The Elasticity of Rubber

The experiments of Rivlin and Saunders and Gent and Rivlin are consistent with W having the form (33) in which C is a constant and f is a function of I 2 −3 only, which decreases monotonically as I 2 −3 increases. With this interpretation of the experiments, the term f ( I 2 −3 ) represents the departure from the predictions of the kinetic theory. This conclusion is reinforced by the finding of Gent and Rivlin that W 1 exhibits no hysteresis, while all of the hysteresis ( i.e. , departure from ideal reversibility) exhibited by the rubber resides in W 2 ( i.e. , in the term f ( I 2 −3 )). This suggests that the model for a vulcanizate adopted in the kinetic theory must be modified by the introduction in the undeformed rubber network of crosslinks which are broken when the rubber is deformed and are re-formed, nearly reversibly, when the rubber returns to its undeformed configuration. However, so far no satisfactory mathematical development of this idea has been carried out; the construction of a convincing theory which accounts for the departure of W from the neo-Hookean form remains an unresolved problem.