Constitutive equations for the nonlinear viscoelastic and viscoplastic behavior of thermoplastic elastomers

Observations are reported in uniaxial tensile tests with constant strain rates at moderate finite deformations, as well as in creep and relaxation tests on a thermoplastic elastomer (ethylene-octene copolymer) at room temperature. A constitutive model is developed for the viscoelastic and viscoplastic responses of a polymer at arbitrary three-dimensional deformations with finite strains. A thermoplastic elastomer is treated as an incompressible heterogeneous transient network of strands. Its viscoelastic behavior is associated with separation of active strands from their junctions and merging of dangling strands with the network. The viscoplastic response reflects sliding of junctions between strands with respect to their reference positions. Stress-strain relations are derived by using the laws of thermodynamics. They involve six adjustable parameters that are found by fitting the experimental data. To examine the accuracy of the model predictions, plane-strain compressive tests with constant strain rates and relaxation tests at compression are performed. Good agreement is demonstrated between the observations and the results of numerical simulation.