Static and Dynamic Experiments on the Stretch and Frequency Dependence of Elastic and Viscoelastic Coefficients of Latex Tubes

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Abstract
Assuming for the wall material (supposed incompressible) of a latex tube a strain‐energy function of the form W = ½Φ (I1−3) +½Ψ (I2−3), (Φ and Ψ constants, i.e., independent of the deformation) a stress‐strain relationship for simple stretch, an equation of motion for small torsional vibrations, and a frequency equation for torsional waves of small amplitude are derived. In the equations of motion Φ and Ψ are replaced by Voigt operators Φ+Φvi (∂/∂t) and Ψ+Ψvi (∂/∂t). Experiments with simple large‐stretch free torsional oscillations of small amplitude and torsional waves of small amplitude superposed on a large stretch showed that the postulates predict the behavior adequately. Φ and Ψ were found to be not only independent of the stretch (1≤λ≤2.3) but also independent of the frequency (0≤f≤33 cps). ωΦvi and ωΨvi appeared at the lower frequencies (free vibrations) to be independent of the stretch and of the frequency. At the higher frequencies a frequency and stretch dependence could not with certainty be detected. The importance of this phenomenon for the study of the arterial system, where waves of small amplitude superposed on a large deformation occur is briefly discussed.