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CMI-ImpEE Teaching and Learning Packages |
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Optimisation of Materials Properties in Living SystemsNote: DoITPoMS Teaching and Learning Packages are intended to be used interactively at a computer! This one-page print-friendly version of the TLP is provided for convenience, but does not display all the content of the TLP. For example, any video clips and answers to questions are missing. The formatting (page breaks, etc) of the printed version is unpredictable and highly dependent on your browser. ContentsAimsOn completion of this tutorial you should:
Before you start
IntroductionAs a result of evolutionary selection, biomaterials are well adapted for their functions, as will be discovered in this TLP. (Note. In this TLP the term biomaterials refers to the materials of living systems and not man-made materials with biomedical applications). Unlike man-made materials, a limited range of ingredients (never metal) is used to display a wide range of properties. Charles Darwin himself noted that, ‘As a general principle, natural selection is continually trying to economise every part of the organisation’. For instance, tendons and muscle are made of collagen, along with the cornea, skin and blood vessels. Whereas the manufacture process determines engineering materials’ properties, in biomaterials the structure’s age and environment affect the materials properties, leading to variation in the properties of a specific biomaterial. Biomaterials tend to be strong, anisotropic and are usually composite materials. Biomaterials have many advantages, as they are sustainable, recyclable and biodegradable, unlike most common engineering materials. However, the hierarchical structure makes replicating the structure of biomaterials complicated and their use is restricted to ambient-temperature applications. Similarly to engineering materials, biomaterials are classed into the following groups corresponding to shared characteristics:
This TLP shows how materials-selection maps can be used to compare biomaterials with common engineering materials, looking specifically at using these maps in conjunction with merit indices. Four of the most commonly used materials-selection maps will be studied:
These are particularly important for choosing the most suitable material for a specific application, and looking at the interesting properties specific to certain biomaterials such as viscid silk found as the capture threads in spiders’ webs.
Young’s Modulus - Density selection mapImagine a material is needed to build an aircraft panel, this will be subject to bending moments, and so the deflection that occurs must be minimised. It is also necessary to keep the mass of the aircraft low and so the density of the material should also be minimised. It is important to find a balance between these different material properties in order to find the most suitable material for the application. This can be achieved by finding the appropriate merit index and comparing its value for different materials. Consider the bending of a flat panel of length L, width w and thickness t, subject to an end load F. The engineering application sets the size of the panel (L and w) and the load it must support (F). Thus L, w and F are not variables in our analysis. On the other hand, the thickness t is a variable in that it is not of direct interest: it may be equally valid to use a thin panel of a dense material, or a thick panel of a light material. The bending moment M at the root of the beam is given by M=FL, and this decreases to zero at the end of the beam.
The second moment of area I (derivation) for such a panel is given by:
Assuming only simple bending occurs (and the panel only deflects as shown in the picture, i.e. not forming any complex shapes), the deflection of the end of the panel
Therefore substituting in the value of I for the panel, we get:
The mass m of the beam is given by:
Hence, having the thickness t as the free parameter, and combining the previous two equations by eliminating t gives:
So to obtain the minimum deflection for a panel of free thickness and given mass, or equivalently the minimum mass for a given deflection, Low density is clearly very important for this merit index and hence wood is favoured for applications requiring a flat sheet in bending as it has a low density due to the large voids contained in the structure. This merit index can now be represented on a materials-selection map, allowing easy comparison of the different materials available for this application. Most materials selection maps, such as the one shown, are plotted on logarithmic scales. This allows a given value of the index to be indicated by a straight line: From the equation for deflection, Hence On the selection map shown below, moving a line of the correct gradient as far as possible to the top and the left (and hence maximising E and minimising
Note: This animation requires Macromedia Flash Player 6 and later, which can be downloaded here.
Other important merit indices used in relation to this chart are:
It can be seen from the materials-selection chart that aluminium alloys behave well in bending, and hence are used in aeroplanes. Wood is also an impressive material for this application, and it was used in the past in the Mosquito aeroplane from World War II:
Wood is able to resist bending with a low mass, as it has evolved so that trees will not bend far in strong winds and lose their leaves. Tree branches and trunks must not bend under their own weight and therefore has developed the materials properties of low density and relatively high Young’s modulus. Strength - Density selection mapMerit indices used in conjunction with these maps are:
Note: This animation requires Macromedia Flash Player 6 and later, which can be downloaded here.
