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 variable which causes 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 pressure histories at its inner and outer surfaces. It is shown that if the reduced time, or 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 the pressure is 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 l...
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