Classification of viscoelastic models with integer and fractional order derivatives

Abstract

In the world literature there exists a wide variety of papers devoted to linear viscoelastic models. This work was initiated by the absence of a single generally accepted classification of viscoelastic models. We focused on the basic mechanical models, namely, the Kelvin-Voigt, Maxwell, standard linear solid and Jeffreys models. All other models are different combinations of basic elements connected in series or in parallel. The classification also includes viscoelastic models with fractional derivatives and fractional operators.