Stability and bifurcation of inflation of elastic cylinders
Open Access
- 8 January 2003
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 459 (2029), 137-156
- https://doi.org/10.1098/rspa.2002.1024
Abstract
A method of obtaining a full (two–dimensional) nonlinear stability analysis of inhomogeneous deformations of arbitrary incompressible hyperelastic materials is presented. The analysis that we develop replaces the second variation condition expressed as an integral involving two arbitrary perturbations, with an equivalent (third–order) system of ordinary differential equations. The positive–definiteness condition is thereby reduced to the simple numerical evaluation of zeros of a well–behaved function. The general theory is illustrated by applying it to the problem of the inflation of axially stretched thick–walled tubes. The bifurcation theory of such deformations is well known and we compare the bifurcation results with the new stability analysis.Keywords
This publication has 10 references indexed in Scilit:
- Nonlinear stability analysis of pre-stressed elastic bodiesContinuum Mechanics and Thermodynamics, 1999
- A nonlinear stability analysis of an incompressible elastic plate subjected to an all-round tensionJournal of the Mechanics and Physics of Solids, 1998
- Resonant-triad instability of a pre-stressed incompressible elastic plateJournal of Elasticity, 1995
- A nonlinear analysis of instability of a pre-stressed incompressible elastic plateProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1994
- Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With ExamplesApplied Mechanics Reviews, 1987
- Minimization in incompressible nonlinear elasticity theoryJournal of Elasticity, 1986
- Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solidsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1972
- On uniqueness and stability in the theory of finite elastic strainJournal of the Mechanics and Physics of Solids, 1957
- General theory of elastic stabilityQuarterly of Applied Mathematics, 1956
- Implications Of Hadamard's Conditions For Elastic Stability With Respect To Uniqueness TheoremsCanadian Journal of Mathematics, 1956