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2015 year, number 6

1.
IDENTIFICATION OF PARAMETERS OF MODELS OF NONLINEAR DEFORMATION OF ISOTROPIC AND COMPOSITE MATERIALS ON THE BASIS OF CALCULATIONS AND EXPERIMENTS AIMED AT ANALYZING THE DYNAMIC BEHAVIOR OF CYLINDRICAL METAL-PLASTIC SHELLS

N. A. Abrosimov, N. A. Novosel'tseva
Research Institute for Mechanics, Nizhny Novgorod, 603950 Russia
Keywords: математическая модель, идентификация, вязкоупругое и упругопластическое деформирование, численные методы, импульсное нагружение, mathematical model, identification, viscoelastic and elastoplastic deformation, numerical methods, pulsed loading

Abstract >>
A method for identification of material parameters of the constitutive relations of elastoplastic and viscoelastic deformation of isotropic and composite materials is developed. The method is based on minimizing the functional of the residue of results of numerical and experimental analysis of unsteady deformation of structural elements made of examined materials. The method is tested, and prospects of its application for determining material parameters of viscoelastic and elastoplastic models of nonlinear deformation of cylindrical metal-plastic shells under explosive loading are demonstrated.



2.
DEVELOPMENT OF A TECHNOLOGY FOR LASER WELDING OF THE 1424 ALUMINUM ALLOY WITH A HIGH STRENGTH OF THE WELDED JOINT

B. D. Annin1, V. M. Fomin2, E. V. Karpov1, A. G. Malikov2, A. M. Orishich2, A. N. Cherepanov2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
annin@hydro.nsс.ru
2Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
fomin@itam.nsc.ru
Keywords: лазерная сварка, алюминиевые сплавы, прочность, структура сварного соединения, ударная и пластическая деформация, laser welding, aluminum alloy, strength, welded joint structure, shock-induced and plastic straining

Abstract >>
Results of an experimental study of properties of joints obtained by using different regimes of laser welding of the 1424 alloy (Al-Mg-Li) are reported. The strength and structure of the welded joints are determined. The influence of various types of welded joint straining on its strength is studied. It is demonstrated that the joint strength increases in the case of plastic straining.



3.
INVESTIGATION OF HIGH ELASTOPLASTIC STRAINING OF SHELLS OF REVOLUTION UNDER COMPLEX TENSILE AND TORQUE LOADING

A. A. Artem'eva, V. G. Bazhenov, D. V. Zhegalov, D. A. Kazakov, E. V. Nagornykh
Research Institute for Mechanics, Nizhny Novgorod, 603950 Russia
aranan@mail.ru
Keywords: осесимметричные оболочки, растяжение и кручение, упругопластичность, большие деформации, численное моделирование, вариационно-разностный метод, явная схема интегрирования, axisymmetric shells, tensile and torque loading, elastoplasticity, high strains, numerical simulation, variational difference method, explicit scheme of integration

Abstract >>
A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported.



4.
ANALOGY BETWEEN AN ENGINEERING HEAT-CONDUCTION PROBLEM AND ONE CLIMATIC EVENT

V. A. Babeshko1, O. V. Evdokimova1, O. M. Babeshko2
1Southern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006 Russia
babeshko41@mail.ru
2Kuban State University, Krasnodar, 350040 Russia
babeshko49@mail.ru
Keywords: граничные задачи, параболические уравнения, смешанные граничные условия, метод Винера -- Хопфа, интегральные уравнения, локализация, boundary-value problems, parabolic equations, mixed boundary conditions, Wiener-Hopf method, integral equations, localization

Abstract >>
A mixed boundary-value problem for a parabolic equation of heat distribution in a layer is considered. Ggradient is specified in one region of the boundary, and temperature in the other. It is assumed that away from the initial conditions, the process is established in time and the temperature decreases slowly and exponentially and then increases. We study temperature localization in one of the regions, and the conditions and consequences of localization in the other region at various stages of temperature change. An analogy is drawn between the temperature distribution pattern in the layer and some climatic events.



