A constitutive model for nonlinear viscoelastic media

A new constitute model is derived for the nonlinear viscoelastic behavior of polymers under isothermal loading. The model extends the concept of adaptive links (entanglements) between polymeric molecules to aging viscoelastic solids. By using data for polypropylene and polyurethane in relaxation tests, material parameters are found. To verify the model, experimental data for loading/unloading with constant rates of strains are employed, which demonstrate fair agreement between measurements and their prediction. The model is utilized to calculate stresses and displacements built-up in a conic pipe under the action of torques applied to its edges. An explicit solution to this problem is derived, where a time-dependent coefficient satisfies a nonlinear integral equation. The effect of geometrical parameters of the pipe and the loading history on stresses and displacements is studied numerically. Two correspondence principles are derived which permit a solution to a viscoelastic problem to be found explicitly in terms of solutions to appropriate elastic problems. Some restrictions on the model nonlinearity are determined which imply these principles.