Rubber high-elasticity laws

Many polymers, such as rubber, are characterized by high elasticity. In the 1950s, Volkestein in Leningrad and Paul Rory at Cornell worked out the details that connect the strain of a polymer to applied stress. Using statistical arguments they showed how the two are linearly related, closely following Hooke s law. 

Thus the relationships (6.21) and (6.21a) are compatible with the isotropy and incompressibility of a rubber and reduce to Hooke s law at small strains. Materials that obey these relationships are sometimes called neo-Hookeian solids. Equation (6.21a) is compared with experimental data in fig. 6.6, which shows that, although equation (6.21a) is only a simple generalisation of small-strain elastic behaviour, it describes the behaviour of a real rubber to a first approximation. In particular, it describes qualitatively the initial fall in the ratio of to k that occurs once k rises above a rather low level. It fails, however, to describe either the extent of this fall or the subsequent increase in this ratio for high values of k. 

It has been mentioned that an amorphous high polymer behaves like a glass at low temperatures, like a rubber at higher temperatures, and like a viscous liquid at still higher temperatures. In other words, depending on the temperature, behavior may be elastic (i.e., in conformity to Hooke s law),... 

Polymers come in many forms including plastics, rubber, and fibers. Plastics are stiffer than rubber, yet have reduced low-temperature properties. Generally, a plastic differs from a rubbery material due to the location of its glass transition temperature Tg). A plastic has a Tg above room temperature, while a rubber will have a Tg below room temperature. Tg is most clearly defined by evaluating the classic relationship of elastic modulus to temperature for polymers as presented in Fig. 1.1. At low temperatures, the material can best be described as a glassy solid. It has a high modulus and behavior in this state is characterized ideally as a purely elastic sohd. In this temperature regime, materials most closely obey Hooke s law ... 

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