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
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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.
- 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 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
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
---, 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
- 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
---, On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticity, J. Appl. Mech. 42, 61–66 (1975)
- J. Casey, A simple proof of a result in finite plasticity, Quart. Appl. Math. 42 (1984), no. 1, 61–71. MR 736505, DOI https://doi.org/10.1090/S0033-569X-1984-0736505-1
- 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
J. Casey and M. Tseng, A constitutive restriction related to convexity of yield surfaces in plasticity, Z. Angew. Math. Phys. 35, 478–496 (1984)
A. E. Green and P. M. Naghdi, A general theory of elastic-plastic continuum, Arch. Rational Mech. Anal. 18, 251–281 (1965)
---, 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
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
---, 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
P. M. Naghdi and J. A. Trapp, Restrictions on constitutive equations of finitely deformed elastic-plastic materials, Quart. J. Mech. Appl. Math. 28, 25–46 (1975)
---, On the nature of normality of plastic strain rate and convexity of yield surfaces in plasticity, J. Appl. Mech. 42, 61–66 (1975)
J. Casey, A simple proof of a result in finite plasticity, Quart. Appl. Math. 62, 61–71 (1984)
M. E. Gurtin, An introduction to continuum mechanics, Academic Press, New York, 1981
J. Casey and M. Tseng, A constitutive restriction related to convexity of yield surfaces in plasticity, Z. Angew. Math. Phys. 35, 478–496 (1984)
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Article copyright:
© Copyright 1993
American Mathematical Society
