Abstract
The main features of the theory of linear viscoelasticity are reviewed. The time-dependent behavior of any viscoelastic material can be described in terms of a complex viscosity η ( s) which must possess a certain specific analytic character, considered as a function of the complex variable s. It is shown that the complex viscosity representing the dynamic response of viscoelastic fluids to oscillatory motion superimposed upon steady shear can not be evaluated in terms of a spectrum of relaxation times and can not be compared on such basis to the complex viscosity measured in the vicinity of equilibrium. Any non-linear theory of viscoelasticity should be compatible with the linear theory. This criterion is discussed; it is shown that a non-linear constitutive equation of the Rivlin—Ericksen type involving only a finite number of derivatives of the strain rate should not be regarded as a proper constitutive equation.
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