5.
INVESTIGATION OF CHANGES IN THE SPHERICAL SHELL SHAPE UNDER THE ACTION OF PULSED LOADING DUE TO CONTACT INTERACTION WITH A RIGID BLOCK

V. G. Bazhenov1, D. A. Varavin2, A. I. Kibets2, A. A. Ryabov2, V. I. Romanov2
1Research Institute for Mechanics, Nizhny Novgorod, 603950 Russia
bazhenov@mech.unn.ru
2Institute of Experimental Physics, Sarov, 607188 Russia
varavin25@mail.ru
Keywords: сферическая оболочка, ``скафандр'', контакт, трение, пластические деформации, выпучивание, spherical shell, ``spacesuit, " contact, friction, plastic strains, buckling

Abstract >>
An axisymmetric problem of high strains in a spherical lead shell enclosed into an aluminum ``spacesuit" under the action of pulsed loading is considered. The shell straining is described with the use of equations of mechanics of elastoviscoplastic media in Lagrangian variables, and the kinematic relations are determined in the current state metrics. Equations of state are taken in the form of equations of the flow theory with isotropic hardening. The problem is solved numerically by using the variational difference method and the ``cross" explicit scheme of integration with respect to time. The influence of the yield stress as a function of the strain rate on changes in the shell shape is studied for different values of loading. The calculated final shape and residual strains are demonstrated to be in good agreement with experimental data.



6.
EXPERIMENTAL AND THEORETICAL STUDY OF PENETRATION OF SPHERICAL SOLIDS INTO WET SAND

V. V. Balandin, Vl. Vl. Balandin, A. M. Bragov, S. V. Krylov, E. V. Tsvetkova
Research Institute for Mechanics, Nizhny Novgorod, 603950 Russia
balandin@mech.unn.ru
Keywords: проникание, обращенный эксперимент, влажный песок, сила сопротивления, модель Григоряна, метод Годунова, penetration, inverted experiment, wet sand, force of resistance, Grigoryan model, Godunov method

Abstract >>
Results of a series of inverted laboratory experiments on the normal impact of spherical bodies onto targets made of wet sand (with humidity of 10$\%$) and water-saturated sand (with humidity of 18-20$\%$) placed into cylindrical metallic containers are reported. Experimental data are compared with results calculated by a modified Godunov difference method. Changes in the forces of resistance to penetration at different stages of the impact interaction process are analyzed, and the influence of humidity and granulometric composition of sand on the maximum values of forces at different impact velocities is studied. The maximum force of resistance for sand with 20$\%$ humidity is found to be smaller by a factor of 1.5-2 than that for dry sand.



7.
EXPERIMENTAL STUDY AND MATHEMATICAL MODELING OF THE BEHAVIOR OF ST.3, 20KH13, AND 08KH18N10T STEELS IN WIDE RANGES OF STRAIN RATES AND TEMPERATURES

A. M. Bragov1, L. A. Igumnov1, V. B. Kaidalov2, A. Yu. Konstantinov1, D. A. Lapshin2, A. K. Lomunov1,3, F. M. Mitenkov2
1Research Institute for Mechanics, Nizhny Novgorod, 603950 Russia
bragov@mech.unn.ru
2Afrikantov Experimental Design Bureau for Mechanical Engineering, Nizhnii Novgorod, 603074 Russia
kaidalov@mail.ru
3Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, 603950 Russia
lomunov@mech.unn.ru
Keywords: диаграмма деформирования, скорость деформации, адиабатический нагрев, метод Кольского, математическая модель, идентификация, верификация, strain diagram, strain rate, adiabatic heating, Kolsky method, mathematical model, identification, verification

Abstract >>
Results of an experimental study of the behavior of St.3, 20Kh13, and 08Kh18N10T steels under static and dynamic loading are reported. The influence of the strain rate and temperature on characteristics of strength and plasticity is studied. Based on the data obtained, the parameters of the Johnson-Cook model are determined. This model is used in commercial software to describe the yield surface radius as a function of loading parameters. The adequacy of the identified model is verified in a series of special test experiments.



8.
UNSTEADY AXISYMMETRIC DEFORMATION OF AN ELASTIC THICK-WALLED SPHERE UNDER THE ACTION OF VOLUME FORCES

V. A. Vestyak1, D. V. Tarlakovskii2
1Moscow Aviation Institute, Moscow, 125993 Russia
v.a.vestyak@mail.ru
2Research Institute of Mechanics, Moscow, 119192 Russia
tdvhome@mail.ru
Keywords: упругая толстостенная сфера, нестационарные осесимметричные объемные силы, ряды по полиномам Лежандра и Гегенбауэра, преобразование Лапласа, функции Грина, elastic thick-walled sphere, unsteady axisymmetric volume forces, series in Legendre and Gegenbauer polynomials, Laplace transform, Green's functions

Abstract >>
This paper considers a homogeneous isotropic elastic body bounded by concentric spheres and acted upon by axisymmetric unsteady volume forces. Displacement fields are determined using series expansions in Legendre and Gegenbauer polynomials, Laplace transforms in time, and integral representations with kernels in the form of Green's functions. Explicit formulas for the Green's functions are constructed that allow accurate determination of the originals. Examples of the calculations are presented.



