The mechanism of fatigue failure of plastics

Based on the study of the kinetics of deformation or rigidity, of the rise in temperature, and of the fracture surfaces, the article describes the mechanism of failure of plastics. It as found that in a cyclically loaded solid there occur two processes: strengthening and loss of strength. The main factors affecting strengthening in fatigue were discovered. Among them are the structure of the material, the degree of crystallinity, the load level, conditions of deformation, etc. The kinetics of rigidity can yield the most accurate information providing an idea of the process of fatigue failure of plastics.Paper read at the 9th International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Kaunas Technological University, Lithuania. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 279–285, March–April, 1996.     

Investigations in the theory of Stochastic equations

This is the author-review of a dissertation presented in the competition of the degree of the Doctor of Physicomathematical Sciences. The dissertation was defended on February 27, 1975 at a meeting of the Scientific Council of V. A. Steklov Mathematics Institute of the Academy of Sciences of the USSR. The official opponents were: A. A. Borovkov, Corresponding Member of the Academy of Sciences of the USSR; A. V. Skorokhod, Corresponding Member of the Academy of Science of the Ukrain. SSR, and V. N. Sudakov, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 20, No. 1, pp. 147–159, July, 1976.     

Staggered solution of fluid-porous-media interaction using the method of local Lagrange multipliers

Surface interaction among non-overlapping bulk-fluid and porous-medium bodies occurs in different situations, e. g., the interaction of blood with a blood vessel wall, a body of water with an earth dam structure, or acoustic waves with acoustic panels used in soundproofing. These are multi-field phenomena, comprising various surface- and volume-coupling mechanisms that should be reflected in the corresponding mathematical models. These models, together with appropriate initial and boundary values, assemble a coupled problem, the solution of which reveals the behaviour of the system under external excitations. The solution is commonly done numerically, following a monolithic or a decoupled approach. Here, the focus is on the latter. To design an efficient decoupled scheme, different types of coupling within the problem are addressed. These are the volume coupling between the degrees of freedom (DOF) within each subdomain, and the surface coupling between the DOF on the common boundaries. In particular, the latter constrains the feasible space of the solution of the problem. In this regard, local Lagrange multipliers (LLM) are employed to reformulate the problem in an unconstrained form. Unlike other domain decomposition methods which are based on using global Lagrange multipliers, the LLM method yields a complete separation of the subdomains and, consequently, facilitates parallel solution of the sub-problems. Moreover, within the subdomains, the penalty method is used to decouple pressure from other DOF. This procedure, on the one hand, reduces the size of the problem that should be solved at the interface and, on the other hand, removes the burden of using mixed finite elements within the subsystems. In the next step, the stability behaviour of the resulting staggered approach is analysed, and the unconditional stability of the method is established. Finally, the method is employed to solve a benchmark example, and using the numerical results, the reliability of the outcomes of the stability analysis is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of the pliability and rigidity of nonbalanced monoclinic composites

Conclusions As the result of a change in the deformation characteristics of the elementary layers, which is asymmetric with respect to the middle plane of the composite, and caused by imperfections of technical character, aging, the effect of temperature, moisture content, corrosive media, and other factors, the balancing of the laminated polymeric composites is disturbed. Formulas were obtained for determining all the pliability and rigidity matrix components of a nonbalanced monoclinic composite from known deformation characteristics, volume, and order of packing of the elementary layers.Institute of Wood Cellulose Chemistry, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1030–1035, November–December, 1976.     

Solvable subgroups of finite simple groups

This article is the author's abstract of his dissertation for the degree Doctor of Physico-mathematical Sciences. The dissertation was defended on September 17, 1973, at the session of the Academic Council on the conferring of academic degrees in the mathematical sciences of the Uralian Order of the Red Banner of Labor of the A. M. Gor'kii State University. The official opponents were: Professor A. I. Shirshov, Corresponding Member of the Academy of Sciences of the USSR and Doctor of Physicomathematical Sciences; Professor A. I. Kostrikin, Doctor of Physicomathematical Sciences; Professor A. I. Starostin, Doctor of Physicomathematical Sciences; Professor L. A. Shemetkov, Doctor of Physico-mathematical Sciences. The chief institution was the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR.Translated from Matematicheskie Zametki, Vol. 16, No. 5, pp. 833–842, November, 1974.     

