Modelisation of the Rheological Behavior of Viscoelastic Materials Using the Fractional Derivatives and Transfer Technique

The aim of this research is to develop a fractional mathematical model of α-order (α), by studying accurately the rheological behavior of viscoelastic materials by mathematical modelisation using derivative and integration fractional technique and Laplace transform method. The rheological model consist of two elements in series: spring introduces elastic material properties, and fractional element introduces the viscous material properties. The transform technique and the direct inverse method and asymptotic develop in short and long times allowed us to obtain all analytical relations required to study the rheological behavior for the greatest number of viscous elastic materials with minimum number of parameters. All analytical and numerical results that we could obtain in this research are good and enough for a accurately study for a lot of polymers by comparing with other results done by a lot of researchers in the material field (domain) in the experimental studies.