Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres

YUAN Xue-gang; ZHU Zheng-you

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(2): 169-177

YUAN Xue-gang, ZHU Zheng-you. Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres[J]. Applied Mathematics and Mechanics, 2005, 26(2): 169-177.

Citation:

YUAN Xue-gang, ZHU Zheng-you. Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres[J]. Applied Mathematics and Mechanics, 2005, 26(2): 169-177.

Citation:

YUAN Xue-gang, ZHU Zheng-you. Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres[J]. Applied Mathematics and Mechanics, 2005, 26(2): 169-177.

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Qualitative Study of Cavitated Bifurcation for a Class of Incompressible Generalized neo-Hookean Spheres

YUAN Xue-gang^1,2,
ZHU Zheng-you¹

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

Received Date: 2002-12-20
Rev Recd Date: 2004-06-25
Publish Date: 2005-02-15

Abstract

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 singlesided 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.
- incompressible generalized neo-Hookean material,
- cavitated bifurcation,
- normal form,
- stability and catastrophe

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References(14)

References

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