Structural changes during torsion of polyethylene

X-ray structural studies on the changes in oriented polyethylene fibers during torsion at large and small angles showed that the crystallites undergo shear deformation, and the angle x between the axes of the macromolecules and the upper (lower) faces of the crystallites deviates appreciably from a right angle. As a result of torsion of the fibers, an axial texture of the fibrill is formed, inside which the crystallites are skewed, while the c axes of the crystallites are inclined to the texture axis. The nature of the more specific changes in the structure depends on the ratio between the temperatures of the preliminary orientational drawing of the samples, and the subsequent torsion.The V. I. Lenin Tadzhik State University, Dushanbe, Institute of Macromolecular Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 160–162, January–February, 1974.     

Numerical inversion of Laplace transform by the method of asymptotic extension of the interval in dynamic viscoelasticity problems

Conclusions 1. A numerical investigation into the process of wave propagation in infinite and finite viscoelastic rods has been carried out by means of the method of asymptotic extension of the interval.2. It is established that use, in the calculations, of kernels of relaxation with weak singularity does not give rise to a stress jump at the wave front.3. The effect of parameters of the Rzhanitsyn kernel on the "erosion" of the wave front has been investigated. It is discovered that the instant of occurrence of a stress that is appreciably different from zero, at points far away from the beginning of the rod, is determined by the long-term modulus of elasticity of the material of the rod.4. The solution of the problem concerned with the propagation of a load impulse of finite duration shows a decrease of the maximum value of the stress in the rod, when the duration of the applied impulse decreases, and an intense change in the shape of the impulse while it propagates along the rod, as a consequence of wave dispersion.P. Stuchka Latvian State University, Riga. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 864–870, September–October, 1976.     

Electron diffraction investigation of the fracture surfaces of filled mixtures of SKS-85 butadiene-styrene copolymer

As the result of an electron microscope study of replicas from the fracture surface during the disintegration of samples of mixtures of SKS-85 butadiene-styrene copolymer with 20 vol.% DG-100 carbon black and chalk, in the temperature range from +60 to –60°C, it is shown that, in the region of vitrification of the copolymer and of the loss of the reinforcing effect of the carbon black, there is a sharp change in the character of the fracture micro-surface, and the particles of carbon black become the sites of additional fracture. In the region of the temperature transition of the copolymer, connected with the mobility of the phenyl groups in the same way as in the vitrification region, there is a sharp decrease in the number of particles of carbon black at the fracture surface, while the fracture surface of a mixture with chalk passes selectively along the contact boundary of a polymer with larger particles. The microstructure of the Wallner lines on the surface of a mixture with carbon black, at Tst, is made up of traces of secondary fracture, arising around the particles of carbon black.Moscow Institute of Technology for the Meat and Dairy Industry. M. V. Lomonosov Institute for the Technology of Fine Chemicals, Moscow. É. L. Ter-Gazaryan State Scientific-Research and Design Institute, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 437–444, May–June, 1970.     

A refined model for three-point bending of sandwich panels. 1. Deflections and bending stresses

Design formulas for the flexural characteristics of sandwich panels under three-point loading by point forces, taking into account local effects, have been derived. Transverse deformation of the normal in the modified model is deduced in terms of the difference between deflections of face layers. It is considered that the rotation of the normal depends also on shear of the filler. The deflections, local curvatures, and bending stresses, dependent on the face-layer thicknesses and transverse characteristics of the filler, are studied. The danger of initial failure caused by the local moment stresses at the central panel section is shown. Comparative estimates refining the conventional designs are established.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 747–767, November–December, 1997.     

Investigation of boundary value problems for elliptic systems of first order

This paper is the author's abstract of a dissertation submitted for the degree of Doctor of Physicomathematical Sciences. The dissertation was defended November 2, 1972 at a session of the Scientific Council of the V. A. Steklov Mathematical Institute of the Academy of Sciences, USSR. Official referees: Corresponding Member of the Academy of Sciences of the USSR Professor A. V. Bitsadze, Corresponding Member of the Academy of Sciences of the USSR Professor M. M. Lavrent'ev, and Doctor of Physicomathematical Sciences, Professor P. I. Lizorkin.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 291–304, August, 1973.     

