Table of contents

Editor's Preface

At the end of 2018, the IX All-Russian scientific conference Current Issues continuum mechanics and celestial mechanics with international participation was held on the basis of Tomsk State University. The event is annual and unites mechanical scientists from various scientific organizations within the framework of five scientific sessions. This time the conference was devoted to the 140^th anniversary of Tomsk State University - the oldest University in Siberia.

Our first meeting took place in 2010. In that distant year, the conference was held as part of the All-Russian Science Festival. From 2010 to 2018, articles in the scientific journal Works of Tomsk State University. Physics and Mathematical Series were published. In 2017, the first English-language articles were published in the International Publishing House IOP. In 2018, a Supplement of the journal Thermal Science was published from selected conference reports. This fact indicates a continuous improvement in the quality of scientific reports. According to statistics for the last five years, every fourth report is supported by various scientific foundations. The last four events were supported by the Russian Foundation for Basic Research. This volume contains 25 articles by conference participants from all scientific sessions of the event.

Special thanks to members of the international program committee for providing a potential opportunity for young scientists from Russia to participate in international projects.

I also thank all the conference participants, reviewers and members of the organizing committee for the successful organization of the event.

I am very grateful to the chairman of the session for organizing the oral and poster sessions, important comments and discussion.

See you in November 2019 in Tomsk State University at our annual event. Follow all the news on the conference website: http://cimcm.tsu.ru

Conference Chair

Maxim Yu. Orlov

List of Co-Chairs of the Program Committee, Editor-in-Chief, Conference Program Committee, International Conference Committee, Conference Session Chairs, Conference Organizing Committee are available in this pdf.

The Conference photograph is available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

In this paper, results of experimental and numerical research of ice destruction under shock and explosive loads were summarized. Full-scale experiments and laboratory impact experiments were performed. Specially for carrying out full-scale tests the mobile laboratory "Explosive destruction of natural materials" was organized. Last year's results of full scale underwater explosive tests are given. The diameter of the polynya (lane) and the state of the ice edge were studied. The results of the experiment in which the target was three-layer ice barriers are presented. The ice was broken into fragments, and the projectile was slightly deformed. Briefly, the mathematical model of ice behavior is described. The numerical method is based on the Lagrangian approach and contained a new way for isolating discontinuity surfaces of material. The capabilities of the non - commercial software package were demonstrated. The results of the quantitative test are given. The deep penetration of a container with inert filler into ice on water was modeled. New research tasks have been formulated.

A robust blast inhibiting bin is the most often used device for damage blast effects suppression. In particular, a top open cylindrical bin significantly reduces a fragmentation effect resulted from a detonation of an explosive device placed inside the bin. However, reduction of blast wave overpressure and impulse by such cylindrical bins is not sufficient. A reasonable alternative to endless increase of height and thickness of robust blast inhibiting bins is a development of destructible inhibitors having no solid elements in their structure and, therefore, excluding secondary fragmentation. So, the family of "Fountain" inhibitors localizes and suppresses damaging blast effects due to multiphase working system. The present study is analysing data obtained in testing of prototypes of new combined inhibitors. Its structure combines robust elements (bottoms, side surfaces) with elements responsible for blast loads reduction due to multi-phase working system (top and low transverse embeddings) and fairings impeding wave propagation in undesirable directions.

In this work studies the influence of the ice cover on the nature of the motion of a submerged body, depending on its length, cross-sectional area, speed, and submergence. Experimental studies of the submarine vessel models motion under the ice cover are carried out in the ice tank. To determine the influence of the cross-sectional area, relative elongation and displacement of the submarine on the parameters of the generated flexural-gravity waves and the nature of the load movement near the lower surface of the ice, nine models have been made in the form of drop-shaped rotation bodies in the scale λ₁=1:120. To conduct the experiments the necessary equipment and measuring system to register vibrations of the modelled ice are designed. By towing the vessel model its velocity and profiles of flexural-gravity waves are determined. The study showed that ice cover can have a significant impact on the nature of the model movement near its lower surface. An increase in the cross-sectional area of the model leads to an increase in values of ice deflections. When the length of the models are increased and the speeds of movement are the same, the efficiency of the ice destruction decreases.

