The Cauchy problem for a system of quasilinear parabolic equations of chemical kinetics type

The Cauchy problem for the class of quasilinear parabolic systems of reaction—diffusion type is considered. Under appropriate assumptions regarding the nonlinearities and the initial functions, the nonlocal solvability of this problem and the stabilization of its solution, uniform with respect to the space variables, are established.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 16, pp. 242–261, 1992.     

Effect of structural-chemical modification of a polycaprolactam block on the retention of strength during thermo-oxidation

The structure and strength of a block of polycaprolactam (PC) have been investigated in relation to diffusion stabilization and thermo-oxidation. It is shown that structural modification of the surface layers of the PC block with zinc iodide has an important effect on the retention of strength during prolonged thermo-oxidation.Kaunas Polytechnic Institute; Institute of Physicotechnical Problems of Energetics, Academy of Sciences of the Lithuanian SSR, Kaunas. Translated from Mekhanika Polimerov, No. 1, pp. 10–14, January–February, 1970.     

Energy dissipation in a glass laminate stressed in cyclic tension-compression

An experimental investigation has established that in a glass laminate most of the mechanical losses are converted into thermal energy. The sum of the mechanical losses increases with increase in the fatigue life of the material, the ratio of thermal losses remaining constant under given deformation conditions. Quantitative data are presented for the energy dissipation in various phases of the fatigue fracture process.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 655–661, July–August, 1969.     

Polymer fractography and fracture kinetics

The fractographic method makes it possible to determine the test temperature and time at which anomalies appear in the temperature-time dependence of the strength of polymethyl methacrylate and polycaprolactam by finding the conditions of disappearance of specular zones from the fracture surfaces of these polymers. For PMMA these values are –40°C and 10^–2 sec, for PCL –120°C and 10^–7 sec, respectively.For communication 1 see [2].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 232–237, March–April, 1971.     

An evaluation of the interlaminar fracture toughness of a thermoplastic composite with offset centre flies

Conclusion The offset DCB specimen has been used to characterize the influence of cooling rate and loading rate on the interlaminar fracture properties of carbon fibre reinforced PEEK. By offsetting the mid-plane fibres by several degrees, the amount of fibre bridging occurring during fracture has been reduced considerably. It has been shown that IM6 carbon fibre PEEK is quite sensitive to the cooling conditions employed after consolidation at 380 °C. Low rates of cooling yield a high level of crystallinity and a reduced fracture toughness. The modified DCB specimen has been successfully applied to highlight a distinct interlaminar fracture rate sensitivity. The high rate properties of this material still leave cause for concern and more work is required before these materials will find widespread use.Published in Mekhanika Kompozitnykh Materialov, No. 4, pp. 476–483, July–August, 1992.     

Role of the supermolecular structure of PMM in the morphology of fracture and features introduced by the type of loading

The spherulitic supermolecular structure of PMM, expressed in the fracture surface, determines the fracture pattern and kinetics. The effect of the type of loading on the morphology of the fracture surface is described. Banding of the fracture surface is attributed to periodic energy pulses leading to quasi-brittle fracture at the moving crack front and selective local crack development at the band edges.Riga Lenin Komsomol Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 776–782, September–October, 1968.     

Statistical laws of fracture and statistical estimation of the static strength of structural elements made from polymeric composites

The basis of the statistical estimation of the strength of structural elements made from fibrous composites is considered; the statistical characteristics of the strength of these materials are described and the limit states are formulated. Special attention is given to the resistance to debonding. The conditions of fracture of this class of materials in plane stress are subjected to a statistical analysis.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Aviation Engineering Institute, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 466–482, May–June, 1972.     

Causes of the fluctuation of the strength of a block of polycaproamide exposed to the action of heat

Fractography and mechanical testing are employed to investigate the fracture mechanism of polyamide blocks exposed to the action of heat. The mode of fracture depends essentially on the dangerousness of the surface defects.Kaunas Polytechnic Institute; Institute of Physicotechnical Problems of Power Engineering, Academy of Sciences of the Lithunian SSR, Kaunas. Translated from Mekhanika Polimerov, No. 4, pp. 642–645, July–August, 1969.     

