Abstract
We formulate a representation of the general defining relations for strain-hardening elastoplastic materials simple in Noll’s sense. The problem of simulation of a special case of the so-called active proportional deformation is analyzed in detail.
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References
C. Truesdell,A First Course in Rational Continuum Mechanics, Johns Hopkins University, Baltimore, MD (1972).
M. Lucchesi and P. Podio-Guidugli, “Materials with elastic range: A theory with a view toward applications. Part 1,”Arch. Rat. Mech. Anal.,102, 23–43 (1988).
M. Lucchesi and P. Podio-Guidugli, “Materials with elastic range: A theory with a view toward applications. Part 2,”Arch. Rat. Mech. Anal.,110, 9–42 (1990).
M. Lucchesi, D. R. Owen, and P. Podio-Guidugli, “Materials with elastic range: A theory with a view toward applications. Part 3,”Arch. Rat. Mech. Anal.,117, 53–96 (1992).
D. Kolarov, A. Baltov, and N. Boncheva,Mechanics of Plastic Media [Russian translation], Mir, Moscow (1979).
A. I. Lur’e,Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).
D. R. Owen, “Thermodynamics of materials with elastic range,”Arch. Rat. Mech. Anal.,31, 91–112 (1968).
D. R. Owen, “A mechanical theory of materials with elastic range,”Arch. Rat. Mech. Anal.,37, 85–110 (1970).
A. S. Pipkin and R. S. Rivlin, “Mechanics of rate-independent materials,”Z. Angewandte Mathem. Phys.,16, No. 3, 313–326 (1965).
M. Silhavy, “On transformation laws for plastic deformations of materials with elastic range,”Arch. Rat. Mech. Anal.,63, No. 2, 169–182 (1977).
A. A. Il’yushin, “On the relationship between stresses and strains in continuum mechanics,”Prikl. Mat. Mekh.,18, No. 6, 641–666 (1954).
A. J. M. Spencer,Theory of Invariants, New York (1971).
R. S. Rivlin and J. L. Ericksen, “Stress-deformation relations for isotropic materials,”J. Rat. Mech. Anal.,4, No. 5, 681–702 (1955).
B. E. Pobedrya,Lectures on Tensor Analysis. A Manual [in Russian], Moscow University, Moscow (1986).
A. E. Green and P. M. Naghdi, “A general theory of an elastic-plastic continuum,”Arch. Rat. Mech. Anal.,18, No. 4, 251–281 (1965).
Additional information
Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 59–70, September–October, 1998.
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Lepikhin, P.P. Simulation of the proportional deformation of elastoplastic continua simple in Noll’s sense. Part 1. Defining relations. Strength Mater 30, 497–506 (1998). https://doi.org/10.1007/BF02522631
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DOI: https://doi.org/10.1007/BF02522631