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Abstract

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

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[1] Chen, Y.C., and Haughton, D.M.: Stability and bifurcation of inflation of elastic cylinders . Proceedings of the Royal Society of London A, 459, 137-156 (2003).

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[4] Haughton, D.M., and Ogden, R.W.: On the incremental equations in non-linear elasticity. I. Membrane theory . Journal of the Mechanics and Physics of Solids, 26(2), 93-110 (1978).

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A Comparison of Stability and Bifurcation Criteria for Inflated Spherical Elastic Shells

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