Constitutive Equations for Rubber under Abrupt Change in Strain Rate Direction

Abstract

We proposed constitutive equations for the strain rate and temperature-dependent behavior of rubber by employing the nonaffine molecular chain network theory and reptation theory. The finite element homogenization method along with the proposed constitutive equations have the capability of predicting the deformation behaviors of particle-filled rubber under changes in volume fractions, distribution patterns, and size heterogeneity of the particles without additional parameters. The only existing problem is the modest estimation of the stiffness of rubber immediately after the abrupt change in strain rate direction (ACSD) as can be seen in the cyclic deformation behavior. We restricted our attention to the generalization of our nonaffine molecular chain network theory to overcome the problems associated with ACSD. We consider the effect of the delay of deformation in surrounding chains on the elasticity modulus by introducing an amplification parameter dependent on the current chain stretch and direction of strain rate immediately after ACSD. The potential of the proposed constitutive equations is examined against the predictability of the experimentally obtained deformation exhibiting ACSD.