THE PRESSURIZED CYLINDER PROBLEM FOR NONLINEAR VISCOELASTIC MATERIALSWITH A STRAIN CLOCK

A constitutive equation for nonlinear viscoelasticity is used to model the mechanical response of solid amorphous polymers such as polycarbo nate. 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 consti tutive equation is that it accounts for yield under different strain a nd stress histories. This constitutive equation is used to study the p roblem 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 ad mit a solution, which has a number of important consequences. First, t he spatial distribution of displacements has the same form as for a li near elastic or linear viscoelastic material. The time evolution depen ds on the material properties. Second, if pressures are specified at t he inner and outer surfaces, the resultant stress distribution is inde pendent of material properties, and is the same as for linear elastic or linear viscoelastic response. Finally it is found that the strain c lock runs at the same rate for all radii. An experiment, based on thes e results, is suggested, which can be used to assess the assumption th at the strain clock depends only on the volumetric strain.