Models of Viscoelastic Materials: A Review on Historical Development and Formulation

Abstract

A classification of different mathematical models of viscoelastic materials is presented. The review covers the classical models of viscoelasticity with integer order derivatives, as well as models with fractional derivatives and fractional operators. This paper provides a detailed historical background of the basic viscoelastic models with their mechanical schemes and mathematical formulations. A comparative analysis of contribution of Western and Russian scientists to the development of linear viscoelasticity is carried out. The paper fully tracks the recent theories on the topic of linear and nonlinear viscoelasticity.