Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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].

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  • [1] 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
  • [2] 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
  • [3] A. A. Il′jušin, On the postulate of plasticity, J. Appl. Math. Mech. 25 (1961), 746–752. MR 0138266, https://doi.org/10.1016/0021-8928(61)90044-2
  • [4] 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, https://doi.org/10.1007/BF00251666
  • [5] -, 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
  • [6] 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 0363086, https://doi.org/10.1093/qjmam/28.1.25
  • [7] J. Casey & P. M. Naghdi, On the characterization of strain-hardening in plasticity, J. Appl. Mech. 48, 1981, 285-296
  • [8] 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, https://doi.org/10.1007/BF01178499
  • [9] -, 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
  • [10] 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
  • [11] -, The significance of formulating plasticity theory with reference to loading surfaces in strain space, Int. J. Engng. Sci. 13, 1975, 785-797
  • [12] P. M. Naghdi, Some constitutive restrictions in plasticity, In Constitutive equations in viscoplasticity: computational and engineering aspects, AMD, 20, 79-93, ASME., 1976
  • [13] Robert G. Bartle, The elements of real analysis, 2nd ed., John Wiley & Sons, New York-London-Sydney, 1976. MR 0393369

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DOI: https://doi.org/10.1090/qam/736505
Article copyright: © Copyright 1984 American Mathematical Society

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