A simple proof of a result in finite plasticity
Author:
J. Casey
Journal:
Quart. Appl. Math. 42 (1984), 61-71
MSC:
Primary 73E05
DOI:
https://doi.org/10.1090/qam/736505
MathSciNet review:
736505
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Abstract: Within the framework of a purely mechanical rate-type theory of finitely deforming elastic-plastic materials, a simple proof is given of a normality condition which has been shown by Naghdi & Trapp [6] to follow from a physically plausible work assumption. In addition, a variation of the proof is used to demonstrate convexity of yield surfaces for a special class of materials, a result which was also originally established by Naghdi & Trapp [10].
- D. C. Drucker, A more fundamental approach to plastic stress-strain relations, Proceedings of the First U. S. National Congress of Applied Mechanics, Chicago, 1951, The American Society of Mechanical Engineers, New York, N. Y., 1952, pp. 487–491. MR 0054502
- P. M. Naghdi, Stress-strain relations in plasticity and thermoplasticity, Plasticity: Proceedings of the Second Symposium on Naval Structural Mechanics, Pergamon, Oxford, 1960, pp. 121–169. MR 0120830
- A. A. Il′jušin, On the postulate of plasticity, J. Appl. Math. Mech. 25 (1961), 746–752. MR 0138266, DOI https://doi.org/10.1016/0021-8928%2861%2990044-2
- A. E. Green and P. M. Naghdi, A general theory of an elastic-plastic continuum, Arch. Rational Mech. Anal. 18 (1965), no. 4, 251–281. MR 1553473, DOI https://doi.org/10.1007/BF00251666
---, A thermodynamic development of elastic-plastic continua, Proc. IUTAM Symp. on Irreversible Aspects of Continuum Mech. and Transfer of Physical Characteristics in Moving Fluids (ed. H. Parkus & L. I. Sedov) 117–131, Springer-Verlag, 1966
- P. M. Naghdi and J. A. Trapp, Restrictions on constitutive equations of finitely deformed elastic-plastic materials, Quart. J. Mech. Appl. Math. 28 (1975), 25–46. MR 363086, DOI https://doi.org/10.1093/qjmam/28.1.25
J. Casey & P. M. Naghdi, On the characterization of strain-hardening in plasticity, J. Appl. Mech. 48, 1981, 285–296
- J. Casey and P. M. Naghdi, A remark on the definition of hardening, softening and perfectly plastic behavior, Acta Mech. 48 (1983), no. 1-2, 91–94. MR 713479, DOI https://doi.org/10.1007/BF01178499
---, Strain-hardening response of elastic-plastic materials, Presented at International Conf. on Constitutive Laws for Engineering Materials: Theory and Application (Tucson, Arizona, 10–14 January, 1983); To appear in Mechanics of Engineering Materials, Wiley
P. M. Naghdi & J. A. Trapp, On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticity, J. Appl. Mech. 42, 1975, 61–66
---, The significance of formulating plasticity theory with reference to loading surfaces in strain space, Int. J. Engng. Sci. 13, 1975, 785–797
P. M. Naghdi, Some constitutive restrictions in plasticity, In Constitutive equations in viscoplasticity: computational and engineering aspects, AMD, 20, 79–93, ASME., 1976
- Robert G. Bartle, The elements of real analysis, 2nd ed., John Wiley & Sons, New York-London-Sydney, 1976. MR 0393369
D. C. Drucker, A more fundamental approach to plastic stress-strain relations, Proc. First U.S. National Cong. of Appl. Mech. (Chicago, 1951), 487–491, ASME, 1952
P. M. Naghdi, Stress-strain relations in plasticity and thermoplasticity, Proc. Second Symp. on Naval Structural Mech. (Brown University, 1960), 121–169, Pergamon Press, 1960
A. A. Il’iushin, On the postulate of plasticity, J. Appl. Math. Mech. (Translation of Prikladnaya Mathematika i Mekhanika) 25, 1961, 746–752
A. E. Green & P. M. Naghdi, A general theory of an elastic-plastic continuum, Arch. Ratl. Mech. Anal. 18, 1965, 251–281
---, A thermodynamic development of elastic-plastic continua, Proc. IUTAM Symp. on Irreversible Aspects of Continuum Mech. and Transfer of Physical Characteristics in Moving Fluids (ed. H. Parkus & L. I. Sedov) 117–131, Springer-Verlag, 1966
P. M. Naghdi & J. A. Trapp, Restrictions on constitutive equations of finitely deformed elastic-plastic materials, Quar.J. Mech. Appl. Math. 28, 1975, 25–46
J. Casey & P. M. Naghdi, On the characterization of strain-hardening in plasticity, J. Appl. Mech. 48, 1981, 285–296
---, A remark on the definition of hardening, softening and perfectly plastic behavior. Acta Mech. 48, 1983, 91–94
---, Strain-hardening response of elastic-plastic materials, Presented at International Conf. on Constitutive Laws for Engineering Materials: Theory and Application (Tucson, Arizona, 10–14 January, 1983); To appear in Mechanics of Engineering Materials, Wiley
P. M. Naghdi & J. A. Trapp, On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticity, J. Appl. Mech. 42, 1975, 61–66
---, The significance of formulating plasticity theory with reference to loading surfaces in strain space, Int. J. Engng. Sci. 13, 1975, 785–797
P. M. Naghdi, Some constitutive restrictions in plasticity, In Constitutive equations in viscoplasticity: computational and engineering aspects, AMD, 20, 79–93, ASME., 1976
R. G. Bartle, The elements of real analysis, Wiley, 1964
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Article copyright:
© Copyright 1984
American Mathematical Society
