Article,
Experimentally determined properties of softening functions in pseudo-elastic models of the Mullins effect
International Journal of Solids and Structures, 44 (11-12): 4145--4157 (June 2007)
Abstract
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; El�as-Z��iga, A., Beatty, M.F., 2002. A new phenomenological
model for stress-softening in elastomers. Zeitschrift f�r 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; El�as-Z��iga, 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.
