DOI 10.21440/2307-2091-2017-2-82-87                                                                                     Publication Date 11.07.2017

Laws of plastic deformation and destruction of solids pdf

A. V. Zhabko

The work is devoted to establishing the regularities of plastic deformation of solids. The author proposes using the functions of surface fluidity and plastic potential, based on his earlier studies. The limiting surface for these functions is the surface of destruction of solids (rocks), described by well-known Coulomb law. In fact, the proposed function is the law of plastic deformation of solids. The author analytically proves that during the process of plastic deformation, a reversal of the structural elements of a solid occurs. These studies explain some of the inconsistencies one observes during rock testing for strength. The author substantiates the possibility of using the rotation of structural elements during plastic deformation for predicting and controlling fracture processes. The article contains energy variational principle of destruction of solids. Based on it, there is the laconic explanation of the appearance of ring structures near some mine workings - the phenomenon of zonal disintegration of rocks. The author proposes a dependence for calculating the scale factor of this phenomenon. The author substantiates the geometric proximity of the slip surface shape in the slopes to the circle arc. In deriving the equations, the author used the fundamental laws and principles of mechanics in a rigorous mathematical formulation of problems.

Keywords: failure criterion; differential equation; principal stresses; angle of inclination of sliding platform; fluidity surface; function of plastic potential; coulomb's law, plastic deformation; dilatancy; variational principle.

REFERENCES

1. Panin V. E. 2000, Sinergeticheskie printsipy fizicheskoy mezomekhaniki [Synergetic principles of physical mesomechanics]. Fizicheskaya mezomekhanika [Physical Mesomechanics], no. 3(6), pp. 5–36.
2. Zhabko A. V. 2014, Napryazhennoe sostoyanie zemnoy kory [Stress state of the earth's crust]. Izv. UGGU [News of the Ural State Mining University], no. 3(35), pp. 57–60.
3. Zhabko A. V. 2014, Uslovie prochnosti gornykh porod [The condition of rock strength]. Izv. UGGU [News of the Ural State Mining University], no. 4(36), pp. 24–28.
4. Zhabko A. V. 2015, Predel'noe napryazhennoe sostoyanie gornykh porod [Extreme stress state of rocks]. Izv. vuzov. Gornyy zhurnal [News of the Higher Institutions. Mining Journal], no. 5, pp. 50–55.
5. Zhabko A. V. 2015, Kriteriy razrusheniya tverdykh tel [Criteria for the destruction of solids]. Problemy nedropol'zovaniya [Subsoil use problems], no. 2(5), pp. 46–51. Available at: http://trud.igduran.ru
6. Zhabko A. V. 2016, Analiticheskaya geomekhanika [Analytical geomechanics], Ekaterinburg, 224 p.
7. Panin V. E., Likhachev V. A., Grinyaev Yu. V. 1985, Strukturnye urovni deformatsii tverdykh tel [Structural levels of deformation of solids], Novosibirsk, 255 p.
8. Vikulin A. V., Melekestsev I. V. 2007, Rotatsionnye protsessy v geologii i fizike [Rotational processes in geology and physics], Moscow, pp. 39–102.
9. Vikulin A. V., Makhmudov Kh. F., Ivanchin A. G., Gerus A. A., Dolgaya A. A. 2016, O volnovykh i reidnykh svoystvakh zemnoy kory [On the wave and reid properties of the earth's crust]. Fizika tverdogo tela [Physics of the Solid State], vol. 58, no. 3, pp. 547–557.
10. Morozov N. F. 1984, Matematicheskie voprosy teorii treshchin [Mathematical problems in the theory of cracks], Moscow, 256 p.
11. Garagash I. A., Nikolaevskiy V. N. 2009, Mekhanika Kossera dlya nauk o Zemle [Cosserat Mechanics for Earth Sciences]. Vychislitel'naya mekhanika sploshnykh sred [Computational Continuum Mechanics], vol. 2, no. 4, pp. 44–66.
12. Kartashov Yu. M., Matveev B. V., Mikheev G. V. et al. 1979, Prochnost' i deformiruemost' gornykh porod [Strength and deformability of rocks], Moscow, 269 p.
13. Odintsev V. N. 1996, Otryvnoe razrushenie massiva skal'nykh gornykh porod [Separated destruction of rock massif], Moscow, 166 p.
14. Stavrogin A. N., Tarasov B. G. 2001, Eksperimental'naya fizika i mekhanika gornykh porod [Experimental physics and mechanics of rocks], St. Petersburg, 343 p.
15. Rebetskiy Yu. L. 2007, Tektonicheskie napryazheniya i oblasti triggernogo mekhanizma vozniknoveniya zemletryaseniy [Tectonic stresses and regions of trigger mechanism of earthquake occurrence]. Fizicheskaya mezomekhanika [Physical Mesomechanics], no. 10(1), pp. 25–37.
16. Zhabko A. V. 2016, Teoriya rascheta ustoychivosti otkosov i osnovaniy. Obshchaya teoriya rascheta ustoychivosti odnorodnykh otkosov [The theory of calculating the stability of slopes and bases. General theory of calculating the stability of homogeneous slopes]. Izv. UGGU [News of the Ural State Mining University], no. 1(41), pp. 72–83.
17. Levin V. A., Morozov E. M., Matvienko Yu. G. 2004, Izbrannye nelineynye zadachi mekhaniki razrusheniya [Selected nonlinear problems of fracture mechanics], Moscow, 408 p.
18. Oparin V. N. 2007, Nauchnye otkrytiya mezhtysyacheletiya v geomekhanike i perspektivy ikh primeneniya [Scientific discoveries of the inter-millennium in geomechanics and prospects for their application]. Geodinamika i napryazhennoe sostoyanie nedr Zemli: trudy konf. s uchastiem inostrannykh uchenykh (Novosibirsk, 2–5 okt. 2007 g.) [Geodynamics and the stressed state of the Earth's interior: the works of the conference with the participation of foreign scientists (Novosibirsk, October 2-5, 2007)], Novosibirsk, pp. 7–30.
19. Kashubin S. N., Vinogradov V. B., Kuzin A. V. 2005, Fizika Zemli [Physics of the Earth], Ekaterinburg, 2 ed., 188 p.