Determinative ratios of a rheological model of a discrete medium with a variable angle of internal friction

Authors

  • O.A. Dorofeyev Khmelnitskyi National University
  • V.V. Kovtun Khmelnitskyi National University

DOI:

https://doi.org/10.31891/2079-1372-2020-95-1-69-77

Keywords:

discrete environment; internal coulomb friction; dilatation.

Abstract

The article deals with determining ratios of a rheological model of a discrete medium with a variable angle of internal friction, which reflect the characteristic features of deformation of a discrete material: the influence of internal Coulomb friction and the manifestation of dilatancy at all stages from the beginning of loading to the onset of the limit state.

The relations are formulated in the form adopted in the theory of plastic flow of material with a variable flow surface. This allowed us to use a well-tested apparatus of the theory of rigidity of a solid body to describe the process of deformation of a discrete material.

To formulate the relations, new concepts of stresses and strains occurring on special conjugate planes, which are convenient for describing the deformation of a discrete material, have been introduced.

The values of its variable parameters necessary for the use of the model in the engineering calculations are proposed to determine by the results of special laboratory tests of macro-samples of a specific material for biaxial compression in conditions of flat deformation.

References

1. Dorofieiev O. A. Reolohichni modeli seredovyshcha z suttievym vnutrishnim tertiam / O. A. Dorofieiev, V. V. Kovtun // Visnyk KhNU. – Tekhnichni nauky. – 2019. – № 3 (271). – S. 50-58.
2. Drucker D. C. Solid Mechanics and Plastic Analysis of Limit Design / D. C. Drucker, W. Prager. // Quarterly of Applied Mathematics. – 1952. – Vol. 10. – №2. – P. 157-165.
3. Malinin N. N. Prikladnaya teoriya plastichnosti i polzuchesti / N. N. Malinin. – M. : Mashinostroenie, 1975. – 397 s.
4. Kovtun V. V. Vyznachalni spivvidnoshennia mekhaniky dyskretnoho seredovyshcha / V. V. Kovtun // Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. – 2008. – №5. – S. 69-76.
5. Dorofeyev О. А. Estimation of the Stress-Strain State of a Discrete Medium by a Plastic Flow Model / О. А. Dorofeyev , V. V. Kovtun // Problems of Trybology. – 2019. – Vol. 24, № 3/93. – P. 29-38.
6. Kovtun V. V. Eksperymentalne obgruntuvannia vykhidnykh polozhen mekhaniky dyskretnoho seredovyshcha i vyznachennia rozrakhunkovykh parametriv modelei / V. V. Kovtun, O. A. Dorofieiev // Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. – 2011. – №3. – S. 20-28.
7. Kovtun V. V. Napruzhennia po potentsialnykh ploshchynkakh kovzannia u sypkomu seredovyshchi / V. V. Kovtun // Visnyk KhNU. – Tekhnichni nauky. – 2010. – № 1. – S. 7–12.
8. Kovtun V. V. Deformatsii vzdovzh potentsialnykh linii kovzannia u sypkomu seredovyshchi / V. V. Kovtun, O. A. Dorofieiev. // Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. – 2010. – №5. – S. 142–150.
9. Rabotnov Yu. N. Polzuchest elementov konstruktsiy / Yu. N. Rabotnov. – M. : Nauka, 1966. – 752 s.
10. Nikolaevskiy V. N. Sovremennyie problemyi mehaniki gruntov / V. N. Nikolaevskiy. // Opredelyayuschie zakonyi mehaniki gruntov. – M. : – 1975. – S. 210-227.
11. Stroganov A. S. Analiz ploskoy plasticheskoy deformatsii grunta / A. S. Stroganov // Inzhenernyiy zhurnal. – 1965. – #4. – S. 734–742.
12. Malyishev M. V. O vliyanii srednego glavnogo napryazheniya na prochnost grunta i o poverhnostyah skolzheniya / M. V. Malyishev // Osnovaniya, fundamentyi i mehanika gruntov. – 1963. – #1. – S. 7–11.
13. Bugrov A. K. Napryazhenno-deformirovannoe sostoyanie osnovaniy i zemlyanyih sooruzheniy s oblastyami predelnogo ravnovesiya : avtoref. dis. na poluchenie nauchn. stepeni d-ra tehn. nauk / A. K. Bugrov. – L. , 1980. – 49 s.
14. A. s. 1158925 SSSR. Pribor dlya issledovaniy svoystv grunta v usloviyah ploskoy deformatsii / V. V. Kovtun, V. G. Beznosyuk, N. A. Mazur. – # 3673183/29-33; zayavl. 16.12.83; opublik. 30.05.85, Byul. # 20.
15. A. s. 1141158 SSSR. Nagruzochnoe ustroystvo dlya ispyitaniy gruntov v priborah trehosnogo szhatiya / V. V. Kovtun, V. G. Beznosyuk, N. A. Mazur. – # 3673169/29-33; zayavl. 16.12.83; opublik. 23.02.85, Byul. # 7.

Downloads

Published

2020-03-24

How to Cite

Dorofeyev, O., & Kovtun, V. (2020). Determinative ratios of a rheological model of a discrete medium with a variable angle of internal friction. Problems of Tribology, 25(1/95), 69–77. https://doi.org/10.31891/2079-1372-2020-95-1-69-77

Issue

Section

Articles