A note on novel generalizations of the Maxwell fluid model

In this note we generalize the classical viscoelastic fluid model due to Maxwell to allow the relaxation time and the viscosity to depend on the stress. Such models are very useful in describing the response of geological and many other polymeric fluids. The procedure that is adopted to carry out the generalization allows one to have the springs and dashpots and their three dimensional generalizations, to be described by implicit constitutive theories thereby greatly enlarging the class of constitutive models that can be put into place to describe the response of complex viscoelastic fluids.

► Generalizes the Maxwell model wherein the relaxation time and viscosity depend upon the stress. ► Develops new models to describe the response of geological and polymeric materials. ► Develops new implicit models for describing response of viscoelastic bodies.