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.
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