A STUDY OF THE CATASTROPHE AND THE CAVITATION FOR A SPHERICAL CAVITY IN HOOKE’S MATERIAL WITH 1/2 POISSON’S RATIO

Abstract

Abstract: 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, is solved analytically. The governing equations are written on the deformed region or on the present configuration. And the conditions are described on moving boundary. A closed form solution is found. Furthermore, a bifurcation solution in closed form is 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 pitchfork bifurcation on the displacement_load curve for a solid sphere. On the pitchfork bifurcation point, there is a cavitation in the solid sphere.

Key words: moving boundary, tangent bifurcation, pitchfork bifurcation, cavitation

2010 MSC Number:

O322

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. Applied Mathematics and Mechanics (English Edition), 1999, 20(8): 928-935.

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References

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