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Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons

Forbes, LK ORCID: 0000-0002-9135-3594, Walters, SJ ORCID: 0000-0002-4480-767X and Reading, AM ORCID: 0000-0002-9316-7605 2021 , 'Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons' , Journal of Elasticity, vol. 146 , pp. 1-27 , doi: 10.1007/s10659-021-09852-6.

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Abstract

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.

Item Type: Article
Authors/Creators:Forbes, LK and Walters, SJ and Reading, AM
Keywords: surface waves, geometric nonlinearity, curvature singularity, peakons, numerical methods
Journal or Publication Title: Journal of Elasticity
Publisher: Kluwer Academic Publ
ISSN: 0374-3535
DOI / ID Number: 10.1007/s10659-021-09852-6
Copyright Information:

© Crown 2021

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