The results of numerical and experimental studies of the penetration and punching by a steel ball of the barriers consisting of packages of metal woven wire grid are presented. In the experiments performed, a packet of meshes was formed by overlaying ten flat woven layers with different sizes of quadrilateral cells. The ball was made of high-strength steel with high yield strength, so that after the experiments it remained intact. Numerical calculations were carried out using the author's program based on a modification of the Godunov method for the calculation of elastic plastic deformation taking into account the accumulation of damage and destruction. Comparison of experimental and calculated data is carried out by fixing the speed of a ball flying behind a barrier and a general dynamic picture of the development of zones of destruction in a barrier.

In the paper we solve the problem of supersonic gas flow in a two-dimensional channel with the moving upper wall making oscillations according to the harmonic law. In order to obtain a numerical solution for gas dynamics equations we have implemented two difference schemes: the scheme with the space and time approximation of the first order and the scheme with the space approximation of the second order. The fluxes were computed using Van Leer's method. A special form of fluxes in the gas dynamics equations is given, which enables to calculate fluxes on cell faces of difference mesh using Van Leer's method. Depending on a type of the harmonic law and initial gas inflow conditions, the peculiarities of oblique-shock wave propagation in moving curvilinear domains have been investigated. It has been determined that under a particular oscillation frequency the presence of wall oscillation practically doesn't have an effect on the flow regime inside the domain. The convergence of the obtained solution is shown by calculations using difference grids with different numbers of cells. While comparing the numerical solution obtained due to our program with the one obtained with Ansys Fluent solver we found that the constructed code operates correctly.

On the basis of the analysis of correlation characteristics of locally-elastic properties of modeling material the task of definition of locally-representative volume at different parameters of porosity is solved. For the analysis of dispersity of pores modeling cellular structures with volume content of 55 % and bimodal system of pores were considered. There were selected accidentally the limits of with representative volume 300 points in which local elastic properties were investigated. For definition of these properties each point on mesoscopical representative volume (MRV) level is presented by a small fragment of modeling frame of a porous media, MRV with characteristic for it geometry of frame of pores. Calculation of elastic properties of each such MRV was carried out by a method of final elements with use of the equipment of calculation of parameters tensely-strained state at mesolevel and their data smoothing. It is revealed that the ratio between the maintenance of large and small pores in dispersible-porous medium plays an important role. The dependence of an effective elastic module on a share of a time of large pores is set.

This paper deals with one of the methods asteroid hazard mitigation. The preventive destruction of a hazardous asteroid during the previous close encounter before its predicted collision is considered. Two variants of the explosion are considered: in the first case a projectile overtakes an asteroid; in the second one the situation is contrary. The second way requires significantly lower velocity of spacecraft delivery. On the other hand, it loses to the first way, since the number of fragments falling to the Earth is about an order of magnitude larger. However, with a more careful approach (non-isotropic explosion), this unfavorable factor can be likely reduced.

The task of calculating a plane axisymmetric elastic-plastic stress state of a thick-walled steel cylindrical pipe under the action of uniform internal pressure is considered. Thick-walled steel pipes are used in mechanical engineering, in heat engineering and heat-and-power engineering, in oil-producing and oil-refining industries, in the chemical industry. When loading in a pipe, two limiting states are realized: the elastic and plastic resistance of the material for two limiting values of pressure. For an intermediate pressure value, the cross-section of the pipe consists of two concentric annular zones – an inner elastic-plastic zone and an outer elastic zone. The exhaustion of the bearing capacity of the pipe occurs when the elastic-plastic deformation zone, spreading from the inner surface of the pipe, reaches its outer surface. Therefore, the presence of an elastic deformation zone at the outer surface of the pipe does not lead to the destruction of the structure. The aim of the work is to create an analytical technique for determining the calculated internal pressure, satisfying the strength condition under elastic-plastic deformation of steel cylindrical thick-walled pipes of different geometry, and leading to the most complete realization of the mechanical properties of the material. Recommendations on the effective search for the specified internal pressure are given.

