Comments on the validity of a common category of constitutive equations

Summary

Many constitutive equations for viscoelastic materials which have appeared in the literature are modifications of the linear viscoelasticity model. Their general form is:

$$\tau = \int\limits_0^\infty {(f_1 C + f_2 C^{ - 1)} ds.} $$

([5])

The memory functionsf ₁ andf ₂, are assumed to depend explicitly on either some instantaneous or some timeaveraged value of the invariants of the rate of strain.

It is shown in this paper that the general theory of simple fluids with fading memory is based on certain assumptions of smoothness for the constitutive functional which are violated by constitutive equations of the type discussed. This implies that, should any real material obey eq. [5], with an explicit dependency of thef _i's on the rate of strain, such a material would not obey the general theorems of the simple fluid theory which are based on different smoothness hypotheses.

A critical analysis of available experimental evidence shows that it supports the validity of the smoothness hypotheses underlying the theory of simple fluids with fading memory, while contradicting those implied by an explicit dependency of the memory functions on the rate of strain.