Computation of the Stress-Strain State under Low-Cycle Loading using the Endochronic Theory of Viscoplasticity

Abstract

The term "endochronic" in relation to the theory of plasticity was introduced by K. Valanis in 1971.It was a good marketing ploy. Since then, this termis being widely used. The "endochron" is the "inner time". The concept of "internal variables" was introduced and used much earlier than that proposed by K. Valanis. In a previous article, the author demonstrated results of introducing the endochronic theory to describe complex mechanical behavior of the highfilled polymer material. This paper presents a critical review of theories with the internal variables, as well as new results of using the theory with internal time for the case of low-cycle loading. The stress-strain state of a part after unloading is of particular interest. The function of internal (endochronic) time is determined by the results of testing on tension, compression, shear, shear with the axial compression and then used in the finite element method in solving the task of the stamp indentation into the high-filled polymer material space. Such computation case has practical value. The advantage of introducing the endochronic theory in the finite element method under the low-cycle loading is shown

Please cite this article as:

Eremichev A.N. Computation of the stress-strain state under low-cycle loading using the endochronic theory of viscoplasticity. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2024, no. 3 (150), pp. 34--40. EDN: ZIZLFA

References

[1] Novozhilov V.V. On complex loading and the prospects of a phenomenological approach to the study of microstresses. Journal of Applied Mathematics and Mechanics, 1964, vol. 28, no. 3, рp. 487--495. DOI: https://doi.org/10.1016/0021-8928(64)90091-7

[2] Coleman B.D., Gurtin M.E. Thermodynamics and internal state variables. J. Chem. Phis., 1967, vol. 47, pp. 598--619.

[3] Sedov L.N. Models of continuous media with internal degrees of freedom. Jornal of Applied Mathematics and Mechanics, 1968, vol. 32, no. 5, pp. 803--819. DOI: https://doi.org/10.1016/0021-8928(68)90001-4

[4] Rice I.R. Internal constitutive relations for solids. An internal variable theory and its application to metal plasticity. Journal Mech. Phis. Solids, 1971, vol. 19, pp. 112--147.

[5] Nemat-Nasser S. On nonequilibrium thermodynamics of continuum. Mechanics Today, 1972, vol. 2, p. 367.

[6] Truesdell C. A first course in rational continuum mechanics. New York, Academic Press Inc., 1977, p. 304.

[7] Valanis K.C. A theory of viscoplasticity without a yield surface. Arch. Mech. Stos., 1971, vol. 23, pp. 517--551.

[8] Vakulenko A.A. Towards the theory of irreversible processes. Bulletin of the Leningrad University, 1969, no. 7, pp. 46--52 (in Russ.).

[9] Wu H.-C. Continuum mechanics and plasticity. CRC Series. Modern Mechanics and Mathematics, Washington, Chapman & Hall/CRC Press, 2005.

[10] Eremichev A.N. On the relationship between the endochronic theory of visco-plasticity with plasticity theory Kadashevich --- Novozhilov. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Enginering], 1980, no. 10, pp. 5--8 (in Russ.).

[11] Kadashevich Yu.N., Novozhilov V.V. The theory of plasticity which takes into account residual microstresses. microstresses. Journal of Applied Mathematics and Mechanics, 1958, vol. 22, no. 1, pp. 104--118. DOI: https://doi.org/10.1016/0021-8928(58)90086-8

[12] Eremichev A.N. A variant of writing physical equations in the finite element method. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Enginering], 1984, no. 6, pp. 3--7 (in Russ.).

[13] Point N.A, Erlicher S. Generalization of the endochronic theory of plasticity based on the introduction of several intrinsic times. Mechanics, Models and Methods in Civil Engineering, 2012, pp. 221--232. DOI: https://doi.org/10.1007/978-3-642-24638-8_14

[14] Valanis K.C., Lee C. Some recent developments of the endochronic theory with applications. Nuclear Engineering and Design, 1982, vol. 69, iss. 3, pp. 327--344.

[15] Valanis K.C. A plasticity constitutive model for concrete under multiaxial compression. Engineering Structures, 2022, vol. 257, pp. 243--271.

[16] Valanis K.C. Experimental observations and data analysis of a commercially grade aluminum alloy (6082T6) for large elastoplastic deformation. Materials Toda: Proceedings, 2021, pp. 141--214.

[17] Valanis K.C. An anisotropic elastic-plastic constitutive model for single and poly-crystalline metals. International Journal of Plasticity, 1998, vol. 132, pp. 642--655.

[18] Wu E.M. Composite materials. Mechanics of Composite Materials, 1974, vol. 2, pp. 353--412.

[19] Sarbaev B.S. An endochronic theory of plastic deformation of fibrous composite materials. Computation Materials Science, 1995, vol. 4, pp. 220--232.

[20] Eremichev A.N. Endochronic theory of viscoplasticity. An example of its practical implementation for highly filled polymeric material. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2018, no. 4 (121), pp. 109--115. DOI: https://doi.org/10.18698/0236-3941-2018-4-109-115

[21] Eremichev A.N. Comprehensive studies to determine the mechanical properties of highly filed polymer material. Inzhenernyy vestnik: elektronniy nauchno-tekhnicheskiy zhurnal [Engineering Bulletin], 2014, no. 9, pp. 17--32 (in Russ.).