Page 486 - Introduction to Continuum Mechanics

470 Linear Maxwell Fluid

We wish to obtain the complex number r 0. Substituting r 12 = t 0e ia>t into the constitutive
equation for r^:

one obtains

The ratio is known as the complex shear modulus, which can be written as

The real part of this complex modulus is

and the imaginary part is

If we write j as G, the spring constant in the spring-dashpot model, we have

and

We note that as limiting cases of the Maxwell model, a purely elastic element has ^M-*<» so
that G' = G and G" = 0 and a purely viscous element has G-»<» so that
G ' = 0 and G " = jua). Thus, G' characterizes the extent of elasticity of the fluid which is
capable of storing elastic energy whereas G " characterizes the extent of loss of energy due to