A method and results of an experimental studying the sedimentation of solid spherical particles in a viscous liquid under non-isothermal conditions at low Reynolds numbers (Re<1) are presented. To determine the dependence of the drag coefficient on the temperature difference between the particles and liquid, a special setup has been developed. The experimental setup for determining the effect of non-isothermal conditions on the gravitational sedimentation of solid spherical particles in a viscous liquid consists of a prismatic cell with a viscous liquid, a particle heating device, a device for incorporating the reference and heated particles into the liquid, and a system for visualization of the particle sedimentation. In the experimental setup, two particles of the same diameter, made of the same material, are introduced into the cell at a zero initial velocity. Immediately before introduction into the liquid, one of the particles is heated (or cooled) to a temperature different from the temperature of the other (reference) particle, equal to the temperature of the liquid. The deposition rate of each of the particles is measured by the time-of-flight method using video of the deposition process through the transparent walls of the cell. As a result of a series of experiments, a decrease in the drag coefficient by 38% was obtained at a maximum temperature difference between the particles and liquid of 280°C.

The technique for producing the large titanium monolithic burning particles with a diameter of 250-550 microns is developed. The combustion of titanium particles in free fall in air was investigated. The characteristic times for the following events – beginning of fragmentation, end of fragmentation, end of burning, as well as the particle's motion law (including the coordinate and the velocity at the moment when the fragmentation process starts) are defined using the video recording. The size of particle at which the fragmentation picture changes from "star" to "spruce branch" is estimated. The combustion condensed products of particle are sampled and investigated. Three types of products are found. Firestone are objects with aerogel structure with overall dimensions up to thousand microns consisting of the oxide spherules chains with an arithmetic mean diameter of spherules of 85 nanometers. Second are spherical oxide particles with diameter of units–tens of microns. Third are the spherical residues of mother particles with sizes up to hundreds microns (in the case of fragmentation in spruce branch mode).

The numerical solution of boundary value problems for the biharmonic equation in irregular domains was obtained by new h-versions of the high-order accuracy least squares collocation method. In particular, we consider discrete boundary and multiply connected domains. It is shown that our approximate solution is high order accurate. We represent some suitable numerical examples. The numerical results are compared with those found by other authors who used a high order finite difference method. The biharmonic equation was applied to model the stress-strain state of isotropic thin irregular plates in the theory of thin plates.

The paper presents the results of an experimental study of the high-temperature combustion of bimetallic strands of Ti/Al and Cu/Al in air at normal pressure. It is shown that the kinetics of combustion is shown to be controlled by capillary mass transfer in metal melts. It was established, using high-speed video filming, dynamic spectrometry, that the effective maximum temperature of the processes is realized in the range of 2400 ÷ 5350 K. The burning rate is within the range of 0.26 ÷ 1.2 m/s. During the reaction conversions the atomic and molecular spectra are observed for Al, Al⁺, Cu, Cu⁺ AlO, CuO and other particles.

A mathematical model of the formation of layered mechanocomposites during the grinding of a binary mixture in an energy-intensive mill is built and studied. Dynamics of structural parameters of the binary mixture (the external and internal surface area of particles, the rate of particle agglomeration into mechanocomposites) as a function of the mechanical treatment time is investigated. Analytical relations are obtained to develop a technique for determining the kinetic constants using the inverse method.

