Effect of damage on the free radial oscillations of an incompressible isotropic tube

Abstract

The effect of damage on the finite-amplitude, free radial oscillations of an arbitrary incompressible, isotropic, homogeneous cylindrical tube is investigated. Pressure is applied to the inner and outer surfaces of the damaged cylinder and constrained from both ends. A purely radial motion is observed when the pressure is removed. The corresponding equation of motion is obtained, incorporating the effect of damage. A simple exponential front factor damage function is introduced in the tube problem. The damage function is a function of the first invariant of the left Cauchy–Green deformation tensor and is dependent on its maximum previous ever value. It is found that the period of oscillation for a thin-walled neo-Hookean membrane varies with the damage function. In contrast, the respective period for an undamaged neo-Hookean membrane is a constant. The described study may help in the surgical procedure of angioplasty, performed during inflammatory diseases such as atherosclerosis. During angioplasty, owing to inflation of the balloon, the arterial wall is damaged; this study may help to gain more insight on the surgical procedure. Both thick- and thin-walled analysis of the damaged cylindrical tube are performed and compared with the undamaged case. Several results are inferred and illustrated graphically for two types of parent material model, namely Gent and neo-Hookean.