Polkunov U.G., Loboda M.U.
CRITERIA OF DEMOLITION OF HARD VISCOUS ROCK BY CONICAL DISK TOOLS ^{[№ 1 ' 2014]}
The article is devoted to the development of criteria of sustainable crack growth on a mixed mechanism of demolition of hard rock by disk conical tools. Adequacy of modeling results was proved with experimental researches.

Polkunova S.Y., Polkunov Y.G.
MATHEMATICAL MODELING IN HISTORICAL STUDY: GROWTH OF PRODUCTION OF LIGHT AND FOOD INDUSTRY IN THE SOUTH URAL REGION IN 1920–1930 ^{[№ 1 ' 2012]}
This article focuses on the development of one of the most important economic segments of the complex — the light and food industry. The authors analyzed the expansion of production processes and the dynamics of gross output at the enterprises of the South Ural region in 20–30 years of XX century, the analysis was based on the developed mathematical models.

Polkunov Y.G., Karakulina E.O.
THE DEVELOPMENT OF CRACKS IN THE DISCRETE MEDIA WITH DIFFERENT DIAMETER OF GRAIN. ^{[№ 9 ' 2010]}
Article is dedicated to the development of model, which describes the process of destroying the grainy materials. Laws governing formation and development of cracks in the discrete media are established here. The results of the numerical calculation of the coefficients of the intensity of the stresses of the first kind taking into account the diameter of grain are represented.

Polkunov Yu.G., Spiridonova E.V.
THE MAHTEMATICA MODEL OF UNWEDGING MATERIAL WITH DIFFERENT LENGTH OF THE BASIC AND GAPING CRACK ^{[№ 9 ' 2010]}
The article represents the numerical solution of the task of the development of the wedging crack in the undivided material with different length of the basic and gaping crack. Solution of problem was achieved by the torn-tape system displacement.

Polkunov Yu.G., Spiridonova E.V.
MATHEMATICAL MODEL OF BRITTLE FAILURE OF GEOMATERIALS IN A MIXED POSING ^{[№ 4 ' 2010]}
The authors of the article presents correlation which determine the relation between tensions and biases with coefficients of stress intensity of the first and second type and describe the mechanism of rupture forming at the mixed type of crack loading.

Polkunov Yu.G., Karakulina E.O.
MATHEMATICAL MODELLING FOR DIAGNOSIS OF ROCK SAMPLES DESTRUCTION ^{[№ 5 ' 2009]}
The article addresses the development of the model describing a process for destruction of granular materials. It proposes the algorithm for numerical calculation that allows determining patterns of formation and development of cracks in discrete environments that are loaded with different tools.

Polkunov Yu.G., Beloborodova S.V.
NUMERICAL CALCULATION FOR THE FIRST KIND STRESS INTENSITY COEFFICIENTS FOR THE CRACK IN THE HALF-SPACE ^{[№ 5 ' 2009]}
The article addresses determination of coefficients for the first kind stress intensity for the crack that is situated under control angle towards the half-space. It defines the dependence of the first kind stress intensity coefficients on the angle between the crack and half-space. Adequacy of the modeling results was confirmed with their comparison with the results made by the other authors.

Polkunov Yu.G., Spiridonova E.V.
CALCULUS OF APPROXIMATIONS OF CRITERIA OF CRACK GROWTH IN MIXED PROBLEMS OF ELASSTICITY THEORY ^{[№ 11 ' 2008]}
The article covers development of calculus of approximations to solve mixed tasks of elasticity theory to determine stress intensity factors for cracks on the edges of which displacement and intensity factors are set.

Polkunov Yu.G., Spiridonova E.V.
MATHEMATICAL MODELING OF ELASTIC PLANE DESTRUCTION WITH HALF-INFINITE CROSSCUTS WITH YAWNING CRACKS ^{[№ 5 ' 2008]}
This article is devoted to attachment working out of disruptive deflections method for coefficient determination of the first and second types voltage intensity for half-infinite crosscuts of elastic plane to banks of which the normal variable and shearing deflection with yawning cracks are attached.

Polkunov Yu.G., Spiridonova E.V.
MODELING OF WEDGE CRACK DEVELOPMENT IN DEFECTIVE MATERIAL ^{[№ 9 ' 2007]}
This article is devoted to working out of criteria of wedge cracks development in plane. Dependences of the first type tensions intension coefficient to physical-mechanical features of material, loading length and distance till inclined crack are determined in this article. Adequacy of modeling results is proved with analytical researches.

Polkunov Yu.G., Karakulina E.O.
MATHEMATICAL MODELING OF UNSTABLE FISSURES DEVELOPMENT AT GRANULAR MATERIALS ^{[№ 5 ' 2007]}
This article is devoted to the mathematical modeling of discrete sphere destructions. Regularities of microfissures forming at the borders of seeds material are established and a criterion of unstable fissures growth with accounting of seed diameter is worked out in this article.

Polkunov Yu.G.
MATHEMATICAL MODELING OF DISSYMMETRIC DISK-SHAPED INSTRUMENTS LOADING, FORMING CHAPS OF NORMAL BREAK ^{[№ 10 ' 2006]}
This article is devoted to the working out of mathematical model of dissymmetric disk-shaped instruments loading at forming of steady main breaks. The dependences of efforts on axis of disk-shaped instruments from geometrical, regime parameters and strength characteristics of competent rocks are established in this article. Adequacy of modeling results was proved with experimental researches.

Polkunov Yu.G.
MATHEMATICAL MODELING OF FISSURES STEADY GROWTH IN GRAINY GEOMATERIAL ^{[№ 5 ' 2006]}
This article is devoted to the working out of two stages mathematical models of geomaterials grainy quasistatic destructions with disk instruments. Results adequacy of modeling and criteria of main fissures steady growth is proved with experimental researches.