The frequency-dependence of the complex modulus we have just discussed can be explained through a linear viscoelastic model. For example, consider the simple, three-element model shown in the figure below:

Figure 14.2: 3 Element model

The stress-strain relation for this model is given by the following equation

(14.1)

where is a geometric parameter.

Assuming a harmonic loading of frequency , we substitute () for the operator in this equation. Then, we get the complex modulus as

(14.2)

Taking the real and imaginary parts of this equation, we obtain

	(14.3)

It can be seen from eqns. (14.3) that the loss modulus has a maxima at , where is the relaxation parameter of the viscous branch.

Congratulations! You have finished Lecture 14.