Wave parameter identification problem for ocean test structure data,part 2, discrete formulation

This paper deals with the solution of the wave parameter identification problem for ocean test structure data. A discrete formulation is assumed. An ocean test structure is considered, and wave elevation and velocities are assumed to be measured with a number of sensors. Within the frame of linear wave theory, a Fourier series model is chosen for the wave elevation and velocities. Then, the following problem is posed: Find the amplitudes of the various wave components of specified frequency and direction, so that the assumed model of wave elevation and velocities provides the best fit to the measured data. Here, the term best fit is employed in the least-square sense over a given time interval.At each time instant, the wave representation involves four indexes (frequency, direction, instrument, time); hence, four-dimensional arrays are required. This formal difficulty can be avoided by switching to an alternative representation involving only two indexes (frequency-direction, instrument-time); hence, standard vector-matrix notation can be used. Within this frame, optimality conditions are derived for the amplitudes of the assumed wave model.A characteristic of the wave parameter identification problem is that the condition number of the system matrix can be large. Therefore, the numerical solution is not an easy task and special procedures must be employed. Specifically, Gaussian elimination is avoided and advantageous use is made of the Householder transformation, in the light of the least-square nature of the problem and the discretized approach to the problem.Numerical results are presented. The effect of various system parameters (number of frequencies, number of directions, sampling time, number of sensors, and location of sensors) is investigated in connection with global or strong accuracy, local or weak accuracy, integral accuracy, and condition number of the system matrix.From the numerical experiments, it appears that the wave parameter identification problem has a unique solution if the number of directions is smaller than or equal to the number of sensors; it has an infinite number of solutions otherwise. In the case where a unique solution exists, the condition number of the system matrix increases as the size of the system increases, and this has a detrimental effect on the accuracy. However, the accuracy can be improved by proper selection of the sampling time and by proper choice of the number and location of the sensors.Generally speaking, the computations done for the discrete case exhibit better accuracy than the computations done for the continuous case (Ref. 5). This improved accuracy is a direct consequence of having used advantageously the Householder transformation and is obtained at the expense of increased memory requirements and increased CPU time.This work was supported by Exxon Production Research Company, Houston, Texas. This paper is based partly on Refs. 1–4.     

Thermal-fluctuation model of a thixotropic rubbery liquid

The isothermal deformation of a viscoelastic liquid, whose structural elements are simulated by the Maxwell elements of the relaxation spectrum, is considered. It is assumed that in the presence of temperature fluctuations the elements of the spectrum can be destroyed and restored. A comparison is made with experiment. A procedure for calculating the relaxation spectrum from the results of shear and normal stress measurements in the steady-state shear flow regime is proposed.Presented at the Symposium on Polymer Rheology, Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow, May, 1970.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 307–317, March–April, 1971.     

Theory of viscoelastic behavior of regular polymeric networks with stable points linking four chains

A regular stable network formed by flexible macromolecules connected into four functional points is considered. Each point of the network is acted on by the elastic forces from neighbors, by the force of viscous resistances, proportional to the relative velocity of the point, and by the effective force of Brownian movement. The kinetic equation is written for the network points in the case of deformation, and the moments of the second-order distribution function are calculated. The relaxation times of the system are found, and the behavior of the network in the presence of homogeneous sinusoidal deformation due to extension and shear is discussed. The complex modulus of elasticity of the network is calculated as a function of the network parameters and frequency.Branch of the Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 209–216, March–April, 1970.     

Bitopological spaces

The paper is, in essence, a monograph devoted to the theory of bitopological spaces and its applications. Not exhausting the entire subject, it reflects basic ideas and methods of the theory. The Introduction gives an idea of the origins of the basic notions, contents, methods, and problems both of the classical (in the spirit of Kelly) and of the general theory of bitopological spaces. The classical theory is described rather schematically in Chapter I, only the theory of extensions of topological and bitopological spaces and the theory of completion of uniform spaces are presented in more detail. The main focus is on the general theory of bitopological spaces (Chapter II). Notions, methods, and results presented here have no analogues in the classical theory. As applications, foundations of the theory of bitopological manifolds, in particular, bitopologically represented piecewise linear manifolds (Chapter III), and the foundations of the theory of bitopological groups are presented (Chapter IV). Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 242, 1997, pp. 7–216. Translated by A. A. Ivanov.     

Instability of thermoelastic interaction between a half-space and a rigid base through a thin liquid layer

We investigate the instability of thermoelastic interaction between elastic and rigid half-spaces through a liquid interlayer under the conditions of heat transfer across the interfaces. Due to the small thickness of the liquid layer, its influence on the temperature field is taken into account by the thermal resistance of the contact between the bodies, which depends on the normal displacement of the boundary of the elastic body. The pressure inside the liquid is equal to the external pressure applied to the bodies. We determined the critical value of the external heat flow for which the instability becomes possible in such a system and studied the dependence of this value on the parameters of the elastic half-space, the thickness of the liquid layer, and its thermal conduction. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 76–82, April–June, 1998.     

