Nonlinearity in the Dynamic Properties of Rubber

The first two sections of this paper deal with the necessity for amending the classical Newtonian equations by assuming a nonlinear stress-strain curve in order to account for the presence of a considerable amount of second harmonic of the test frequency in the restoring forces in a rubber, in both forced-vibration and positive-displacement dynamic testers. The nonlinear stress-strain curve is applied also to a damped free-vibration curve of the Yerzley type, and is shown to account for the asymmetry of the envelope of the vibration curve. The latter part of the paper obtains a relationship between the dynamic modulus of loaded rubbers and amplitude of vibration, leading to equations analogous to those used in rheology to deal with rate of shear effects in non-Newtonian liquids, and to explain the effects of fillers on the static modulus and hardness of vulcanized rubbers. A resonance curve from a resonant vibrator is analyzed and the variation of modulus with amplitude is shown to exhibit the typical thixotropic effect associated with loaded rubbers subjected to vibrations. The last section discusses how the decrease of modulus with increasing amplitude can be attributed to two different mechanisms: (1) thixotropic breakdown of filler structure, (2) in compression, nonlinearity of the stress-strain curve.