THE PRESSURIZED SPHERE PROBLEM FOR NONLINEAR VISCOELASTIC MATERIALS WITH 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 variable which cause s stress relaxation to occur faster as strain increases. This reduced time is referred to as a 'strain clock'. This constitutive equation is used to study the problem of a hollow sphere subjected to different p ressure histories at its inner and outer surfaces. It is shown that if the reduced time, or strain clock, depends only on the volumetric str ain, then the governing equations admit a solution which has a number of important consequences. First the spatial distribution of displacem ents has the same form as for a linear elastic or linear viscoelastic material. The time evolution depends on the material properties. Secon d, if the pressure is specified at the inner and outer surfaces, the r esultant stress distribution is independent of material properties, an d is the same as for linear elastic or linear viscoelastic response. F inally, it is found that the strain clock runs at the same rate for al l radii.