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:	Refereed Article
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