Nonlinear stress relaxation of filled rubber compounds: A new theoretical model and experimental investigation

A new nonlinear hyper-viscoelastic constitutive model was developed to describe the mechanical behavior of filled rubbers. It consists of a conventional strain energy density function like Arruda-Boyce weighted by a four-parameter decay relationship, designed as a function of time and the deviatoric part of the first invariant of the left Cauchy-Green deformation tensor. It was implemented in Abaqus code as a user subroutine. A SBR/BR rubber compound filled with carbon black was selected as the test material. The material parameters were determined by calibrating the data from the uniaxial stress-strain tensile, volumetric, and stress relaxation tests using an optimization loop designed in Isight program. To validate the proposed model, a series of simulations were performed on two rubber strips and a rubber cylinder under extensive and compressive loads, respectively. Comparison with their corresponding experimental data confirmed the accuracy, and validity of the proposed model and approach.