The Pressurized Cylinder Problem for Nonlinear Viscoelastic Materials with a Strain Clock

Abstract

A constitutive equation for nonlinear viscoelasticity is used to model the mechanical response of solid amorphous polymers such as polycarbonate. The nonlinearity arises from a reduced time, which causes stress relaxation to accelerate with increasing strain. This reduced time is referred to as a "strain clock". An important feature of the constitutive equation is that it accounts for yield under different strain and stress histories. This constitutive equation is used to study the problem of a hollow cylinder subjected to different pressure histories on its inner and outer surfaces. It is shown that if the strain clock depends only on the volumetric strain, then the governing equations admit a solution, which has a number of important consequences. First, the spatial distribution of displacements has the same form as for a linear elastic or linear viscoelastic material. The time evolution depends on the material properties. Second, if pressures are specified at the inner and outer surfaces, the resultant stress distribution is independent of material properties, and is the same as for linear elastic or linear viscoelastic response. Finally, it is found that the strain clock runs at the same rate for all radii. An experiment, based on these results, is suggested, which can be used to assess the assumption that the strain clock depends only on the volumetric strain.