Stability and bifurcation of inflation of elastic cylinders

Yi-Chao Chen (1) , David Haughton (2)

1 Department of Mechanical Engineering, University of Houston
2 Department of Mathematics

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 di¬erential equations. The positive-de­ niteness 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 in®a-tion 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.

Domaines: Sciences de l'ingénieur [physics]

Yi-Chao Chen, David Haughton. Stability and bifurcation of inflation of elastic cylinders. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2002, ⟨10.1098/rspa.2002.1024⟩. ⟨hal-01302963⟩