very strong man squats in the gym, with a 200 kg barbell say,  the muscles at the front of each thigh
are exerting a force equivalent to about one tonne! When you think how small even the most muscular thigh is,
that's impressive that such a small muscle can be so strong.

What are bones made from? Bones contain a lot of collagen and cylinders of a stony material called calcium
hydroxyappetite. The hydroxyappetite is made up of tiny crystals that fit together lick bricks in a wall and they
surround a meshwork of collagen fibres. Does this sound familiar? This is the same type of arrangement that
we have in steel-reinforced concrete. The collagen (steel) gives the material tensile strength, whilst the calcium
hydroxyappetite (concrete) gives it compressive strength.

How strong are bones? Bones are similar in tensile strength to steel and stronger in compression than
concrete!
Bones are a very high performance material. Bones have another advantage over steel and concrete
- bones are light. In a human, bone density varies from about 1.3 in the arms (which do less work) to about 1.7
in the thighs (which do more work) to about 2 in the skull (which is protective armour), but these values are all
low compared to steel (7.87). This gives the muscles less work to do when they move the bones around.

Getting tired of all this tech? If not, then stay tuned because we will be talking about how materials fatigue - that
is how they fail or break. This will reveal other strengths that biomaterials have over the materials that
engineers on Earth use.
Welcome to biomaterials!

Here I shall say a few things about the quality materials that make up living creatures. This gets a little
technical, but I shall explain it in simpler terms as best I can. If you like then skip all the numbers and get the
general gist.  Begin by looking at the mysterious table below:
Table: the properties of various materials