The population of the geostationary region with space debris less than 20 cm in size has been very poorly studied in contrast to low Earth orbits. Low orbits (up to 1000 km) were studied by radar (up to 1 cm in size), optical and space instruments, there are models of the distribution of objects (up to 1 mm in size) at these heights based on experimental data [1]. The Zeiss-2000 telescope of the Terskol peak observatory is the largest telescope regularly used for space debris research, and the fragments of space debris smaller than 10 cm in size at a distance of 40 thousand km or more from the Earth are detected and studied using this instrument [2]. For example, for only 9 nights in October 2018, more than 15 previously unobserved small fragments were discovered. The data on some small-sized fragments of space debris discovered in 2018 are presented in this paper.

Combustion of calcium with zirconium oxide, as well as calcium and calcium nitride with titanium oxide in nitrogen is studied. The products obtained by the combustion of mixtures with titanium and subjected to acid enrichment contain no more than 15% of particles with a size larger than 40 microns, and more than 32% after the combustion of mixtures with zirconium. The use of a calcium and calcium nitride mixture as a reducing agent decreases the combustion temperature. Significant increasing the amount of calcium in the initial mixture decreases the particle size of the product.

The paper is devoted to the numerical investigation of inelastic deformation and fracture of porous alumina ceramics. A structural model of the mesovolume is developed with the use of an experimental scanning electron microscopic image. The mechanical behavior of the matrix is described by two constitutive models from plasticity theory and continuum damage mechanics. Uniaxial tension and compression of the mesovolume are numerically simulated in a two-dimensional formulation. The features of fracture patterns in the cases of the two constitutive models adopted are analysed. Effective mechanical characteristics of the studied ceramics are determined from the performed calculations. The results obtained can be used to specify the characteristics of the Drucker–Prager material for macroscopic modeling.

The proposals had been considered for development an analytical engineering methodology for the preliminary assessment of the impact of the space debris (SD) value object charge on the dynamics of its descent from orbit. The Earth's magnetic field is taken as a dipole, and the charge of SD is taken as a point charge. The orbital motion of the SD is approximated by the Archimedes spiral, the choice of its parameter (spiral step) provides a close approximation to the orbital motion of the SD. The use of the proposed analytical engineering methodology allows to make reasonable design decisions on the control system and charge formation on the SD at the early stages of designing systems propellantless deorbiting. The results have a methodological nature and are intended to provide preliminary estimates.

A new technique for measurement of the drag coefficient of spherical particle at condition of gas injection from its surface is presented. Results of investigation of the effect of the gas injection from a surface of a solid spherical particle on the drag coefficient are presented. In the investigation, the ratio of the gas injection rate and the velocity of the flow blowing around the particle was varied. Based on the obtained results, it is shown that the drag coefficient in condition the absence of the gas injection from the particle surface in the examined range of the Reynolds numbers are consistent with the standard drag dependence for the turbulent flow regime. At the same time, when at condition of gas injection from the particle surface, the drag coefficient is decreased (this effect is more pronounced with a decrease in the flow rate). The dependences of the change in the drag coefficient on the Reynolds number with changing the rate of the gas injection from the particle surface.

Magnesium aluminate spinel is obtained in the MgO-Al₂O₃-Al system using the method of self-propagating high-temperature synthesis. The leading SHS reaction is the oxidation of aluminum in an oxidizing environment. The composition and structure of spinel were studied by X-ray diffraction (DRON-UM-1), infrared spectroscopy (Nicolet 5700) and scanning electron microscopy (Philips SEM 515). The mineralizer NaCl used in the amount of 1 wt.% increases the conversion depth during SHS. Initial components are ground in a M3 planetary mill for 60 s results to obtain MgAl₂O₄ that does not contain impurities of initial oxides. The grain size of magnesium aluminate spinel obtained is ≤1 microns.

The paper presents the results of an experimental study of thermal explosion characteristics of mechanical oactivated powder mixtures of titanium-nickel. It was found that the changes in the characteristic temperatures at different heating rates are wave-like regardless of the heating rate during the thermal explosion. The correlation of the cyclical changes in the thermal characteristics of the explosion and morphological changes of the powder mixture during mechanical activation was found. Nonmonotonic changes in the behavior of characteristic temperatures are associated with changes in particle powder sizes and layered agglomerates during mechanical activation. An increase in the critical temperature and a decrease in the maximum temperature occurs in the investigated time interval of mechanical activation with an increase in the heating rate in the subsequent thermal explosion. The decreases of the combustion temperature of the titaniunm – nickel activated mixture up to 400°C, and the realization of the synthesis in the solid-phase mode was recorded.