9.
ASSESSMENT OF THE SERVICE LIFE OF STRUCTURAL STEELS BY USING DEGRADATION MODELS WITH ALLOWANCE FOR FATIGUE AND CREEP OF THE MATERIAL

I. A. Volkov1, V. V. Egunov2, L. A. Igumnov2, D. A. Kazakov2, Yu. G. Korotkikh1, F. M. Mitenkov3
1Volga State University of Water Transport, Nizhny Novgorod, 603950 Russia
pmptmvgavt@yandex.ru
2Research Institute for Mechanics, Nizhny Novgorod, 603022 Russia
vegunov@mech.unn.ru
3Afrikantov Experimental Design Bureau for Mechanical Engineering, Nizhny Novgorod, 603074 Russia
MitenkovFM@gmail.com
Keywords: пластичность, ползучесть, малоцикловая усталость, долговечность, механика поврежденной среды, базовый эксперимент, материальные параметры, поврежденность, разрушение, plasticity, creep, low-cycle fatigue, service life, damaged medium mechanics, basic experiment, material parameters, damage, fracture

Abstract >>
A mathematical model is developed within the framework of equations of damaged medium mechanics to describe the processes of viscoplastic straining and damage accumulation in structural steels with allowance for fatigue and creep of the material. A model of damage summation due to interaction of low-cycle fatigue and creep of the material is proposed. Material parameters and scalar functions of equations of mechanics of damaged media are determined. Viscoplastic straining and fatigue-induced damage accumulation in 08Kh18N10T and 12Kh18N9 are studied numerically, and the data obtained are compared with available results of physical experiments.



10.
DISTRIBUTION OF THE ENERGY OF A PIEZOELECTRIC ACTUATOR BETWEEN TRAVELING WAVES EXCITED IN AN ELASTIC LAYER

E. V. Glushkov, N. V. Glushkova, A. A. Evdokimov
Kuban State University, Krasnodar, 350040 Russia
evg@math.kubsu.ru
Keywords: упругий волновод, пьезоактуатор, контактная задача, волновая энергия, elastic waveguide, piezoelectric actuator, contact problem, wave energy

Abstract >>
The distribution of the energy of a piezoelectric actuator between normal modes (Lamb waves) as a function of the source parameters and frequency is studied by solving the dynamic contact problem of the interaction between a flexible piezoelectric patch and a flexible elastic substrate with explicit representations for the excited traveling waves. Zones of the maximum and minimum energy of the fundamental modes are determined in the “oscillation frequency-piezoelectric patch width” plane.



11.
PARAMETRIC IDENTIFICATION OF CRYSTALS HAVING A CUBIC LATTICE WITH NEGATIVE POISSON'S RATIOS

V. I. Erofeev1,2, I. S. Pavlov1,2
1Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Nizhny Novgorod, 603024 Russia
erf04@sinn.ru
2Research Institute for Mechanics at the Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, 603950 Russia
ispavl@mts-nn.ru
Keywords: кристалл c кубической решеткой, отрицательные коэффициенты Пуассона, параметры микроструктуры, параметрическая идентификация, crystal with a cubic lattice, negative Poisson's ratios, microstructure parameters, parametric identification

Abstract >>
A two-dimensional model of an anisotropic crystalline material with cubic symmetry is considered. This model consists of a square lattice of round rigid particles, each possessing two translational and one rotational degree of freedom. Differential equations that describe propagation of elastic and rotational waves in such a medium are derived. A relationship between three groups of parameters is found: second-order elastic constants, acoustic wave velocities, and microstructure parameters. Values of the microstructure parameters of the considered anisotropic material at which its Poisson's ratios become negative are found.



12.
TWO-DIMENSIONAL NONSTATIONARY PROBLEM OF ELASTIC DIFFUSION FOR AN ISOTROPIC ONE-COMPONENT LAYER

A. V. Zemskov1, D. V. Tarlakovskii2
1Moscow Aviation Institute, Moscow, 125993 Russia
azemskov1975@mail.ru
2Institute of Mechanics, Moscow, 119192 Russia
tdvhome@mail.ru
Keywords: нестационарная упругая диффузия, изотропный слой, преобразования Лапласа и Фурье, ряды Фурье, nonstationary elastic diffusion, isotropic layer, Laplace and Fourier transforms, Fourier series

Abstract >>
A locally equilibrium model of mechanodiffusion which comprises a coupled system of motion equations for an elastic body and a mass transfer equation is used to solve the two-dimensional nonstationary problem of elastic diffusion for an isotropic one-component layer. The solution is constructed using Fourier series, Laplace time transforms, and Fourier transforms for the spatial coordinate. The Laplace transform originals are found analytically, and the Fourier transforms are inverted by quadrature formulas.



