1.5Visco-elastic fluid behaviour
In the classical theory of elasticity, the stress in a sheared body is directly proportional to the strain. For tension, Hooke’s law applies and the coefficient of proportionality is known as Young’s modulus, G
where dx is the shear displacement of two elements separated by a distance dy. When a perfect solid is deformed elastically, it regains its original form on removal of the stress. However, if the applied stress exceeds the characteristic yield stress of the material, complete recovery will not occur and ‘creep’ will take place–that is, the ‘solid’ will have flowed. At the other extreme, in the Newtonian fluid the shearing stress is proportional to the rate of shear, equation (1.1). Many materials show both elastic and viscous effects under appropriate circumstances. In the absence of the time-dependent behaviour mentioned in the preceding section, the material is said to be visco-elastic. Perfectly elastic deformation and perfectly viscous flow are, in effect, limiting cases of visco-elastic behaviour. For some materials, it is only these limiting conditions that are observed in practice. The elasticity of water and the viscosity of ice may generally pass unnoticed! The response of a material depends not only its structure but also on the conditions (kinematic) to which it has been subjected; thus the distinction between ‘solid’ and ‘fluid’ and between ‘elastic’ and ‘viscous’ is to some extent arbitrary and subjective
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