Complex Modulus of Viscoelastic Materials

Consider the generalised stress-strain relationship as follows:

For harmonic excitation at steady state applying

and

We get

Therefore

This ratio could be denoted as complex Young's modulus such that

where is the storage modulus and is the loss modulus. The loss factor is expressed as

Hence,

Similarly, the shear modulus of VEM

and the bulk modulus of VEM

The various modululli are interrelated as