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Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons
journal contribution
posted on 2023-05-21, 04:23 authored by Lawrence ForbesLawrence Forbes, Stephen WaltersStephen Walters, Anya ReadingAnya ReadingAn 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.
Funding
Australian Research Council
History
Publication title
Journal of ElasticityVolume
146Pagination
1-27ISSN
0374-3535Department/School
School of Natural SciencesPublisher
Kluwer Academic PublPlace of publication
Van Godewijckstraat 30, Dordrecht, Netherlands, 3311 GzRights statement
© Crown 2021Repository Status
- Restricted