Page 480 - Introduction to Continuum Mechanics

464 Linear Maxwell Fluid

In this chapter, we shall discuss several special constitutive equations and one general one
which define idealized viscoelastic fluids exhibiting various characteristics of Non-Newtonian
behaviors.

Part A Linear Viscoelastic Fluid

8.1 Linear Maxwell Fluid

The linear Maxwell fluid is defined by the following constitutive equation:

where —pi is the isotropic pressure which is constitutively indeterminate due to the incom-
pressibility property of the fluid, T is called the "extra stress" which is related to the rate of
deformation D by Eq. (S.l.lb).

In the following example, we show, with the help of a mechanical analogy, that the linear
Maxwell fluid possesses elasticity.

Example 8.1.1
Figure 8.3 shows the so-called linear Maxwell element which consists of a spring (an elastic
element) with spring constant G, connected in series to a viscous dashpot (viscous element)
with a damping coefficient rj. The elongation (or strain) of the Maxwell element can be divided
into an elastic portion e e and a viscous portion e v, i.e.,

Fig. 83