Axisymmetric bifurcations of thick spherical shells under inflation and compression

Type
Article

Authors
deBotton, G.
Bustamante, R.
Dorfmann, A.

KAUST Grant Number
KUK-C1-013-04

Date
2013-01

Abstract
Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before.© 2012 Published by Elsevier Ltd.

Citation
deBotton G, Bustamante R, Dorfmann A (2013) Axisymmetric bifurcations of thick spherical shells under inflation and compression. International Journal of Solids and Structures 50: 403–413. Available: http://dx.doi.org/10.1016/j.ijsolstr.2012.10.004.

Acknowledgements
This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The work by G. deBotton and A. Dorfmann was supported by the United States - Israel Binational Science Foundation (BSF) under the Research Grant 2008419. R. Bustamante would like to express his gratitude for the financial support provided by FONDECYT (Chile) under Grant No. 11085024.

Publisher
Elsevier BV

Journal
International Journal of Solids and Structures

DOI
10.1016/j.ijsolstr.2012.10.004

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