Modelling of fractional relaxation behaviour characteristic in polysaccharide systems

ABSTRACT

Fractional calculus has become an important tool in the analysis of slow relaxation phenomena, such as stress-strain relationships in polymeric materials. The Zener model is an extension of the Maxwell model, which consists of a spring and dashpot in series, with an additional spring in parallel. A fractional rheological description is obtained by replacing the first order time-derivatives in the Maxwell-Zener equation with fractional derivatives of order q and micro. The fractional Zener model relating stress to strain is used to fit several experimental results on polysaccharide. The comparisons between the experimental results and the theoretical predictions are found to be satisfactory