Computational framework for common visco-elastic models in engineering based on the theory of rheology

This paper presents a constitutive framework of generating common visco-elastic models that have been used in recent years for the modelling of viscous materials such as asphalt binders and mixtures. The paper provides a brief introduction into the experimental and theoretical aspects of rheological modelling using fractional time derivatives. A differential equation of a rheological element is formulated from which a wide variety of simpler elements such as the fractional Newton element, the fractional Kelvin element and the fractional Standard Linear Solid can be derived. This same development is expanded to include the well known Huet, Huet–Sayegh, and 2S2P1D models. The equations presented may be implemented in standard numerical approaches such as multi-layer theory or the finite element method to solve pavement engineering problems. In addition to this, the Cole–Cole plots, Black Diagrams, and master curves of the elements mentioned above are presented and discussed.