Elasticity

September 15, 2011 by · Leave a Comment 

tufailIn physics, elasticity (or stretchiness) is the physical property of a material that returns to its original shape after the stress (e.g. external forces) that made it deform or distort is removed. The relative amount of deformation is called the strain.

The elastic regime is characterized by a linear relationship between stress and strain, denoted linear elasticity. The classic example is a metal spring. This idea was first stated by Robert Hooke in 1675 as a Latin anagram “ceiiinossssttuu” whose solution he published in 1678 as “Ut tensio, sic vis” which means “As the extension, so the force.”

This linear relationship is called Hooke’s law. The classic model of linear elasticity is the perfect spring. Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor, when considering simple situations of higher symmetry such as a rod in one dimensional loading, the relationship may often be reduced to applications of Hooke’s law.

Because most materials are elastic only under relatively small deformations, several assumptions are used to linearize the theory. Most importantly, higher order terms are generally discarded based on the small deformation assumption. In certain special cases, such as when considering a rubbery material, these assumptions may not be permissible. However, in general, elasticity refers to the linearized theory of the continuum stresses and strains.

Above a certain stress known as the elastic limit or the yield strength of an elastic material, the relationship between stress and strain becomes nonlinear. Beyond this limit, the solid may deform irreversibly, exhibiting plasticity. A stress-strain curve is one tool for visualizing this transition.

Furthermore, not only solids exhibit elasticity. Some non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow like a liquid, with some viscosity.

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Rubber

August 11, 2011 by · Leave a Comment 

sci“Rubber” means the natural rubber which comes from the latex contained by some trees and other plants – as opposed to synthetic rubber (elastomer) which is generally an oil byproduct. In this description we use the terms elastomer and rubber as synonyms.

Elastomers are a class of materials which differ quite obviously from all other solid materials in that they can be stretched, easily and almost completely reversibly, to high extensions. An ordinary postal rubber band illustrates this behavior. It will generally be made from natural rubber, and can be stretched perhaps 600% (i.e. to seven times its original length), after which – before reaching its ultimate breaking elongation – it can be released and will rapidly recover to almost exactly the original length it had before stretching. The material is said to be elastic.

Most synthetic elastomers are not as elastic as natural rubber, but all can be stretched (or otherwise deformed) in a reversible manner to an extent which easily distinguishes them from all other solid materials. (n.b. a metal spring exhibits high reversible elasticity, but this is a feature of its wound shape. The actual metal itself of which the spring is made only deforms slightly, by twisting locally, at any particular point – nothing like the high deformations of which elastomers are capable.)

Elastomers are a special case of the wider group of materials known as polymers. Polymers are not made up of discrete compact molecules like most materials, but are made of long, flexible, chain-like or string-like, molecules. At this scale the inside of a piece of rubber can be thought of as resembling a pile of cooked spaghetti. In spaghetti, however, the chains, though intertwined, are all separate. But in most practical elastomers each chain will be joined together occasionally along its length to one or more nearby chains with just a very few chemical bridges, known as crosslinks. So the whole structure forms a coherent network which stops the chains from sliding past one another indefinitely – although leaving the long sections of chain between crosslinks free to move. The process by which crosslinks are added is known as vulcanization. To achieve vulcanization the raw rubber is mechanically mixed with a number of compounding ingredients carefully chosen to give the properties required for the particular application. The reason why elastomers behave as they do is associated with the type of molecular structure described above.

Against this background the reason why rubber can stretch so much is that, at normal temperatures, each long chain-like molecule (like any molecule) is in a constant state of agitation (thermal motion). For these flexible long-chain molecules the movement is considerable, and the molecule is agitated so much that it can take up a highly kinked shape. Because of this kinking, the distance between the two ends of the chain is very much less than its fully stretched length. This gives the rubber its flexibility. When a rubber band is stretched some of the highly kinked chains are simply being stretched out. Stretching can then continue until many of the chains are fully extended, or until the rubber breaks.

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