DOI: 10.1090/qam/77386. On uniqueness in the theory of plasticity

On uniqueness in the theory of plasticity

10.1090/qam/77386

Crossref journal-article

American Mathematical Society (AMS)

Quarterly of Applied Mathematics (14)

Abstract

The fundamental definitions of work-hardening and perfect plasticity have far reaching implications with respect to uniqueness of solution for elastic-plastic bodies. Satisfaction of the basic postulate, that in a cycle work cannot be extracted from the material and the system of forces acting upon it, guarantees an existing solution to be stable but not necessarily unique. Uniqueness follows for the usual linear relation between the increments or rates of stress and strain and also for combinations of such linear forms. Conversely, lack of uniqueness results for an elastic-perfectly plastic body when, for example, the maximum shearing stress criterion of yield is employed with the Mises flow rule.

Bibliography

Drucker, D. C. (1956). On uniqueness in the theory of plasticity. Quarterly of Applied Mathematics, 14(1), 35â42.

Authors 1

D. C. Drucker (first)

References 12 Referenced 109

10.1002/sapm19482711 / J. Math. Physics / A variational principle for plastic materials with strain-hardening by Hodge, P. (1948)
{'volume-title': 'The Mathematical Theory of Plasticity', 'year': '1950', 'author': 'Hill, R.', 'key': '2'} / The Mathematical Theory of Plasticity by Hill, R. (1950)
B. Budiansky, Fundamental theorems and consequences of the slip theory of plasticity, Ph.D. thesis, Brown University, Providence, R. I., 1950
10.1090/qam/59769 / Quart. Appl. Math. / Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface by Koiter, W. T. (1953)
{'key': '5', 'first-page': '487', 'article-title': 'A more fundamental approach to plastic stress-strain relations', 'author': 'Drucker, D. C.', 'year': '1952'} / A more fundamental approach to plastic stress-strain relations by Drucker, D. C. (1952)
10.1090/qam/34210 / Quart. Appl. Math. / Some implications of work hardening and ideal plasticity by Drucker, D. C. (1950)
{'issue': '1871', 'key': '7', 'first-page': '33', 'article-title': 'A mathematical theory of plasticity based on the concept of slip', 'volume': '1949', 'author': 'Batdorf, S. B.', 'year': '1949', 'journal-title': 'Tech. Notes Nat. Adv. Comm. Aeronaut.', 'ISSN': 'http://id.crossref.org/issn/0097-2177', 'issn-type': 'print'} / Tech. Notes Nat. Adv. Comm. Aeronaut. / A mathematical theory of plasticity based on the concept of slip by Batdorf, S. B. (1949)
10.1080/14786445108561065 / Philos. Mag. (7) / A theory of the plastic distortion of a polycrystalline aggregate under combined stresses by Bishop, J. F. W. (1951)
W. Prager, General theory of limit design, Proc. 8th Internatl. Congr. Theoret. Appl. Mech. Istanbul (1952)
J. L. Sanders, Plastic stress-strain relations based on infinitely many plane loading surfaces, Proc. 2nd U. S. Natl. Congr. Appl. Mech., Ann Arbor, Mich., 1954, pp. 455-460
{'volume-title': 'Theory of perfectly plastic solids', 'year': '1951', 'author': 'Prager, William', 'key': '11'} / Theory of perfectly plastic solids by Prager, William (1951)
D. C. Drucker, The significance of the criterion for additional plastic deformation of metals, J. Colloid Sci. 4, pp. 299-311 (1949) (10.1016/0095-8522(49)90011-2)

Dates

Type	When
Created	8 years, 8 months ago (Dec. 14, 2016, 5:01 p.m.)
Deposited	10 months, 1 week ago (Oct. 25, 2024, 11:51 a.m.)
Indexed	1 month, 4 weeks ago (July 7, 2025, 3:28 p.m.)
Issued	69 years, 5 months ago (April 1, 1956)
Published	69 years, 5 months ago (April 1, 1956)
Published Print	69 years, 5 months ago (April 1, 1956)

Funders 0

None

BibTeX

@article{Drucker_1956, title={On uniqueness in the theory of plasticity}, volume={14}, ISSN={1552-4485}, url={http://dx.doi.org/10.1090/qam/77386}, DOI={10.1090/qam/77386}, number={1}, journal={Quarterly of Applied Mathematics}, publisher={American Mathematical Society (AMS)}, author={Drucker, D. C.}, year={1956}, month=apr, pages={35–42} }

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