一类KdV-Burgers方程的奇摄动解与孤子解

讨论了一类具有大Reynolds数且弱频散性的KdV-Burgers方程, 在数学上表示为一类奇摄动KdV-Burgers方程.KdV-Burgers方程中含有的非线性项与频散项互补作用形成稳定向前传播的孤立子.通过数学分析, 描述了孤立子的传播途径和传播速度等物理量的发展变化规律.通过奇摄动展开方法, 构造了该问题的渐近解.首先,用Riemann-Earnshaw方法求得退化解, 得到了简单波, 该简单波波形中的任意一点与初始点都存在一个传播速度差, 这使得波在传播过程中波形不断畸变, 最终形成冲击波面, 即间断面, 在它的两侧质点的速度有一个跳跃, 且随时间不断变化;其次, 在退化解的间断曲面处做变量替换, 构造一种修正的行波变换, 得到了内解展开式的孤子解, 并证明了内外解的存在性与唯一性;最后,通过一致有界逆算子的存在性做了余项估计, 并得到渐近解的一致有效性.结果表明, KdV-Burgers方程在大Reynolds数且弱频散性的性质下,扰动集中在退化解的间断面附近,孤立子链接两侧质点,其传播途径不是时间与空间的线性形式,而是沿着退化解的间断面附近传播,形成稳定的波形.     

Finite-dimensional perturbations of Volterra operators

This paper is a review by the author of his dissertation, presented in competition for the academic degree of Doctor of Physicomathematical Sciences. This dissertation was defended on December 20, 1973 at the Scientific Council of the Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. The examining committee consisted of Professor A. G. Kostyuchenko, Doctor of Physicomathematical Sciences; Professor A. F. Leont'ev, Corresponding Member of the Academy of Sciences of the USSR; and Professor M. K. Fage, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 669–680, October, 1974.     

Nonlocal quantum field theory,nonlinear interaction lagrangians,and the convergence of the perturbation-theory series

Conclusions Thus, for a definite class of significantly nonlinear interaction Lagrangians, we were able to construct, within the framework of nonlocal quantum field theory, the S-matrix of the theory in the form of a convergent perturbation-theory series in the Euclidean formulation of the theory. It was shown earlier that after a continuation into the physical domain, the S-matrix will be unitary in every order of perturbation theory. The next problem is the study of the behavior of the amplitudes of physical processes within the framework of the complete converging series which represents the total S-matrix of the theory.Joint Institute for Nuclear Research. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 2, No. 3, pp. 302–310, March, 1970.     

考虑成本、等待时间和安全水平的分类安检模式研究

近年来,随着民航机场旅客吞吐量快速增加,机场安检部门的工作压力正不断加大,旅客等待时间也正在逐渐增加。针对该问题,引入了分类安检模式。然而,分类安检模式通常需要额外的投资成本,可能会产生较大的财务负担。因此,以成本为目标,综合考虑旅客等待时间和安全水平的要求,研究了分类安检模式和传统安检模式的比较以及最优决策性质等相关问题。首先,考虑安全水平和旅客等待时间的约束,分别为传统安检模式和分类安检模式建立了模型,并分析了其最优运营决策性质。其次,从成本的角度,对两种安检模式做了比较研究。研究结果表明,当旅客数量多、安检犯错容忍度较高或旅客等待敏感时,分类安检模式比传统安检模式表现更优;反之,传统安检模式更优。此外,在分类安检模式中,分配到高风险安检通道的旅客比例存在一个最优值,并且其通常在20%到30%之间取到。最后,通过数值分析验证了分类安检模式的最优服务配置。     

Main features of the viscoelastic behavior of carbon fiber-reinforced plastics with a polymer matrix: Model study and calculation

It was shown that below the glass transition temperature of the amorphous matrix, its viscoelastic behavior in a composite is described by the Halpin-Tsao equation for composites, as modified by Nielsen, with a sufficient degree of reliability. However, when the matrix passes into the highly elastic and especially the viscous flow state characteristics of thermoplastic matrices, a significant difference is observed in the experimental and calculated temperature curves of the elastic and matrix loss moduli. It is possible to hypothesize that this is due to hindrance of plastic deformation of the matrix in the composite not accounted for in the Halpin-Tsao model. Using simple models of the one-sided coating and sandwich type, it was shown that consideration of the stress state of a matrix in contact with a rigid coating can result in the same kind of effects as in a composite, namely, apparent toughening of the matrix in the highly elastic region and shifting of the maximum of the mechanical loss modulus to the high-temperature region.Institute of Macromolecular Compounds. Russian Academy of Sciences, St. Petersburg, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, 690–703, September–October, 1997.