Experimentally determined properties of softening functions in pseudo-elastic models of the Mullins effect

This paper aims to identify the true source of limitations of pseudo-elastic models for describing the stress-softening phenomenon in elastomers which were recently proposed in the literature [Ogden, R.W., Roxburgh, D.G., 1999. A pseudo-elastic model for the Mullins effect in filled rubber. Proceedings of the Royal Society of London A 455 (1988), 2861–2877; Elías-Zúñiga, A., Beatty, M.F., 2002. A new phenomenological model for stress-softening in elastomers. Zeitschrift für angewandte Mathematik und Physik (ZAMP) 53 (5), 794–814]. These models as well as their modified versions [Mars, W.V., 2004. Evaluation of pseudo-elastic model for the Mullins effect. Tire Science and Technology, TSTCA 32 (3), 120–145; Elías-Zúñiga, A., 2005. A phenomenological energy-based model to characterize stress-softening effect in elastomers. Polymer 46 (10), 3496–3506] fail to give fully satisfactory coincidence of experimental data and theoretical predictions. In this paper a suitable analysis of experimental data published in the open literature is presented. This analysis shows several interesting features regarding the nature of the stress-softening phenomenon (widely known as the Mullins effect). In particular, it is shown that the magnitude of stress softening varies with strain in a non-monotonous manner and this non-monotonous character of the stress-softening phenomenon strongly depends on magnitude of the pre-strain. This experimental fact is in contradiction with the basic assumption used in pseudo-elastic models that the stress softening is described by a monotonously increasing function of strain. The common theoretical basis of pseudo-elastic models of stress softening and the source of this conflict are clarified.