Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Indentation pressure of a smooth circular punch


Author: E. Levin
Journal: Quart. Appl. Math. 13 (1955), 133-137
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/69736
MathSciNet review: 69736
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Abstract: A smooth, flat, rigid punch under increasing normal load presses against a half space of a perfectly plastic material which obeys Tresca's yield criterion. An admissible velocity field is constructed for an arbitrary smooth punch hence, for any particular case, a limit design theorem of Drucker, Prager and Greenberg may be used to compute an upper bound for the punch indentation pressure. A lower bound for any convex area of indentation has been given by Shield and Drucker. The results of the present paper are used to compute an upper bound for a punch with circular cross section. It is conjectured that this is an upper bound for an arbitrary punch.


References [Enhancements On Off] (What's this?)

  • [1] D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381-389 (1952) MR 0045573
  • [2] H. Tresca, Mémoire sur l'écoulement des corps solides, Mémoires presentés par divers Savants 18, 733-799 (1868)
  • [3] R. Hill, The plastic yielding of notched bars under tension, Quart. J. Mech. and Appl. Math. 2, 40-52 (1949) MR 0029686
  • [4] R. T. Shield and D. C. Drucker, The application of limit analysis to punch indentation problems, J. Appl. Mech. 20, 453-460 (1953)

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DOI: https://doi.org/10.1090/qam/69736
Article copyright: © Copyright 1955 American Mathematical Society

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