A note on a reappraisal and generalization of the Kelvin–Voigt model

In this short note we show that expressing the strain and the symmetric part of the velocity gradient as functions of the stress instead of providing constitutive relations for the stress, as is the norm, allows one to obtain a far wider class of models to describe the response of viscoelastic bodies than those that are possible within the classical framework. Such an approach is used to describe the Kelvin–Voigt solid and several of its generalizations. A further generalization that recognizes that a certain class of viscoelastic solids, such as the Kelvin–Voigt solid, can be thought of a mixture of a dissipative fluid and an elastic solid, allows one to develop models wherein implicit relationships can be provided for the dissipative response and the elastic response.