Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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.

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DOI: https://doi.org/10.1090/qam/67719
Article copyright: © Copyright 1955 American Mathematical Society

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