LINEAR VISCOELASTIC BEHAVIOR OF COMPLEX POLYMERIC MATERIALS - A FRACTIONAL MODE REPRESENTATION

A theological constitutive equation for complex polymeric materials is derived starting from a special formulation of the relaxation function. This relaxation function contains six parameters and is divided into three regions: the plateau region, an intermediate power-law region and the terminal region of rapid stress decay. Material functions like the complex modulus G* and the logarithmic density function of the relaxation time spectrum H and of the retardation time spectrum L respectively are derived. Material parameters like the zero shear viscosity eta(0) and the equilibrium shear compliance J(e) are also calculated. The comparison of the measured dynamic moduli of II-shaped polystyrenes, associating terminally functionalized polyisoprenes and randomly associating polybutadienes with the theoretical predictions of the proposed phenomenological model shows an excellent agreement.