SYMMETRY GROUPS AND SIMILARITY SOLUTIONS FOR RADIAL MOTIONS OF COMPRESSIBLE HETEROGENEOUS HYPERELASTIC SPHERES AND CYLINDERS


SUHUBI E.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, vol.32, no.5, pp.817-837, 1994 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 5
  • Publication Date: 1994
  • Doi Number: 10.1016/0020-7225(94)90063-9
  • Title of Journal : INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
  • Page Numbers: pp.817-837

Abstract

The general formalism which was previously developed for partial differential equations of balance type is employed to determine the infinitesimal generators (or isovector fields in the language of exterior calculus) inducing the symmetry group associated with radial motions of a heterogeneous isotropic hyperelastic material. The most general group structure is found and the results obtained are applied to a heterogeneous Ko material in which the initial density and the modulus of the material vary according to certain power laws. The nonlinear ordinary differential equations satisfied by the similarity solution corresponding to the symmetry group admitted by the material are provided.