Jin Ming, Huang Kefu, Wu Jike. A Study of the Catastrophe and the Cavitation for a Spherical Cavity in Hooke’s Material with 1/2 Poisson’s Ratio[J]. Applied Mathematics and Mechanics, 1999, 20(8): 867-874.
Citation: Jin Ming, Huang Kefu, Wu Jike. A Study of the Catastrophe and the Cavitation for a Spherical Cavity in Hooke’s Material with 1/2 Poisson’s Ratio[J]. Applied Mathematics and Mechanics, 1999, 20(8): 867-874.

A Study of the Catastrophe and the Cavitation for a Spherical Cavity in Hooke’s Material with 1/2 Poisson’s Ratio

  • Received Date: 1998-01-14
  • Rev Recd Date: 1999-02-08
  • Publish Date: 1999-08-15
  • In this paper, the catastrophe of a spherical cavity and the cavitation of a spherical cavity for Hooke. s material with 1/2 Poisson's ratio are studied. A nonlinear problem, which is a moving boundary problem for the geometrically nonlinear elasticity in radial symmetric, was solved analytically. The governing equations were written on the deformed region or on the present configuration. And the conditions were described on moving boundary. A closed form solution was found. Furthermore, a bifurcation solution in closed form was given from the trivial homogeneous solution of a solid sphere. The results indicate that there is a tangent bifurcation on the displacement-load curve for a sphere with a cavity. On the tangent bifurcation point, the cavity grows up suddenly, which is a kind of catastrophe. And there is a pit chfork bifurcation on the displacement-load curve for a solid sphere. On the pitchfork bifurcation point, there is a cavitation in the solid sphere.
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