13.
EXPERIMENTAL TESTING OF THE FRACTURE OF CONCRETE AND REINFORCED CONCRETE PLATES UNDER IMPACT

A. A. Konyaev, V. F. Tolkachev, T. M. Platova
National Research Tomsk State University, Tomsk, 634050 Russia
alexk@niipmm.tsu.ru
Keywords: эксперимент, удар, ударник, бетон, железобетон, плита, проникание, разрушение, experiment, impact, projectile, concrete, reinforced concrete, plate, penetration, fracture

Abstract >>
This paper describes the results of experimental studies on penetration of cylindrical projectiles into concrete and reinforced concrete at impact velocities reaching 0.5 km/s. An algorithm is proposed for calculating the depth of penetration of a projectile, making it possible to find the depth of penetration of high-strength steel projectiles with a mass of up to 13.5 kg into concrete on the basis of measurements of the specific work required to remove concrete using projectiles with a mass of up to 8 g.



14.
ENERGY FUNCTIONAL DERIVATIVE OF THE LENGTH OF A CURVILINEAR OBLIQUE CUT IN THE PROBLEM OF EQUILIBRIUM OF A TIMOSHENKO PLATE

N. P. Lazarev1,2
1Scientific Research Institute of Mathematics, Yakutsk, 677000 Russia
nyurgun@ngs.ru
2Lavrent'ev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: наклонная трещина, вариационное неравенство, пластина Тимошенко, условие непроникания, производная функционала энергии, oblique crack, variational inequality, Timoshenko plate, nonpenetration condition, energy functional derivative

Abstract >>
This paper describes the dependence of the solution of the problem of equilibrium of a Timoshenko plate and the total energy functional of the plate on the surface perturbation, which is an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which simulate mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.



15.
BOUNDARY ELEMENT SIMULATION OF SURFACE WAVES ON A DEFORMED HALF-SPACE

S. Yu. Litvinchuk, A. A. Belov, I. P. Markov, A. A. Ipatov, A. N. Petrov
Research Institute for Mechanics, Nizhny Novgorod, 603950 Russia
litvinchuk@mech.unn.ru
Keywords: трехмерные задачи, полупространство, слой, метод граничных элементов, вязкоупругость, пороупругость, анизотропия, обращение преобразования Лапласа, three-dimensional problems, half-space, layer, boundary element method, viscoelasticity, poroelasticity, anisotropy, inversion of the Laplace transform

Abstract >>
Homogeneous and two-layer half-spaces consisting of an anisotropic elastic, isotropic viscoelastic, or poroelastic material are considered. The Kelvin-Voigt model and the model with the Abel kernel are used as models of the viscoelastic material; the poroelastic material is studied within the framework of the model of the compressible Biot material. The case where the half-space contains a cavity is also considered. Propagation of surface waves is studied by the boundary element method. The numerical solution involves the method of collocations for a regularized boundary integral equation.



16.
MODELING THERMOMECHANICAL PROCESSES IN SHAPE MEMORY POLYMERS UNDER FINITE DEFORMATIONS

A. A. Rogovoi, O. S. Stolbova
Institute of Mechanics of Continuous Media, Ural Branch Russian Academy of Sciences, Perm, 614013 Russia
rogovoy@icmm.ru
Keywords: конечные деформации, полимеры, релаксационный переход, память формы, finite deformation, polymers, relaxation transition, shape memory

Abstract >>
A model taking into account finite deformations is constructed for the behavior of a shape memory polymer which undergoes a transition from the highly elastic to the vitreous state and back during deformation and temperature change. The obtained relations are tested on problems which have experimental support.



17.
SLIDING OF TWO SMOOTH INDENTERS ON A VISCOELASTIC FOUNDATION IN THE PRESENCE OF FRICTION

F. I. Stepanov
Ishlinskii Institute of Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia
stepanov_ipm@mail.ru
Keywords: контактная задача, вязкоупругость, скольжение индентора, contact problem, viscoelasticity, indenter sliding

Abstract >>
The axisymmetric contact problem of sliding of two solid parabolic indenters on a viscoelastic half-space with constant velocity is considered. Shear stresses modeling the adhesive component of the friction force act in the contact area. The model of the foundation material is described by an integral operator with an exponential kernel characterized by one relaxation time. The problem is solved by the boundary element method. The dependences of the contact characteristics on the sliding velocity, the normal load, and the distance between the centers of the indenters is analyzed. The results can be used to study the effect of the roughness elements modeled by two indenters on the contact characteristics and the deformation component of the friction force.



