Zone estimates in the elastic-plastic torsion problem
Author:
Wan Lee Yin
Journal:
Quart. Appl. Math. 35 (1977), 410-414
MSC:
Primary 73.35
DOI:
https://doi.org/10.1090/qam/462082
MathSciNet review:
462082
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Abstract: Using continuity and jump conditions across the elastic-plastic interface, we show that the curvature of the shearing stress lines in the plastic zone of a simply connected bar under torsion is bounded above by a number proportionate to the twisting angle. For sufficiently large torsion the above geometrical condition defines a region in the cross-section which is a priori elastic. This lower bound for the elastic zone in the sense of set inclusion is supplemented by an upper bound for the zone area.
- R. Hill, The Mathematical Theory of Plasticity, Oxford, at the Clarendon Press, 1950. MR 0037721
W. Prager and P. G. Hodge, Jr., Theory of perfectly plastic solids, Wiley, New York, 1951, p. 68
- Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers John Wiley & Sons, Inc. New York-London-Sydney, 1964. With special lectures by Lars Garding and A. N. Milgram. MR 0163043
R. Hill, The mathematical theory of plasticity, Oxford, 1950, pp. 84–89
W. Prager and P. G. Hodge, Jr., Theory of perfectly plastic solids, Wiley, New York, 1951, p. 68
L. Bers, F. John and M. Schechter, Partial differential equations, Interscience, New York, 1964, p. 151
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Article copyright:
© Copyright 1977
American Mathematical Society