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Published May 1985 | public
Journal Article

Plasticity and Constitutive Relations in Soil Mechanics


After early attempts to describe the behavior of beams under load, equations of equilibrium were first formulated correctly in 1827. Isotropic elastic behavior was described shortly after. Plasticity studies were initiated and failure conditions were established in the period 1860 to 1920. By 1900, correct equations of plasticity for soils had been proposed, and solutions had been obtained to a number of practical cases by graphical integration. Punch or footing problems were examined in the 1920s. By 1950, the mathematical basis of plasticity for metals was firmly established. Since that time, they have been extended by many investigators to account for the peculiarities of soil behavior, including yielding under hydrostatic stresses. The present state of incremental plasticity theory, necessitating the use of computers for solutions, requires consideration of three basic conditions: A yield criterion, a hardening law, and a flow rule.

Additional Information

© 1985 American Society of Civil Engineers. Discussion open until October 1, 1985. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on November 2, 1984. This paper is part of the Journal of Geotechnical Engineering, Vol. 111, No. 5, May, 1985. As far as possible, the writer has confined his examination to the area of mechanics in general and plasticity in particular, to keep from overlapping aspects of the history of soil mechanics which were well-described by Skempton (102). It will be apparent that the historical works of Todhunter and Pearson (113) and Timoshenko (112) have been used as guides, but the writer examined the important papers in their original forms himself. For the theoretical portion of this paper, the writer owes much to extensive conversations with J.-P. Bartlet. The writer is indebted to Dr. G. W. Housner for tracking down the first da Vinci reference after the writer had mislaid it, for finding the second reference, and for many enjoyable conversations through the years on curiosities in the history of mechanics. The writer is grateful to Professor H. B. Sutherland of Glasgow University for first introducing him to the peculiarities of soil mechanics. Y. Dafalias and A. Rosakis provided information on Greek etymology. Thanks go to S. Beckenbach and particularly to G. Jackson for their patience in typing innumerable drafts of this paper.

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