The relation of bifurations in a biaxially loaded rubber sheet and the constitutive modeling of rubber
- Univ. of Maryland, College Park, MD (United States)
Treloar`s experiments on a thin rubber sheet under in-plane biaxial tensile loads produced asymmetric as well as equal in-plane stretches. At two loads, the two stretches differed by 7.5% and 12.4% respectively. At an intermediate load, there was a stable equal stretches state. Treloar later said that relaxation was negligible since the results were reproducible and independent of the order of force application. Specimen anisotropy and lack of strain uniformity were also eliminated as a cause. Kearsely first pointed out the significance of these experiments to studies of elastic stability of rubber models. The predictability of this result is a test for the validity of the various constitutive models for rubber. First, Ogden`s plane stress stability and bifurcation criteria are reviewed. A coordinate transformation of a generalized energy function for the biaxially loaded sheet makes it possible to describe the Mooney-Rivlin bifurcation as a cusp catastrophe and to verify that the neo-Hookean and other classical models have no bifurcations. The Mooney-Rivlin model predicts unstable equal stretch states above the bifurcation value, but Treloar`s experiments contradict this. These models cannot, then, be the correct constitutive models for rubber. Preliminary ideas on the conditions that an isothermal constitutive model must satisfy to reproduce Treloar`s experiments are proposed. A thermoelastic generalization of the Mooney-Rivlin model, developed with N. N. Zeng, predicts that raising the temperature slightly lowers the value of the bifurcation load. Nonequilibrium processes such as relaxation or sinusoidal loading are modeled using a generalized energy function in place of classical viscoelastic constitutive relations.
- OSTI ID:
- 175225
- Report Number(s):
- CONF-950686--
- Country of Publication:
- United States
- Language:
- English
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