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A boundary value problem of elastoplastic deformation process theory: Existence and uniqueness theorems

Published online by Cambridge University Press:  17 February 2009

Dao Huy Bich
Dao Huy Bich
Affiliation:
School of Mathematics and Statistics, Curtin University of Technology, Perth, Western Australia. On leave from State University of Hanoi, Vietnam.
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Abstract

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This paper deals with the complete constitutive relations of elastoplastic deformation process theory, based on llyushin's postulate of isotropy and hypotheses of local determinancy and complanarity in plastic stage with complex loading. The formulation of the boundary value problem is given and existence and uniqueness theorems are considered.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 4 , April 1994 , pp. 506 - 524
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Dao, H. B., “On the hypothesis of local determinancy in plasticity theory”, Bulletin of the Moscow State University 2 (1965) 67–75, in Russian.Google Scholar
[2]Dao, H. B., “Some properties of functions in fundamental stress-strain relations. Selection ‘applied solidity and plasticity’”, Gorky USSR 17 (1981) 37–45, in Russian.Google Scholar
[3]Dao, H. B., “Uniqueness theorem of boundary value problem of plasticity using the hypothesis of local determinancy”, Mechanics of Solids 17 (1982) 110–115, translated by Allerton Press Inc.Google Scholar
[4]Dao, H. B., “Research of the local theory of elastoplastic deformation processes”, Dr Sc. Thesis, The Moscow State University, 1987, in Russian.Google Scholar
[5]llyushin, A. A., “On the stress-strain relationship in mechanics of continuum media”, J. of Applied Mathematics and Mechanics 18 (1954) 641–666, in Russian.Google Scholar
[6]Lensky, V. S., “Analysis of plastic behaviour of metals under complex loading. Plasticity”, Proc. 2nd Symposium on naval structural mechanics, New York (1960) 259–278.Google Scholar
[7]Lensky, V. S., “Hypothesis of local determinancy in plasticity theory”, Transactions of USSR Academy of Sciences 5 (1962) 154–158, in Russian.Google Scholar
[8]Lensky, V. S. and Lensky, E. V., “Three-terms relation of general plasticity”, Mechanics of Solids 20 (1985) 111–115.Google Scholar
[9]Minty, G. J., “Monotone (nonlinear) operators in hilbert space”, Duke Math. J. 29 (1962) 341–346.CrossRefGoogle Scholar
[10]Tanaka, E., “Hypothesis of local determinancy for five dimensional strain trajectories”, Acta mechanica 52 (1984).CrossRefGoogle Scholar
[11]Tokuda, M., Ohashi, Y. et al. , “On the hypothesis of local determinancy and a concise stress-strain relation for curved strain path”, Bulletin of JSME 26 (1983) 1475–1480.CrossRefGoogle Scholar