On large bending deformations of transversely isotropic rectangular elastic blocks

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Kassianidid, F. ; Ogden, R. (2007)

In this paper we examine the classical problem of finite bending of a rectangular block of elastic material into a sector of a circular cylindrical tube in respect of compressible transversely isotropic elastic materials. More specifically, we consider the possible existence of isochoric solutions. In contrast to the corresponding problem for isotropic materials, for which such solutions do not exist for a compressible material, we determine conditions on the form of the strain-energy function for which isochoric solutions are possible. The results are illustrated for particular classes of energy function.
  • References (20)
    20 references, page 1 of 2

    [1] M. Aron, Y. Wang: On deformations with constant modified stretches describing the bending of rectangular blocks, Quart. J. Mech. Appl. Math., 48 (1995), 375-387.

    [2] M. Aron, Y. Wang: Remarks concerning the flexure of a compressible nonlinearly elastic rectangular block, J. Elasticity, 40 (1995), 99-106.

    [3] O. T. Bruhns, H. Xiao, A. Meyers: Finite bending of a rectangular block of an elastic Hencky material, J. Elasticity, 66 (2002), 237-256.

    [4] M. A. Dowaikh, R. W. Ogden: On surface waves and deformations in a compressible elastic half-space, Stability Appl. Anal. Contin. Media, 1 (1991), 27-45.

    [5] A. E. Green, J. E. Adkins: Large elastic deformations, second edition, revised by A. E. Green, Clarendon Press, Oxford 1970.

    [6] A. E. Green, W. Zerna: Theoretical elasticity, second edition, Clarendon Press, Oxford 1968.

    [7] X. Jiang: On deformations of compressible hyperelastic material, PhD Thesis, University of Glasgow 1998.

    [8] X. Jiang, R. W. Ogden: On azimuthal shear of a circular cylindrical tube of compressible elastic material, Quart. J. Mech. Appl. Math., 51 (1998), 143-158.

    [9] X. Jiang, R. W. Ogden: Some new solutions for the axial shear of a circular cylindrical tube of compressible elastic material, Int. J. Non-Linear Mech., 35 (2000), 361-369.

    [10] J. Merodio, R. W. Ogden: Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation, Arch. Mech., 54 (2002), 525-552.

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