Exact Solution for Depth of Impact Crater into Granular Bed
Publication: Journal of Engineering Mechanics
Volume 144, Issue 1
Abstract
When a sphere impacts a granular bed such as a sand bed, the penetration depth is often determined by empirical scaling laws or numerical simulations. This paper uses a unified force law for granular impact cratering to obtain a simple, explicit, and exact solution for the maximum penetration depth in terms of the Lambert function. The exact solution is confirmed with published laboratory data and numerical simulations; thus it can be used to determine the drag coefficients accurately.
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Acknowledgments
The author thanks J. Crassous and A. Seguin, who provided the data in Fig. 3.
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Information
Published In
Journal of Engineering Mechanics
Volume 144 • Issue 1 • January 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Mar 22, 2017
Accepted: Jul 20, 2017
Published online: Nov 13, 2017
Published in print: Jan 1, 2018
Discussion open until: Apr 13, 2018
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