Background of phenomenological theory

The viscoelastic properties of a material are entirely characterized by the constitutive equation whidi relates the stress tensor Oap(t) to the velodty 

In polymeric liquids the constitutive equation becomes quite complicated the stress depends on the previous values of the velocity gradient tensor and the dependence is generally not linear hence the relation is written only by a nonlinear functional relation  

However, in the special case that the perturbation by the velodty gradient is small, the relation between the stress and the velocity gradient becomes linear and is written as  

This constitutive equation includes only one material function G(t) called the shear relaxation modulus. 

Though the applicability of eqn (7.11) is limited, linear viscoelasticity has been studied in great detail as it represents a property of the material in a well-defined limit. 

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