The merit index Consider a beam of length L, width w and height h, subject to an end load F. The second moment of area is:
and the mass of the beam is: which can be rearranged in terms of the free parameter h as:
For beam bending,
Substituting in the value for I gives:
To find the desired merit index the free parameter h can then be eliminated from the equation giving:
Hence maximising
Looking at the materials-selection map, it can be seen that silk and cellulose are good materials for these applications. Silk is used in nature by silk worms to form their cocoons, and so must be strong and not easily breakable, as this would kill the silkworm, preventing it maturing into a moth and reproducing. Silkworms originate from China, India and Japan, and have been used to make silk by humans since at least 3,000 BC. Although silkworms only live for two months, they manage in this time to eat roughly 30,000 times their initial weight. It is estimated that 2,500 to 3,000 cocoons are needed to make just one yard of silk fabric, so despite silk being an excellent material for making fibres it is also expensive to produce. Cellulose is found in wood as the main fibre in the composite material, and hence must be strong so that when trees are bent the fibres will not break causing the tree trunk or branch to snap. Young’s Modulus - Strength selection map The Young’s modulus – strength materials-selection map is used in conjunction with merit indices relating to elastic deformation and elastic energy storage. For simple tensile loading, to assess differences in maximum recoverable elastic deformation, the merit index
Note: This animation requires Macromedia Flash Player 7 and later, which can be downloaded here.
To derive the merit index From the definition of Young’s modulus, while the material is behaving elastically:
Therefore the maximum elastic strain (i.e. the deformation at the yield point) is:
For brittle materials the material will break before it yields, so for maximum recoverable deformation:
For ductile materials, So to find the material with the greatest maximum recoverable deformation, the merit index Cartilage is found on the end of bone in joints and so it is important that it will not be permanently deformed or break when the joints bend. The same argument applies to skin, it would be rather gruesome if our skin split open every time we bent our elbow! The merit index Viscid silk has a high value of this merit index and also of Toughness - Young’s Modulus selection mapMerit indices commonly used in conjunction with this materials-selection map are:
Note: This animation requires Macromedia Flash Player 7 and later, which can be downloaded here.
The following method is used to derive the merit index Consider stretching a material, the strain (or amount of stretching) of the material is given by the equation:
The amount of stretching at the fracture point is:
The stress to give fracture is given by the formula:
Thus:
Therefore, in order to maximise the stretching of the material without failure,
Try this for yourself and you will see that skin is the best biomaterial for this application. Skin clearly needs to be stretchable and not crack, as skin is constantly being stretched in the body. Different materials show good values for other merit indices, for instance, antler has a high value of toughness, GC. Antler is a composite material made of the ceramic hydroxyapatite and the polymer collagen, similarly to compact bone, giving it such a high toughness. This enables stags to fight with their antlers, generating large impacts, without the antlers cracking. Stags fight in this way, called rutting, as a mating ritual to prove to females that they are the strongest stag and hence will produce the healthiest offspring. Antlers are shed and re-grown each year, and so can be used to make furniture and artwork.
Wood has the highest fracture toughness, Kc value, for a biomaterial as it is a fibre composite made up of cellulose fibres in a lignin matrix. Trees could easily get small cracks in them and so it is important that they do not fail under their own weight. Comparison of engineering and biomaterials Sometimes it is important to look at more than one materials-selection map and merit index. For instance on comparison of the use of steel and aluminium as a material for aircraft, the merit index
However aluminium performs well under the elastic bending of beams and flat panels, having a greater value than steel for the merit indices It may also be important for a material to have high values of more than one merit index. For example a material may be wanted that will be tough and also have a good value of Young’s modulus for a low relative cost per unit volume:
Looking at the materials-selection maps, good materials that fit these requirements are lead alloys, Zinc (Zn) alloys and steels. Consider a comparison of biomaterials to man-made materials, specifically commonly used engineering materials such as steel, aluminium alloys, titanium alloys, alumina and polyethylene. It can be seen that alumina, aluminium alloys, steel and titanium alloys perform quite well in terms of Young’s modulus – density related merit indices. This is due to their high values of Young’s modulus, despite their high densities. Polyethylene compares poorly with biomaterials in this respect however, due to its low value of Young’s modulus.
Alumina, aluminium alloys, steel and titanium alloys are more commonly used in engineering applications than biomaterials. This is despite biomaterials, particularly types of wood, outperforming these materials for some of the merit indices on this materials-selection map. It is important to note that the distinction between the materials of living systems and conventional engineering materials is not absolute. Wood is more widely used than these engineering materials for low-tech applications, and is in fact the world’s principal material for building. This makes wood among the most common and important structural engineering materials. Although wood has only a quarter the strength of steel, it has four times the specific strength (
Looking at the strength – density materials selection chart:
Alumina clearly outperforms biomaterials when loading a tie under tension, it has a high value of the merit index
Only when all these factors along with the merit indices and materials-selection maps have been considered, can the best material for a particular application be found. Materials-selection maps and merit indices can only be used to compare broad ranges of different materials to discover roughly which few materials are most suitable. Each material would then need to be assessed in more detail to discover which material is truly best for a specific use.