The paper simulates the aerodynamics of a two-phase flow in the cylindrical part of the screw auger precipitation centrifuge in order to estimate the centrifugal forces in the central region of the centrifuge, due to problems of sedimentation of the solid fraction from the suspension. According to the obtained velocity field, the time and the trajectory of the deposition of solid particles of different diameters of a two-phase flow of different diameters are calculated. This is necessary to estimate the speed of rotation and the pitch of the screw for outputting solid sediment to the discharge windows. The resulting model will optimize the existing apparatus for centrifuging two-phase flows, as well as help in the design of new plants.

The results of modeling shock waves interaction with spheres are presented. The Mach number was chosen so as the temperature behind the shock waves front would not exceed the auto-ignition temperature of hydrogen in air. A mathematical model and a reduced kinetic scheme of chemical reactions verified previously were used. The dependences of the mixture time of ignition beginning along the width of the channel and its location from the Mach number of the shock wave were refined. The flow pictures for two spheres located one behind the each other were obtained. The analysis of the results was carried out.

The paper represents the numerical simulation of severe plastic deformation of a copper sample under dynamic channel-angular pressing. The initial sample velocity and the value of pressure acting on the back surface of the sample during the process were determined based on the analysis of experimental data. Numerical computations were carried out using the author's numerical code created in the integrated development environment Delphi. A modified finite element method (without constructing a global stiffness matrix) was used as a numerical method. The behavior of the material was described by an elastic-plastic model using the active type fracture model. Testing of the numerical code was carried out on the Taylor problem. The velocity and pressure values required for the successful dynamic channel-angular pressing were determined. A uniform distribution of the ultrafine-grained structure in almost the entire volume of the copper sample was revealed.

The purpose of the work is to calculate the stress-strain state of the III-type road, as well as to determine the load factor for road pavement and roadbed. A model of non-rigid road pavement consisting of 4 layers is considered: dense-graded asphalt concrete, open-graded asphalt concrete, gravel roadbed, ground roadbed (silt sandy loam). A numerical code is developed for calculating the principal physical and mechanical parameters of road pavement. C++ is used as a programming language. A method of evaluating the shear resistance of roadbed is proposed. To calculate the load factor of roadbed, the Drucker-Prager strength criterion is used without the term responsible for the intensity of tangential stress. A T-90 tank fitted with special rubber track pads is considered to be a static load. The computations reveal the maximum vertical deflection, equal to 0.004 m, in the contact area of the tracks. In the same area, the load factor of road pavement is 9 ÷ 10, which indicates a high bearing capacity of dense-graded asphalt concrete. The analysis of shear resistance shows the presence of irreversible deformations in gravel roadbed in the contact area of the tracks, while the load factor of silt sandy loam is 3 ÷ 10.

Deformation and fracture of laminates under high-velocity impact were numerically investigated. Targets consisting of alternating layers of intermetallide (Al₃Ti) and titanium alloy (Ti-6Al-4V) were used as laminate composites. A high-strength steel core was used as a projectile. Impact velocities were varied in the range of 2000-5000 m/s. Fracture of intermetallic layers is described by the brittle fracture model, and fracture of titanium alloy layers is described by the active-type kinetic model. The erosion fracture model is used to simulate the fracture of the material under intensive deformation. The modified finite element method (without a global stiffness matrix) was used for numerical computations. It is revealed the increasing role of shock wave processes in the fracture of targets with increasing an impact velocity. The metal-intermetallic laminate target delaminates due to the fracture of intermetallic layers in shock waves and the formation of main cracks in these layers.