ИСТИНА

Abstract. The constitutive equations for viscoelastic finite strains that generalize the differential elementary Maxwell model and use the Cauchy stress tensor, the strain rate tensor and the one-parameter family of objective Gordon – Showalter time derivatives are studied in the paper. Objective derivatives of Oldroyd, Cotter – Rivlin and Jaumann are the particular cases of this family for values of the parameter a equal to 1, -1, 0 respctively. The proposed family of constitutive equations is used in two problems for incompressible viscoelastic material: simple shear and cylinder torsion without elongation. The obtained analytical solutions of these problems showed that the used constitutive equations allow to describe the Poynting effect for any value of the parameter a. For the stepwise process of deformation of the cylinder, the result also qualitatively coincides with the available experimental data. The effect of the parameter a on the stress state in the mentioned above problems is also revealed.