Effect of axial prestretch on inflation instability in finitely extensible thin-walled tube

Abstract

Mechanical response of elastic materials undergoing large deformations exhibit several kinds of a loss of stability. Such a situation may occur, for instance, when a thin-walled cylinder is inflated by an internal pressure. The loss of stability is manifested by a non-monotonic relationship between the inflating pressure and the circumferential stretch of the tube. The results, known from the literature, show that hyperelastic materials with so called limiting chain extensibility property always exhibit a stable response for sufficiently small values of the limiting extensibility parameter Jm. In other words, rapid large strain stiffening prevents elastomeric materials from an onset of instability. The present study demonstrates how axial prestretch of the thin-walled tube affects the stability of the deformation. It is shown that for axial prestretches z = 1 (non-prestretched), 1.05, 1.1, 1.2, 1.5, 2, 3, and 5 the stable inflation is obtained for materials with Jm = 19.11, 20.32, 21.55, 24.06, 32.1, 47.43, 87.23, and 207.8, respectively. From which can be concluded that the higher the prestretch is, the more compliant material will show stable inflation. It was also found that the higher the prestretch is, the lower is the pressure at which the instability occurs.