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On the relative energies of the Rivlin and cavitation instabilities for compressible materials


Reference:

Lloyd, J. G. and Sivaloganathan, J., 2012. On the relative energies of the Rivlin and cavitation instabilities for compressible materials. Mathematics and Mechanics of Solids, 17 (4), pp. 338-350.

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    Official URL:

    http://dx.doi.org/10.1177/1081286511418275

    Abstract

    In 1948, Rivlin showed that if a cube of incompressible neo-Hookean material is subjected to a sufficiently large uniform normal dead-load on its boundary, then an asymmetric deformation is the minimizer of the energy in the class of homogeneous deformations. Ball showed in 1982 that, for classes of compressible elastic materials, if a ball of the material is subjected to a sufficiently large uniform radial dead-load, then a deformation forming a cavity is the minimizer of the energy in the class of radial deformations. In this paper we consider compressible hyperelastic materials and show that under such dead-loading, if a local minimizer of the radial energy forms a cavity, then there necessarily exists an asymmetric homogeneous deformation with less energy. Our approach extends and generalizes previous results of Abeyaratne and Hou for the incompressible case.

    Details

    Item Type Articles
    CreatorsLloyd, J. G.and Sivaloganathan, J.
    DOI10.1177/1081286511418275
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code31186

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