Page 487 - Introduction to Continuum Mechanics
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Non-Newtonian Fluids 471
viscous dissipation of the fluid. Thus, G ' is called the storage modulus and G " is called the
loss modulus.
writing
where
and
we have,
Therefore, taking the real part of Eq. (v), we obtain, with Eq. (ix)
Thus, for a Maxwell fluid, the shear stress response in a sinusoidal oscillatory experiment under
the condition that the inertia effects are negligible is
The angle <5 is known as the phase angle. For a purely elastic material in a sinusoidally
oscillation, the stress and the strain are oscillating in the same phase (d - 0 ) whereas for a
purely viscous fluid, the stress is 90° ahead of the strain.
8.2 Generalized Linear Maxwell Fluid with Discrete Relaxation Spectra
A linear Maxwell fluid with N discrete relaxation spectra is defined by the following
constitutive equation:
where
