Combined simple and sinusoidal shearing in elastic liquids

A survey of constitutive equations for application to superposed simple and time-dependent shearing is made. Few of the equations so far proposed are capable of showing the experimentally observed cut-off of relaxation processes with rates less than the simple shearing rate. Using rubber-like elasticity theory as a guide, and introducing the concept of network rupture at a given strain magnitude, an integral-type constitutive equation is proposed. This model shows the observed type of behaviour in the combined flow, reasonable numerical agreement for normal stress data in simple shearing and qualitative agreement with the scanty data for extensional flow. Since the numerical quantities occurring in the constitutive equation may be found from dynamic small-strain shear measurements and viscometric flows only, some predictive ability is displayed. Further generalizations and the application of the experimental results to dynamically loaded bearings are also discussed.