How does axial prestretching change the mechanical response of nonlinearly elastic incompressible thin-walled tubes

Abstract

An analytical model of an incompressible thin-walled closed tube was used to simulate the mechanical response of an initially prestretched tube to internal pressure. Four different situations were considered: (I) a hyperelastic material with a large strain stiffening property, (II) a neo-Hookean material, (III) a neo-Hookean material with small strains but large displacements (second order linear elasticity), and (IV) a neo-Hookean material with small strains and small displacements (first order linear elasticity). The results have shown that the positive effect of axial prestretch is not a property exclusively related to anisotropy. It has been proved that nonlinear effects are crucial. Nonlinear constitutive models depending on more than one parameter can both enhance and suppress the circumferential distensibility of the tube due to prestretching. However, a one-parameter neo-Hookean model showed only increased circumferential distensibility. A reduction in second order linear elasticity led to mechanical responses that exhibited only a slight effect of being prestretched. Total linearization proved that axial prestretch has a positive effect only to the point where deformed configuration and reference configuration are distinguished.