Use of a One-Parameter Family of Gordon–Schowalter Objective Derivatives to Describe Finite Strains of Viscoelastic Bodies / E. D. Martynova and N. S. Stetsenko. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 6. P. 64-68 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 153-156].
A constitutive relation is considered for viscoelastic materials at finite strains. 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.
Key words: finite deformations of viscoelastic materials, simple shear, one-parameter family of Gordon–Schowalter derivatives, Poynting effect.