The plastic indentation of a layer by a flat punch
Author:
R. T. Shield
Journal:
Quart. Appl. Math. 13 (1955), 27-46
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/67719
MathSciNet review:
67719
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Abstract: Upper and lower bounds for the average pressure in the indentation by a flat, smooth punch of the plane surface of a layer of elastic-perfectly plastic material resting on a rough, rigid base are obtained by the application of the limit-design theorems. The material of the layer is assumed to obey Tresca’s yield criterion of constant maximum shearing stress during plastic deformation. The square punch problem is considered in detail for layers whose thickness is greater than one-fourteenth of the width of the punch. For thinner layers, reasonably close upper and lower bounds for the average pressure over the square punch are obtained as functions of the relative thickness of the layer. The circular punch is considered briefly, and the bounds obtained determine the indentation force with sufficient accuracy for layers which are not too thick compared with the width of the punch.
A. Wang and E. H. Lee, Plastic flow in a thin sheet of perfectly plastic material laid on a rough rigid base and compressed by a smooth flat disc, Report AC-47 to Armstrong Cork Co., Brown University, 1953.
R. T. Shield and D. C. Drucker, The application of limit analysis to punch-indentation problems, J. Appl. Mech. 20, 453-460 (1953).
H. J. Greenberg and W. Prager, Limit design of beams and frames, Proc. Am. Soc. Civil Engrs. 77, Separate No. 59 (1951); Trans. A.S.C.E. 117, 447-484 (1952).
- D. C. Drucker, H. J. Greenberg, and W. Prager, The safety factor of an elastic-plastic body in plane strain, J. Appl. Mech. 18 (1951), 371–378. MR 0051119
- D. C. Drucker, W. Prager, and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9 (1952), 381–389. MR 45573, DOI https://doi.org/10.1090/S0033-569X-1952-45573-2
R. T. Shield, Plastic potential theory and Prandtl bearing capacity solution, J. Appl. Mech. 21, 193-194 (1954).
L. Prandtl, Ueber die Haerte plastischer Koerper, Nachrichten Ges. Wiss. Goettingen, Math. Phys. Kl. 1920, pp. 74-85 (1920).
A. Wang and E. H. Lee, Plastic flow in a thin sheet of perfectly plastic material laid on a rough rigid base and compressed by a smooth flat disc, Report AC-47 to Armstrong Cork Co., Brown University, 1953.
R. T. Shield and D. C. Drucker, The application of limit analysis to punch-indentation problems, J. Appl. Mech. 20, 453-460 (1953).
H. J. Greenberg and W. Prager, Limit design of beams and frames, Proc. Am. Soc. Civil Engrs. 77, Separate No. 59 (1951); Trans. A.S.C.E. 117, 447-484 (1952).
D. C. Drucker, H. J. Greenberg and W. Prager, The safety factor of an elastic-plastic body in plane strain, J. Appl. Mech., 73, 371-378 (1951).
D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems for continuous media, Q. Appl. Math. 9, 381-389 (1952).
R. T. Shield, Plastic potential theory and Prandtl bearing capacity solution, J. Appl. Mech. 21, 193-194 (1954).
L. Prandtl, Ueber die Haerte plastischer Koerper, Nachrichten Ges. Wiss. Goettingen, Math. Phys. Kl. 1920, pp. 74-85 (1920).
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Article copyright:
© Copyright 1955
American Mathematical Society