18.
FRACTURE OF BRITTLE GEOMATERIAL WITH A CIRCULAR HOLE UNDER BIAXIAL LOADING

S. V. Suknev
Chersky Institute of Mining of the North, Siberian Branch, Russian Academy of Sciences, Yakutsk, 677980 Russia
suknyov@igds.ysn.ru
Keywords: разрушение, геоматериалы, масштабный эффект, концентрация напряжений, отверстие, нелокальные критерии разрушения, fracture, geomaterials, size effect, stress concentration, hole, nonlocal fracture criteria

Abstract >>
The influence of boundary conditions on the fracture of brittle geomaterial in the stress concentration zone under biaxial loading with account for the size effect is theoretically and experimentally studied. The calculation results are compared with the experimental data.



19.
OSCILLATIONS OF A CYLINDRICAL BODY SUBMERGED IN A FLUID WITH ICE COVER

L. A. Tkacheva
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
tkacheva@hydro.nsc.ru
Keywords: поверхностные волны, изгибно-гравитационные волны, колебания погруженного цилиндра, резонансные частоты, присоединенные массы, коэффициенты демпфирования, метод Винера -- Хопфа, surface waves, flexural-gravity waves, oscillations of submerged cylinder, resonant frequencies, added masses, damping coefficients, Wiener-Hopf method

Abstract >>
The linear plane problem of oscillations of an elliptic cylinder in an ideal incompressible fluid of finite depth in the presence of an ice cover of finite length is solved. The ice cover is modeled by an elastic plate of constant thickness. The hydrodynamic loads acting on the body are determined as functions of the oscillation frequency and the positions of the cylinder and plate.



20.
MODELING THE FLUID DYNAMICS AND HEAT TRANSFER IN UNSTEADY AND PERIODIC FLOW OF A HIGHLY CONCENTRATED GRANULAR MEDIUM OVER AN OBSTACLE IN A CHANNEL

A. V. Shvab, N. A. Chinchikeeva
National Research Tomsk State University, Tomsk, 634050 Russia
avshvab@inbox.ru
Keywords: нестационарное течение, гранулированная среда, скольжение, трение, теплообмен, unsteady flow, granular medium, slip, friction, heat exchange

Abstract >>
The unsteady isothermal flow of a dense layer of a granular medium around an obstacle in a plane channel is modeled using the momentum transfer equations for an incompressible viscous liquid medium based on the slip of the medium at the walls. The validity of this approach is tested by comparing the calculated and experimental data for the flow of a highly concentrated granular medium with high flowability. The effect of periodic change in the flow rate of the granular medium over time in the inlet section of the plane channel on the unsteady distributions of the velocity and temperature fields is studied.



21.
ANOMALOUS CHANGE IN THE MATERIAL MODULI OF THIN FILMS OF BARIUM TITANATE

V. B. Shirokov1,2, V. V. Kalinchuk1,2, R. A. Shakhovoi2,3, Yu. I. Yuzyuk2
1Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006 Russia
shirokov-vb@rambler.ru
2Southern Federal University, Rostov-on-Don, 344090 Russia
kalin@ssc-ras.ru
3National Centre for Scientific Research, Orleans F-45071, France
r.a.shakhovoy@gmail.com
Keywords: сегнетоэлектрики, тонкие пленки, вынужденная деформация, материальные константы, пьезоэлектрические модули, упругие модули, ferroelectrics, thin films, forced strain, material constants, piezoelectric moduli, elastic moduli

Abstract >>
A method is proposed to determine the moduli of thin ferroelectric films subjected to forced deformation due to the mismatch between the crystal lattice sizes of the film and substrate materials and the difference of their thermal expansion coefficients. Models of single-crystal films of barium titanate are studied using the eighth-degree Landau thermodynamic potential. It is shown that in the considered range of forced strain of the barium titanate film, three main states exist: a tetragonal phase ($c$ phase) of 4mm symmetry with spontaneous polarization directed along the normal to the film plane; an orthorhombic phase ($aa$ phase) of 2 mm symmetry with polarization oriented along the diagonal plane of the film; monoclinic phase ($r$ phase) of $C_\rm m$ symmetry with the intermediate direction of polarization. All phases are separated by the lines of transitions of the second kind. Dependences of the elastic, electric and piezoelectric moduli on the magnitude of forced strain are plotted. It is shown that at the phase boundaries there is an anomalous change in the constants of the ferroelectric film and in the region of existence of the $r$ phase, some moduli reach extreme values.