Rubber Viscoelasticity Using the Physically Constrained System's Stretches as Internal Variables

Abstract

Abstract The simulation of rubber viscoelasticity with the tube reptation model for topological interactions is investigated for large dynamic strains. The chemically crosslinked (CC) system of molecules acts as a constraint box per unit volume for the physically constrained (PC) system and carries the PC system during the deformation process. A stick—slip model is used to simulate the interaction between the CC and PC systems Stretch ratios describe the history of the PC system's energy. Rubber energy density functions for both the CC and time dependent PC systems are shown to model large strain viscoelastic deformations. In this approach the energy is split into two terms. The long term energy function for the CC molecules represents one part and a time dependent energy function for the PC molecules comprises the second part. The PC systems' stretches then appear as internal variables in the expression of the total energy. The relaxation of the PC molecules during a general deformation is determined by the history of the CC system's strain state and the box (tube) stick—slip relaxation equation(s). Examples are presented in which step-strain relaxation test data and strain rate data are simulated for large deformations of a rubber compound with differing short and long term energy functions.