The effect of damage on small-amplitude radial oscillations of an incompressible isotropic tube under pressure

This study investigates the small-amplitude radial oscillations of a damaged incompressible isotropic homogeneous limited elastic cylindrical Gent tube under constant inflation pressure. The proposed work focuses on incorporating damage into an infinitesimal stability analysis, mainly for a class of materials characterized by their limited molecular-chain extensibility. These materials mimic the responses of soft biological tissues. A stability analysis of a damaged radially oscillating cylindrical tube is necessary for studying angioplasties, surgical procedures used to correct some inflammation-based cardiac disorders. Stability theory is inferred both from the mathematical formulas presented and the graphical results obtained for pressure-stretch and frequency-stretch curves. Finally, a stability analysis for an incompressible damaged Gent cylindrical membrane is presented, and universal relations are obtained. Infinitesimal stability of a long, damaged cylindrical Gent cavity is further explored, and all results are illustrated graphically.