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Elastoplastic deformation of elements of an isotropic solid along paths of small curvature: Constitutive equations incorporating the stress mode

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Abstract

Constitutive equations relating the components of the stress tensor in a Eulerian coordinate system and the linear components of the finite-strain tensor are derived. These stress and strain measures are energy-consistent. It is assumed that the stress deviator is coaxial with the plastic-strain differential deviator and that the first invariants of the stress and strain tensors are in a nonlinear relationship. In the case of combined elastoplastic deformation of elements of the body, this relationship, as well as the relationship between the second invariants of the stress and strain deviators, is determined from fundamental tests on a tubular specimen subjected to proportional loading at several values of stress mode angle (the third invariant of the stress deviator). Methods to individualize these relationships are proposed. The initial assumptions are experimentally validated. The constitutive equations derived underlie an algorithm for solving boundary-value problems

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References

  1. N. N. Tormakhov, S. P. Gemma, S. M. Zakharov, and A. V. Marishchuk, A Strain Gauge [in Russian], USSR Inventor’s Certificate No. 1288492 MKI G-01B 5/30, Byul. Izobr., No. 5, February 7 (1987).

  2. V. V. Novozhilov, Theory of Elasticity [in Russian], Sudpromgiz, Leningrad (1958).

    Google Scholar 

  3. Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, Combined Thermoviscoelastoplastic Deformation of Structural Members [in Russian], Naukova Dumka, Kyiv (1992).

    Google Scholar 

  4. Yu. N. Shevchenko and R. G. Terekhov, Physical Equations of Thermoviscoplasticity [in Russian], Naukova Dumka, Kyiv (1982).

    Google Scholar 

  5. M. E. Babeshko and Yu. N. Shevchenko, “Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells,” Int. Appl. Mech., 42, No. 6, 669–676 (2006).

    Article  Google Scholar 

  6. M. E. Babeshko and Yu. N. Shevchenko, “Elastoplastic axisymmetric stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different moduli,” Int. Appl. Mech., 41, No. 8, 910–916 (2005).

    Article  Google Scholar 

  7. Yu. I. Lelyukh and Yu. N. Shevchenko, “On finite-element solution of spatial thermoviscoelastoplastic problems,” Int. Appl. Mech., 42, No. 5, 507–515 (2006).

    Article  Google Scholar 

  8. Yu. N. Shevchenko and I. V. Prokhorenko, “Thermoelastoplastic stress-strain state of rectangular plates,” Int. Appl. Mech., 41, No. 10, 1130–1137 (2005).

    Article  Google Scholar 

  9. Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, “Constitutive equations for describing the elastoplastic deformation of elements of a body along small-curvature paths in view of the stress mode,” Int. Appl. Mech., 42, No. 4, 421–430 (2006).

    Article  Google Scholar 

  10. Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, “Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity with strain hardening,” Int. Appl. Mech., 43, No. 3, 291–302 (2007).

    Article  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv

    Yu. N. Shevchenko, R. G. Terekhov & N. N. Tormakhov

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  1. Yu. N. Shevchenko
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  2. R. G. Terekhov
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  3. N. N. Tormakhov
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 43–55, June 2007.

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Shevchenko, Y.N., Terekhov, R.G. & Tormakhov, N.N. Elastoplastic deformation of elements of an isotropic solid along paths of small curvature: Constitutive equations incorporating the stress mode. Int Appl Mech 43, 621–630 (2007). https://doi.org/10.1007/s10778-007-0060-4

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  • DOI: https://doi.org/10.1007/s10778-007-0060-4

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