Exact solution for depth of impact crater into granular bed

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2 Scopus citations


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.

Original languageEnglish (US)
Article number06017018
JournalJournal of Engineering Mechanics
Issue number1
StatePublished - Jan 1 2018


  • Drag law
  • Granular flow
  • Impact crater
  • Lambert function
  • Nonlinear dynamics
  • Sphere impact

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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