MECHANICS AND MATHEMATICAL MODELS FOR BEHAVIOR OF THE DEFORMABLE SOLID AND ELASTIC MEDIUMS WITH REGARD TO THEIR INTERNAL STRUCTURE

Zhuravkov M.A., Doctor of Physical and Mathematical Sciences, Professor, Pro-rector of Research of the Belarusian State University, Head of the Department of Theoretical and Applied Mechanics, Mechanics and Mathematics Faculty, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.
Makaeva T.A., Postgraduate Student, Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

The article shows the possible ways of building mechanical and mathematical models of the behavior of deformable solid and elastic mediums with regard to their internal structure. The constructions are made in the framework of continuum mechanics to static problems of deformation of elastic bodies. The considerable factor in this is that the internal structure of the accounting environment does not allow a physical equations describing the behavior of the environment (the connection between the components of the stress-strain state), using Hooke's law in standard form. The model was developed for three-dimensional case which proposed in [4] for two-dimensional case, describing the stress-strain state of rock massifs of the block structure. The results performed on the basis of the proposed model, the numerical analysis of the stress-strain state of the model structure (plate) and then comparing the results with the behavior of structures whose state is described by the classical Hooke's elastic model.

block structure, deformation model , microstructure, VAT, continuity array, slip lines

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