Use of a one-parameter family of Gordon–Showalter objective derivatives to describe finite deformations of viscoelastic bodies

A constitutive relation is considered for viscoelastic materials under finite deformations. This relation is obtained using a one-parameter family of Gordon–Schowalter objective derivatives and generalizes the elementary Maxwell model. It is shown that, in the problem of simple shear of an incompressible viscoelastic material, this constitutive relation allows one to obtain the Poynting effect for any parameters of the model.