Inversion point and internal volume of pressurized nonlinearly elastic tube

Abstract

The mechanical response of a hollow circular cylinder to internal pressure represents an important theoretical model which can be helpful in the design of tubular structures, and in the biomechanical research of tissues like arteries. It has been shown that arteries in vivo, in addition to pressure loading, sustain significant axial extension. It is manifested as a retraction that is observed when they are excised from a body. Previous research has shown that the axial prestretch ensures that the longitudinal motion of arteries is negligible under physiological conditions. The magnitude of the axial prestretch at which a tube does not change its length during pressurization, is referred to as the inversion point, because at this point mechanical response changes from pressure-induced elongation to pressure-induced shortening. In the present paper, another property observed when a nonlinear elastic tube is inflated at a constant axial load is studied. It is shown that at axial prestretching corresponding to the inversion point, when a tube exhibits no axial movement, the maximum internal volume of the pressurized tube is attained. This property is shown for thin-walled tubes made from material that is characterized with Mooney–Rivlin and Gent strain energy density function. Differences in the inflation–extension response obtained for Gent’s material, and for the human abdominal aorta that is considered to be anisotropic and is described with exponential strain energy density, are studied in the paper. To the best of our knowledge, our study is the first showing that the maximum internal volume of the inflated tube is intimately linked with its axial prestretch.