Nonlinear Stability Analysis of a Pre-stressed Elastic Half-space

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Ogden, RW ; Fu, YB (1996)
  • Publisher: International Centre for Numerical Methods in Engineering
  • Subject: QA75

In this paper the nonlinear evolution of near-neutral modes in a pre-stressed elastic half-space governed by an infinite system of evolution equations is discussed. The theory is illustrated for the case in which the pre-stress is a uniaxial compression and the perturbation consists initially of a single mode. It is shown that excitation of harmonics due to nonlinear interaction always leads to the formation of shocks, whether the elastic half-space is super-critically or sub-critically near-neutral and that when the half-space is super-critically near-neutral shocks always form before any significant growth in amplitude has taken place. In considering the static specialization of the evolution equations, two existing methods are assessed critically and shown to be flawed.
  • References (11)
    11 references, page 1 of 2

    [1] R.W. Ogden, Non-linear elastic deformations, Ellis Horwood, Chichester (1984).

    [2] C.H. Wu and G.Z. Cao, Buckling problems in finite plane elasticity-harmonic materials, Q. Appl. Math., 41 (1984) 461-474.

    [3] M.A. Dowaikh and R.W. Ogden, On surface waves and deformations in a prestressed incompressible elastic solid, IMA J. Appl. Math., 44 (1990) 261-284.

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

    [5] Y.B. Fu and G.A. Rogerson, A nonlinear analysis of instability of a pre-stressed incompressible elastic plate, Proc. R. Soc. Lond., A446 (1994) 233-254.

    [6] Y.B. Fu, On the instability of inextensible elastic bodies: nonlinear evolution of non-neutral, neutral and near-neutral modes, Proc. R. Soc. Lond., A443 (1993) 59-82.

    [7] Y.B. Fu, A nonlinear analysis of instability of pre-stressed inextensible elastic bodies, in Proc. IUTAM Symposium on Nonlinear Waves in Solids, (eds J.E. Wegner and F.R. Norwood), pp. 83-88, ASME, New Jersey (1995).

    [8] D.F. Parker and F.M. Talbot, Analysis and computation for nonlinear elastic surface waves of permanent form, J. Elasticity, 15 (1985) 389-426.

    [9] M.F. Hamilton, Y.A. II'insky, and E.A. Zabolotskaya, On the existence of stationary nonlinear Rayleigh waves, J. Acoust. Soc. Am., 93 (1993) 3089-3095.

    [10] Y.B. Fu and B. Devenish, Effects of pre-stresses on the propagation of nonlinear surface waves in an incompressible elastic half-space, Q. J. Mech. Appl. Math., 49 (1996) 65-80.

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