Three-dimensional constitutive equations for Styrene Butadiene Rubber at high strain rates

Tensile stress–extension ratio and force–extension curves for Styrene Butadiene Rubber dumbbell and sheet specimens, respectively, were obtained from a Charpy tensile impact experiment and used to develop high rate-dependent constitutive equations for the rubber. The tensile tests were performed up to material failure and under constant strain rates ranging from 76 s−1 to 450 s−1. The rubber became stiffer with increasing strain rate but above 370 s−1, the stress–extension ratio curve remained almost the same when the extension ratio was greater than 100%. This suggested that the characteristic relaxation time associated with long chain extension was on the order of a few milliseconds. A hyper-viscoelastic constitutive equation was proposed to describe the rate-dependent material behavior of the rubber based on thermodynamics principles. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the tensile impact response of the rubber sheets in the experiments. Numerical predictions for the transient deformation of the rubber sheet using the proposed constitutive equation were within 7% of experimental results.