The Mullins Effect in the Transverse Vibration of a Non-Gaussian Rubber String

Millard F. Beatty, Professor Emeritus
Department of Engineering Mechanics
University of Nebraska-Lincoln and
University of Kentucky

Date:  Friday, October 17, 2003
Time:  3:30 p.m.
Place:  110 Othmer Hall

A phenomenological model for the stress-softened material response arising from microstructural damage in general isotropic and incompressible hyperelastic rubberlike materials is presented. The strain energy function for a uniform distribution of arbitrarily oriented molecular chains due to Treloar and Riding, characterizes the virgin material response. Then based on the classical non-Gaussian, Kuhn-Grün probability distribution function for the chain energy, this leads to the Wu and van der Giessen constitutive equation for the virgin material. An average-stretch, full-network constitutive equation is then derived by approximation of this formidable equation. Finally, the theory is applied to investigate the Mullins (stress-softening) effect in the easy problem of the small transverse vibration of a rubber cord. The softening effect in the cord vibration frequency is illustrated graphically. Frequency versus stretch results for the non-Gaussian molecular network model are compared with experimental data for four varieties of rubber cords, for each of which only three experimentally determined material constants are needed. It is shown that the theoretical predictions stand in excellent agreement with test data.