On the influence of material properties on the wave propagation in Mindlin-type microstructured solids

Salupere, Andrus; Tamm, Kert

doi:10.1016/j.wavemoti.2013.05.004

Cited by 7 publications

(1 citation statement)

References 27 publications

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“…Secondly, a surface-wave singularity in the curvature may be produced within finite time, for sufficiently intense initial disturbances. This manifests as a discontinuity in the derivative of the surface profile at a wave peak, and so has been labelled a "peakon" by some authors using weakly nonlinear asymptotic theories to study such phenomena [6], [21]. We discuss a possible physical meaning for these peakon curvature singularities in Section 6.…”

Section: Introductionmentioning

confidence: 99%

Large-Amplitude Elastic Free-Surface Waves: Geometric Nonlinearity and Peakons

Forbes,

Walters,

Reading

2021

Preprint

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An instantaneous sub-surface disturbance in a two-dimensional elastic half-space is considered. The disturbance propagates through the elastic material until it reaches the free surface, after which it propagates out along the surface. In conventional theory, the free-surface conditions on the unknown surface are projected onto the flat plane y = 0, so that a linear model may be used. Here, however, we present a formulation that takes explicit account of the fact that the location of the free surface is unknown a priori, and we show how to solve this more difficult problem numerically. This reveals that, while conventional linearized theory gives an accurate account of the decaying waves that travel outwards along the surface, it can under-estimate the strength of the elastic rebound above the location of the disturbance. In some circumstances, the non-linear solution fails in finite time, due to the formation of a "peakon" at the free surface. We suggest that brittle failure of the elastic material might in practice be initiated at those times and locations.

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Section: Introductionmentioning

confidence: 99%