Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: A Review

This paper reviews the recent research in the application of fractional calculus in the models of linear viscoelasticity utilized in dynamic problems of mechanics of solids. The brief historical survey reflecting the contribution of Soviet mechanicians in the development of hereditary mechanics is provided. Different fractional derivative models of viscoelastic materials have been analyzed, among them those considering the bulk relaxation. It is shown that the models with time-dependent Poisson’s operators allow one to describe the properties of viscoelastic auxetics, i.e. materials with negative Poisson’s ratios. A companion article will review boundary-value dynamic problems utilizing the rheological models considered in the given paper and will provide a critical estimation of the results obtained in the field during last decade in the light of new apprehensions of the role and place of the fractional calculus in engineering practice.