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 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.
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Communicated by Huang Yongnian
Foundation item: the National Natural Science Foundation of China (19672001, 19990510); Doctoral Foundation of the National Education Committee of China; Foundation of the National Key Laboratory of China
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Ming, J., Kefu, H. & Jike, W. A study of the catastrophe and the cavitation for a spherical cavity in Hooke's material with 1/2 poisson's ratio. Appl Math Mech 20, 928–935 (1999). https://doi.org/10.1007/BF02452493
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DOI: https://doi.org/10.1007/BF02452493