Dynamic extension of a compressible nonlinearly elastic membrane tube

Erbay H., Tuzel V.

IMA JOURNAL OF APPLIED MATHEMATICS, vol.70, no.1, pp.25-38, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 1
  • Publication Date: 2005
  • Doi Number: 10.1093/imamat.hxh061
  • Title of Journal : IMA JOURNAL OF APPLIED MATHEMATICS
  • Page Numbers: pp.25-38

Abstract

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.