Finite deformations of an initially stressed cylindrical shell under internal pressure

Abstract

International audienceThis paper investigates the large deformations of an extended thick cylindrical tube under internal pressure, with emphasis on the static nonlinear behavior and instabilities of the shell. Thick elastic tubes that undergo large elastic deformations under internal pressure can exhibit novel instabilities. After some deformation, part of the tube becomes highly deformed taking the form of a bulge, while the remainder appears almost unchanged. This local instability phenomenon corresponds to a limit point along the nonlinear equilibrium path. After the onset of these highly nonuniform deformations, the local bulge initially grows with a marked decrease in internal pressure while the rest of the tube unloads. First, a detailed experimental analysis is carried out involving different geometries and initial axial forces and the influence of the axial force and of the internal pressure on the critical pressure is investigated. The shell used in the experiments is composed of an isotropic, homogeneous and hyperelastic rubber, which is modeled as a Mooney–Rivlin incompressible material, described by two elastic constants. These constants are obtained by comparing the experimental and numerical solutions for the shell under axial tension. The governing shell equations are solved numerically using the finite-element method, using the program ABAQUS. The experimental results are, as shown in the paper, in satisfactory agreement with the numerical analysis

Localized bulging in an inflated cylindrical tube of arbitrary thickness – the effect of bending stiffness

“…It is clear from this deduction that localized bulging must necessarily occur before any bifurcation into periodic patterns. This fact is consistent with all experimental observations (Kyriakides & Chang, 1990Pamplona et al, 2006;Goncalves et al, 2008).…”

“…This is consistent with the observations made with regards Fig.6. Results shown in this figure can also be used directly to interpret the experimental results reported in Goncalves et al (2008). We observe, however, that in the above-mentioned paper the authors used a Mooney-Rivlin material model in their numerical simulations.…”

“…The latter case of a fixed axial stretch corresponds to the situation when the tube is first subjected to an axial extension and then both ends are fixed. Such a setup was used in the experiments of Goncalves et al (2008), and is also how arteries are in situ.…”

“…Localized bulging in an inflated isotropic rubber tube was first documented by Mallock (1891), and later studied experimentally and numerically by Kyriakides & Chang (1990, Pamplona et al (2006), Goncalves et al (2008), and Shi & Moita (1996). The propagation stage was recognized by Yin (1977) and Chater & Hutchinson (1984) as a twophase deformation governed by Maxwell's equal area rule, but the character of the initiation stage, and its connection with the so-called limit-point instability (Alexander, 1971;Kanner & Horgan, 2007), was not fully understood until more recently.…”

“…We also plot the bifurcation condition as a curve in the pressure/axial stretch plane so that the effects of axial stretch are graphically displayed. This enables us to make a direct comparison with the experimental results reported in Goncalves et al (2008). In Section 6 we propose a two-term asymptotic bifurcation condition for computing the initiation pressure; the first term corresponds to the membrane theory whereas the second term incorporates the effect of bending stiffness.…”