Effect of Stress-softening on the Dynamics of a Load Supported by a Rubber String

The Mullins effect in the oscillatory motion of a load under gravity and attached to a stress-softening, neo-Hookean rubber string is investigated. Equations for the small amplitude vertical oscillations of the load superimposed on the finite static stretch of both the virgin and stress-softened cords, the latter subjected to varying degrees of preconditioning, are derived. The vibrational frequency of the small motion exhibits behavior similar to that observed in experiments by others on postmortem, human aortic tissue for which no stress-softening is reported. Standard numerical methods are applied to study the finite amplitude motion of the load in the stress-softened case. The resultant motions and their various physical aspects under free-fall and general initial conditions are described in several examples. Oscillations that engage all three phases of motion consisting of the suspension, the free-flight, and the retraction of the load in its general vertical motion are illustrated. Effects due to the degree of stress-softening are discussed; and the motion response for two values of the model softening parameter is compared in several examples. All results are illustrated graphically and numerous tabulated numerical results are provided.