Model of nonlinear deformation of granular composites

Authors

  • E. N. Shikula S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv
  • N. B. Zhukova S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv https://orcid.org/0000-0002-2699-3771

DOI:

https://doi.org/10.17721/1812-5409.2023/2.30

Keywords:

granular composite material, nonlinearity of deformation of components, efficient deformative properties, stress-strain state, influence of nonlinearity

Abstract

The model of nonlinear deformation of a granular composite material of a stochastic structure with physically nonlinear components was constructed. The basis is the stochastic differential equations of the physically nonlinear theory of elasticity by L.P. Khoroshun. The solution to the problem of the stress-strain state and effective deformable properties of the composite material is built using the averaging method. An algorithm for determining the effective properties of granular material with physically nonlinear components has been developed. The solution of nonlinear equations, taking into account their physical nonlinearity, is constructed by the iterative method. The law of the relationship between macrostresses and macrostrains in granular material and the dependence of average strains and stresses in its components on macrostrains has been established. Curves of deformation of the material were constructed for different values of the volume content of its components. The dependence of the effective deformable properties of the granular material on the volume content of the components was studied. The effect of component nonlinearity on the deformation of granular composite material was studied. It was established that the nonlinearity of the components significantly affects the effective deformable properties and the stress-strain state of granular materials.

Pages of the article in the issue: 168 - 171

Language of the article: Ukrainian

References

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KHOROSHUN L.P. Metod uslovnyih momentov v zadachah mehaniki kompozitnyih materialov. Prikladnaya mehanika. 23 (10). p. 100-108.

KHOROSHUN L.P., MASLOV B.P., SHIKULA E.N., NAZARENKO L.V. (1993) Mehanika kompozitov. (Vols. 1-12). Vol. 3. Statisticheskaya mehanika i effektivnyie svoystva materialov. Kiev: Naukova dumka.

GUZ A.N., KHOROSHUN L.P., MIHAYLOVA M.I., BABICH D.V., SHIKULA E.N. (2003) Mehanika kompozitov. (Vols. 1-12). Vol. 12. Prikladnyie issledovaniya. K: «A.S.K.»

KREGERS A.F. (1988) Matematicheskoe modelirovanie termicheskogo rasshireniya prostranstvenno armirovannyih kompozitov Mehanika kompozitnyih materialov. 3. P. 433-441.

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Published

2023-12-23

How to Cite

Shikula, E. N., & Zhukova, N. B. (2023). Model of nonlinear deformation of granular composites. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 168–171. https://doi.org/10.17721/1812-5409.2023/2.30

Issue

Section

Differential equations, mathematical physics and mechanics