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IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):25-38; doi:10.1093/imamat/hxh061
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IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

Dynamic extension of a compressible nonlinearly elastic membrane tube*

H. A. Erbay1 § and V. H. Tüzel2 ¶

1 Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak 34469, Istanbul, Turkey, 2 Department of Mathematics, Faculty of Science and Letters, Isik University, Maslak 34398, Istanbul, Turkey  §

The dynamic response of an isotropic compressible hyperelastic membrane tube is considered when one end is fixed and the other is subjected to a suddenly applied dynamic extension. The equations governing dynamic axially symmetric deformations of the membrane tube are presented for a general form of compressible isotropic elastic strain-energy function. Numerical results, obtained using a Godunov-type finite volume method and valid up to the time at which reflections occur at the fixed end of the tube, are given for two specific forms of the strain-energy function that characterizes a class of compressible elastomers (the Blatz–Ko model). The question of how the numerical results are related to the exact solution obtained for a limiting case is discussed.

Keywords: Blatz–Ko material; compressible; membrane tubes; nonlinear elasticity.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday

§ Corresponding author. Email: erbay{at}itu.edu.tr

Present address: University of Minnesota, School of Mathematics, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, USA


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