A Study On Viscoelasticity and the Mullins Effect of Elastomers

Although rubber is capable of very large elastic deformation, it also shows significant viscoelastic behavior and a strain-induced stress-softening phenomenon (the Mullins effect). In this paper, tensile, planer tension and equal biaxial cyclic tests are used to study the viscoelastic and stress-softening effects of rubbers and a numerical method is proposed to evaluate the stress relaxation function and the model constants of constitutive equations from the cyclic tests. 

Carbon black-filled rubbers are studied with the proposed method.  The results show that the stress relaxation function obtained from the stress relaxation test cannot satisfactorily describe the hysteresis loop in the cyclic tests. In addition, the scaling coefficient method used in most commercial finite element codes to model the Mullins effect is inadequate for the rubber compounds studied.  By allowing the model constants of the constitutive equations (such as the Gent model and the Arruda-Boyce model) to be a function of the maximum first strain invariant in the prior loading history, a consistent fit is obtained for tensile, planar tension and equal biaxial cyclic tests.