Dynamic measurements - the complex modulus and compliance

Dynamic methods involve oscillatory deformation and it is therefore necessary to consider the strain generated by a sinusoidal applied stress. 

10 A schematic diagram of apparatus for studying extensional creep. 

Linearity implies that the strain is sinusoidal, with an amplitude proportional to that of the stress, but there will be a phase lag 8. The strain and stress at angular frequency a can thus be represented by 

It can be shown (see problem 7.6) that the energy A.S dissipated per cycle per unit volume of material is given by 

Thus the imaginary part Gi is often called the loss modulus and the real part Gi is called the storage modulus. The ratio G2/G1 = tan 5. 

---