Summary
QuestionsQuick questionsYou should be able to answer these questions without too much difficulty after studying this TLP. If not then you should go through it again! Deeper questionsThe following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP. Going furtherBooksCD-ROMWebsites
Academic consultant: Prof. Lindsay Greer
Additional support for the development of this TLP came from the UK Centre for Materials Education. |
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is given by:
must be maximised. This is an example of a merit index. As the other values in the equation are engineering parameters, the material chosen will not alter these values, and so they are excluded from the merit index, which is based only on materials parameters.
, where 
where 
is a different constant 
.
) will give materials with the best value of the merit index. Try this by moving the line for the appropriate merit index on the following materials-selection maps for engineering alloys and biomaterials.
relating to the minimum deflection achievable on loading a strut or tie in tension with the cross section as a free parameter, or the minimum deflection achievable on bending a beam with the width as a free parameter,
relating to the minimum deflection achievable on bending a beam with the cross sectional area (of fixed shape) as a free parameter.
Mosquito aeroplane.
, used to find the material giving the strongest strut or tie in tension, for a given mass with the cross-sectional area of the beam as the free parameter.
, used to find the material giving the strongest beam (i.e. that supporting the largest bending moment before the onset of plastic yielding or other failure on the surface of the beam) of a given mass, on bending a beam with a specified cross-sectional shape but free cross-sectional area.
for maximising the strength of a beam under a bending load for a given mass, with a specified beam width, and unspecified height will now be derived:
and 
(
or 
by moving the merit index line towards the top and the left of the above materials-selection map gives the material that is strongest for a given mass.
Silkworm and cocoon. 
is used. To compare maximum elastic strain energy per unit volume, the merit index is 
used, and for the maximum elastic strain energy per unit mass, the merit index 
is used.
, the cross-sectional shape of the tie in tension of the structure need not be considered, and engineering parameters are not involved in the derivation, making this a simple merit index to derive as follows:
is comparable to 
. As a result, 
is maximised using the materials-selection chart shown. This involves moving the merit index line towards the bottom and the right of the map. From doing this it can be seen that cartilage, viscid silk, resilin and skin have good values of this merit index.
Spider's web.
, with viscid silk being able to stretch up to three times its own length. Viscid silk makes up capture threads in a spider’s web. It must entangle flies and absorb elastic energy into the threads on impact. This gives an advantage in a high 
value. Viscid silk also needs to store elastic energy so that the kinetic energy of the fly is not returned to the fly, rebounding it back out of the web. This results in a high 
value. This is discussed further in the 
to maximise the elastic stretching of a material before the onset of brittle facture (cracking).
, and a similar method can be used to derive the other merit indices given.
, where 2
or 
must be maximised by moving the line corresponding to the merit index towards the top and the left of the materials-selection map above.
Stags rutting.
for loading a tie in tension shows that steel outperforms aluminium in this context. In fact, steel wires were used by the Wright brothers and in World War I biplanes:
Wright brother's plane.
and 
, and hence aluminium alloys are now used to make certain parts of aircraft whereas steel is not.
) and is renewable, recyclable and requires only a low energy input to make. This makes the price of wood 1/60th per tonne the price of steel with 109 tonnes being used annually worldwide, which is comparable to the amount of iron and steel used globally. Wood has many uses such as the hubs and rims of traditional wheels (for which elm and oak, respectively, are used), longbows (made from yew) and cricket bats (made of willow). However wood is strongly anisotropic, highly susceptible to water damage and unable survive and to perform at high temperatures. There is also a large amount of variability in wood, as different growing conditions for trees of the same species lead to differing mechanical properties. It is possible to limit the anisotropy of wood by using plywood, which involves creating layers of wood with orthogonal “grains” (orientation of the tracheid/ fibre cell structure). The other limitations cannot so easily be overcome, limiting wood’s use as an engineering material with light specifications.
Palm trees can survive very high winds and behave extremely well under bending moments. 
and performs well for all merit indices shown on the above map. Aluminium alloys, titanium alloys, and particularly steel and polyethylene, have merit indices inferior to those of many biomaterials. This is due to their greater density and in polyethylene’s case relatively low strength. This doesn’t necessarily mean that biomaterials will be chosen over common engineering materials however. Other factors to be considered in choosing a material for an engineering application once merit indices have been compared include:
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value)?
.
.