Page 488 - Introduction to Continuum Mechanics

472 Generalized Linear Maxwell Fluid with Discrete Relaxation Spectra

The mechanical analog for this constitutive equation may be represented by N Maxwell
elements connected in parallel. The shear relaxation function is the sum of the N relaxation
functions each with a different relaxation time A n:

It can be shown that Eqs. (8.2.1) is equivalent to the following constitutive equation

We demonstrate this equivalence for the case of N = 2 as follows: When N = 2,

and

Thus

and

Adding Eqs. (i) and (ii), we obtain

Let

we have