Endochronic Theory of Viscoplasticity. An Example of its Practical Implementation for Highly Filled Polymeric Material

Авторы: Ерёмичев А.Н. Опубликовано: 02.08.2018
Опубликовано в выпуске: #4(121)/2018  

DOI: 10.18698/0236-3941-2018-4-109-115

Раздел: Энергетическое машиностроение | Рубрика: Ядерные энергетические установки, топливный цикл, радиационная безопасность  
Ключевые слова: plasticity, viscoplasticity, thermodynamics, internal variables, K. Valanis, endochronic theory, highly filled polymer material, finite element method, testing of materials

Сomplex mechanical behaviour of materials differs from elastic deformation and implies plasticity, creep, changes in Poisson‘s ratio during deformation and other microscopic phenomena. A detailed description of them can lead to the most complete and accurate equations, but currently it is impossible in practice. To circumvent these difficulties we usually use a phenomenological approach. In this case, a mathematical model describing the experimental data for the material with the required degree of accuracy is created. In 1971, K. Valanis introduced the term "endochronic" to the theory of plasticity. The article is prepared using the materials of lectures given by the author. The paper is for readers who are not proficient in the endochronic theory framework. The article is prepared using the materials of lectures given by the article presents the results of using the endochronic theory to describe complex mechanical behavior of a highly filled polymer material (HFPM). We determined the internal (endochronic) time function based on test results concerning tension, compression, shear and shear combined with axial compression. We then used this function in the finite element method (FEM) to solve the problem of a rigid die indenting a HFPM volume. We show the advantage of using the endochronic theory in the FEM


[1] Valanis K.C. A theory of viscoplasticity without a yield surface. Arch. Mech. Stos., 1971, vol. 23, pp. 535–551.

[2] Coleman B.D., Gurtin M.E. Thermodynamics and internal state variables. J. Chem. Phis., 1967, vol. 47, no. 2, pp. 598–619. DOI: 10.1063/1.1711937

[3] Sedov L.N. Models of continuous media with internal degrees of freedom. PMM, 1968, vol. 32, no. 5, pp. 771–758 (in Russ.). (Eng. version: Journal of Applied Mathematics and Mechanics, 1968, vol. 32, no. 5, pp. 803–819.)

[4] Truesdell C. A first course in rational continuum mechanics. Academic Press, 1977. 304 p.

[5] Eringen A., Groot R. Continuum theory of nonlinear viscoelasticity. Mech. and Chem. of Solid Propellant Symposium. London, 1967. Pp. 125–138.

[6] Rice J.R. Inelastic constitutive relation for solids. J. Mich. Phis. Solids., 1971, vol. 19, pp. 433–455.

[7] Kadashevich Y.I., Pomytkin S.P. Endochronic theory of plasticity generalizing sanders — Klushnikov theory. Inzhenerno-Stroitelnyy Zhurnal [Magazine of Civil Engineering], 2013, no. 1, pp. 82–86, 128, 129 (in Russ.).

[8] Eremichev A.N. Comprehensive studies to determine the mechanical properties of highly filled polymer material. Inzhenernyy Vestnik [Engineering Bulletin], 2014, no. 9 (in Russ.). Available at: http://engsi.ru/doc/726783.html

[9] Eremichev A.N. On the relationship between the endochronic theory of viscoplasticity with plasticity theory Kadashevich — Novozhilov. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building], 1980, no. 10, pp. 5–8 (in Russ.).