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Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons
Citation
Forbes, LK and Walters, SJ and Reading, AM, Large-amplitude elastic free-surface waves: geometric nonlinearity and peakons, Journal of Elasticity, 146 pp. 1-27. ISSN 0374-3535 (2021) [Refereed Article]
Copyright Statement
© Crown 2021
DOI: doi:10.1007/s10659-021-09852-6
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 Details
Item Type: | Refereed Article |
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Keywords: | surface waves, geometric nonlinearity, curvature singularity, peakons, numerical methods |
Research Division: | Mathematical Sciences |
Research Group: | Applied mathematics |
Research Field: | Theoretical and applied mechanics |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | Forbes, LK (Professor Larry Forbes) |
UTAS Author: | Walters, SJ (Mr Stephen Walters) |
UTAS Author: | Reading, AM (Professor Anya Reading) |
ID Code: | 147927 |
Year Published: | 2021 |
Funding Support: | Australian Research Council (DP190100418) |
Deposited By: | Physics |
Deposited On: | 2021-11-24 |
Last Modified: | 2022-08-23 |
Downloads: | 0 |
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