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Bifurcation and stability of homogeneous deformations of an elastic body under dead load tractions with Z 2 symmetry

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Abstract

An analysis is given of bifurcation and stability of homogeneous deformations of a homogeneous, isotropic, incompressible elastic body subject to three perpendicular sets of dead-load surface tractions of which two have equal magnitude. A minimization problem is formulated within the framework of non-linear elasticity, which leads to a bifurcation problem with Z 2 symmetry. Various bifurcation diagrams are deduced by using singularity theory, and stabilities of solution branches are examined.

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References

  1. L.R.G. Treloar, Stresses and birefringence in rubber subjected to general homogeneous strain. Proc. Phys. 60 (1948) 135–144.

    Google Scholar 

  2. E.A. Kearsley, Asymmetric stretching of a symmetrically loaded elastic shelt. Int. J. Solids Structures 22 (1986) 111–119.

    Google Scholar 

  3. G.P. MacSithigh, Energy-minimal finite deformations of a symmetrically loaded elastic sheet. Q.J. Mech. Appl. Math. 39 (1986) 111–123.

    Google Scholar 

  4. J.M. Ball and D.G. Schaeffer, Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions. Math. Proc. Camb. Phil. Soc. 94 (1983) 315–339.

    Google Scholar 

  5. Y.C. Chen, Stability of homogeneous deformations of an incompressible elastic body under dead-load surface tractions. J. Elasticity 17 (1987) 223–248.

    Google Scholar 

  6. J.M. Ball, Personal communication.

  7. M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. I, Springer-Verlag New York Inc. (1985).

  8. M. Golubitsky, I. Stewart and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. II, Springer-Verlag New York Inc. (1988).

  9. H. Whitney, Differentiable even functions. Duke Math. J. 10 (1943) 159–160.

    Google Scholar 

  10. G. Dangelmayr and D. Armbruster, Classification of Z(2)-equivariant imperfect bifurcations with Corank 2. Proc. London Math. Soc. 46 (1983) 517–546.

    Google Scholar 

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Author notes

  1. Yi-Chao Chen

    Present address: Department of Mechanical Engineering, University of Houston, 77204, Houston, TX, USA

Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, Cornell University, 14853-1503, Ithaca, NY, USA

    Yi-Chao Chen

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  1. Yi-Chao Chen
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Chen, YC. Bifurcation and stability of homogeneous deformations of an elastic body under dead load tractions with Z 2 symmetry. J Elasticity 25, 117–136 (1991). https://doi.org/10.1007/BF00042461

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  • DOI: https://doi.org/10.1007/BF00042461

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