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Qualitative study of cavitated bifurcation for a class of incompressible generalized neo-Hookean spheres

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Abstract

The problem of spherical cavitated bifurcation was examined for a class of incompressible generalized neo-Hookean materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. The condition of void nucleation for this problem was obtained. In contrast to the situation for a homogeneous isotropic neo-Hookean sphere, it is shown that not only there exists a secondary turning bifurcation point on the cavitated bifurcation solution which bifurcates locally to the left from trivial solution, and also the critical load is smaller than that for the material with no perturbations, as the parameters belong to some regions. It is proved that the cavitated bifurcation equation is equivalent to a class of normal forms with single-sided constraints near the critical point by using singularity theory. The stability of solutions and the actual stable equilibrium state were discussed respectively by using the minimal potential energy principle.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics; Department of Mathematics, Shanghai University, 200072, Shanghai, P.R. China

    Yuan Xue-gang & Zhu Zheng-you

  2. Department of Mathematics and Informational Science, Yantai University, 264005, Yantai, Shandong, P.R. China

    Yuan Xue-gang

Authors
  1. Yuan Xue-gang
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  2. Zhu Zheng-you
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Additional information

Communicated by GUO Xing-ming

Foundation items: the National Natural Science Foundation of China (10272069); the Municipal Key Subject Program of Shanghai of China

Biographies: YUAN Xue-gang, Associate Professor, Doctor, E-mail: mengjn@ytu.edu.cn; ZHU Zheng-you, Professor, E-mail: chjcheng@mail.shu.edu.cn

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Xue-gang, Y., Zheng-you, Z. Qualitative study of cavitated bifurcation for a class of incompressible generalized neo-Hookean spheres. Appl Math Mech 26, 185–194 (2005). https://doi.org/10.1007/BF02438240

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  • DOI: https://doi.org/10.1007/BF02438240

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2000 Mathematics Subject Classification

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