Torsion Processes for Cylindrical Samples Made of Incompressible Viscoelastic Materials of the Maxwell Type

Abstract

Analytical solutions are obtained for the problem of torsion of incompressible cylinders, whose materials are described by the constitutive relations of viscoelastic media, generalizing the relations of the elementary Maxwell model for the case of finite deformations. Constitutive relations differ from each other in the value of the parameter specifying the type of an objective derivative used from the Gordon-Showalter family, including the Oldroyd, Cotter-Rivlin, and Jaumann derivatives.

It is shown that a longitudinal compressive force (the Poynting effect) is generated when twisting a cylinder with a constant length, whose material is described by any constitutive relation from the one-parameter family under consideration. For stepwise deformation processes, a qualitative description of a number of available experimental data are also obtained.