Hookeian behaviour

A fluid in which the shear stress is proportional to the shear velocity, corresponding to this law, is called an ideal viscous or Newtonian fluid. Many gases and liquids follow this law so exactly that they can be called Newtonian fluids. They correspond to ideal Hookeian bodies in elastomechanics, in which the shear strain is proportional to the shear. A series of materials cannot be described accurately by either Newtonian or Hookeian behaviour. The relationship between shear stress and strain can no longer be described by the simple linear rule given above. The study of these types of material is a subject of rheology. 

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. 

The conclusions to be drawn from the results above are that, although the predictions of equation (6.26) for the simple neo-Hookeian solid do not describe the behaviour of rubbers well at high extensional strains, they describe it well for low extensional strains, for compressional strains and for quite large simple shear strains. Discussion of modifications to the neo-Hookeian equation is deferred until section 6.5, after consideration of a more physical theory of rubber elasticity in the next section. 

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See also in sourсe #XX -- [ ]

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