Dynamic extension of a compressible nonlinearly elastic membrane tube
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CitationErbay, H. A. & Tüzel, V. H. (2005; 2004). Dynamic extension of a compressible nonlinearly elastic membrane tube. IMA Journal of Applied Mathematics (Institute of Mathematics and its Applications), 70(1), 25-38. doi:10.1093/imamat/hxh061
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.