Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Normality and convexity of the yield surface in nonlinear plasticity

Authors: Roger Fosdick and Eric Volkmann
Journal: Quart. Appl. Math. 51 (1993), 117-127
MSC: Primary 73G20; Secondary 73E05
DOI: https://doi.org/10.1090/qam/1205941
MathSciNet review: MR1205941
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An elementary proof of the normality condition is given. In addition, the convexity-concavity character of the yield surface is found to be related to the changes in elastic stiffness that take place during plastic loading.

References [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] -, A thermodynamic development of elastic-plastic continua, Proc. IUTAM on Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids (H. Parkus and L. I. Sedov, eds.), Springer-Verlag, New York, 1966, pp. 117-131
  • [3] J. Casey and P. M. Naghdi, Constitutive results for finitely deforming elastic-plastic materials, Constitutive Equations: Macro and Computation Aspects (K. J. William, ed.), ASME, New York, 1984, pp. 53-71
  • [4] -, Strain-hardening response of elastic-plastic materials, Mechanics of Materials (C. S. Desai and R. H. Gallagher, eds.), Wiley, New York, 1984, pp. 61-89
  • [5] 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
  • [6] -, On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticity, J. Appl. Mech. 42, 61-66 (1975)
  • [7] J. Casey, A simple proof of a result in finite plasticity, Quart. Appl. Math. 42 (1984), no. 1, 61–71. MR 736505, https://doi.org/10.1090/S0033-569X-1984-0736505-1
  • [8] Morton E. Gurtin, An introduction to continuum mechanics, Mathematics in Science and Engineering, vol. 158, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 636255
  • [9] J. Casey and M. Tseng, A constitutive restriction related to convexity of yield surfaces in plasticity, Z. Angew. Math. Phys. 35, 478-496 (1984)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73G20, 73E05

Retrieve articles in all journals with MSC: 73G20, 73E05

Additional Information

DOI: https://doi.org/10.1090/qam/1205941
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society