Modelling of cyclic creep deformations of nonlinear viscoelastic materials using Heaviside function

Authors

  • Y. V. Pavlyuk S.P. Timoshenko Institute of Mechanics NAS Ukraine, 03057, Kyiv, 3 Nesterov Str.

DOI:

https://doi.org/10.17721/1812-5409.2021/4.9

Keywords:

cyclic creep, nonlinear viscoelasticity, Heaviside function, heredity kernel

Abstract

The problem of calculating the deformations of the cyclic creep of nonlinear viscoelastic materials is considered, which is given in the form of cyclic alternations of loads and unloadings of equal amplitude over rectangular cycles, where the duration of loading and unloading half-cyclescoincide. The program of loading is realized in the form of sequence of elementary loadings set by means of unit functions of Heaviside. A nonlinear creep model with a time-independent nonlinearity of Yu. Rabotnov's model is used to describe the deformation process. The fractional-exponential function is used as the nucleus of heredity. The paper develops a nonlinear viscosity model with time-independent nonlinearity due to the use of instantaneous deformation diagrams as isochronous for zero time and smoothing cubic splines, as approximations of nonlinear instantaneous deformation diagrams that define the nonlinearity of the model. The concept of a single isochronous deformation diagram for the studied material is experimentally substantiated. A system of solution equations of nonlinear creep under cyclic loading is formulated. The problem of calculating the deformations of stationary and cyclic creep for nylon fibers FM 10001 is solved and experimentally tested.

Pages of the article in the issue: 62 - 65

Language of the article: Ukrainian

References

GOLUB, V.P. and PAVLYUK, Y.V. and FERNATI, P.V. (2017) Determining Parameters of Fractional–Exponential Heredity Kernels of Nonlinear Viscoelastic Materials. Int Appl Mech, 53(4). P.419–433. https://doi.org/10.1007/s10778-017-0826-2

MARIN, J., WEBBER А.С. and WEISSMANN G.F. (1954) Creep–time relations for nylon in tension, compression, bending, and torsion. Proc. ASTM. 1954. Vol. 54. Р. 1313–1343.

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Published

2021-12-21

How to Cite

Pavlyuk, Y. V. (2021). Modelling of cyclic creep deformations of nonlinear viscoelastic materials using Heaviside function. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (4), 62–65. https://doi.org/10.17721/1812-5409.2021/4.9

Issue

Section

Differential equations, mathematical physics and mechanics