Growth of arterial cracks in polymethyl methacrylate plates containing "silver" cracks

Conclusions 1. We have studied the influence of previously formed surface SC of various orientations on the force and kinetic characteristics of a slowly growing arterial FC. The subject of investigation was industrial glass based on polymethyl methacrylate. Steady growth of the FC was achieved in our experiments by applying torque in order to split lamellar samples.2. We have found that for no mutual disposition of the two kinds of cracks do surface SC ease the conditions of FC growth. On the contrary, in a number of cases the presence of SC having linear dimensions of only 3–5% of the front length interrupt the steady growth of the FC, reduce its average velocity, and sometimes stop it altogether. For the growth of the FC to be renewed the load has to be augmented, so that the limiting specific work of fracture W_lim increases by 10–40%. The growth of an FC is opposed most strongly by SC lying at right angles to it.3. The results of our experiments indicate comparatively easy fracture of the SC, and also show that FC prefer to develop along earlier-formed SC, subject to appropriate mutual orientation.4. By virtue of the presence of elastic interactions between different sections, any action applied to a small part of the leading edge (front) will alter the conditions of material fracture along the whole FC front.Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 609–615, July–August, 1976.     

Tensile strength of unidirectionally reinforced plates stretched at an angle to the direction of reinforcement

Conditions for the fracture of a unidirectionally reinforced plate under uniaxial tension at an arbitrary angle to the direction of reinforcement are proposed. The fracture conditions are applicable to the case where the adhesion strength between the bond and reinforcement is greater than the strength of the polymer bond. The strength of the polymer bond in the volume stressed state is determined by an energy criterion.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 482–486 May–June, 1973.     

Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays

Convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov functional method, M-matrix properties, some inequality technique and nonnegative semimartingale convergence theorem are used in our approach. These criteria ensuring the different exponential stability show that diffusion and delays are harmless, but random fluctuations are important, in the stochastic continuously distributed delayed reaction–diffusion RNNs with the structure satisfying the criteria. Two examples are also given to demonstrate our results.     

Partial stability and stabilization of dynamical systems

We prove the theorem on necessary and sufficient conditions of partial instability and the theorem on partial stabilization of nonlinear dynamical systems. We obtain sufficient conditions of controllability for systems linear with respect to control. We also study the problem of control and stabilization of an angular motion of a solid body by rotors.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 186–193, February, 1995.     

Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system

This paper presents some simple feedback control laws to study global stabilization and global synchronization for a special chaotic system described in the generalized Lorenz canonical form (GLCF) when τ = −1 (which, for convenience, we call Shimizu–Morioka system, or simply SM system). For an arbitrarily given equilibrium point, a simple feedback controller is designed to globally, exponentially stabilize the system, and reach globally exponent synchronization for two such systems. Based on the system’s coefficients and the structure of the system, simple feedback control laws and corresponding Lyapunov functions are constructed. Because all conditions are obtained explicitly in terms of algebraic expressions, they are easy to be implemented and applied to real problems. Numerical simulation results are presented to verify the theoretical predictions.     

Experimental study of fracture toughness and energy in composite materials

The paper presents an experimental investigation of fracture characteristics of composite materials. The post-peak response of the load-crack opening displacement of notched specimens is used to evaluate the fracture energy associated with progressive matrix damage and crack growth. Effects of fiber orientation and other geometric characteristics on fracture parameters are studied. The load versus crack opening displacement as well as crack length, fracture toughness, and energy versus the number of loading cycles are obtained for different specimens. Based on the experimental results of this study, concepts of the fracture mechanics are applied to evaluate the evolution of fracture toughness and energy.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Department of Mechanical & Industrial Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 323–332, May–June, 1998.     

Conditions of the ductile-brittle transition in failure of polymer materials

Conclusions The polymer materials are characterized by the transition from ductile to brittle fracture with increasing loading rate and decreasing temperature. The brittle fracture susceptibility of the material can be determined on the basis of the critical size of the defect/ crack. The measure of the cracking resistance of plastics can often be represented by the material scale of the crack length. The quality of the critical size of the defect/crack to the material scale of the crack length can be used as a criterion determining the conditions of transition from ductile to brittle fracture.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 779–785, September–October, 1988.     

Comparison of the reliefs of fracture surfaces in PMMA under static and cyclic loading

Investigations of the relief of fracture surfaces in PMMA with the help of optical and interference microscopes have shown that there are no qualitative differences in the appearance of the fracture surfaces obtained under static and cyclic loading conditions. Quantitative studies have established that the size of the specular zone increases linearly with increase in the logarithm of the lifetime at a given test temperature. Other conditions being equal, in cyclic tests the specular zone is larger than in static tests. The results obtained are considered to be further confirmation of the validity of the theory that under any loading conditions fracture is based on the same thermo-fluctuation mechanism.Mekhanika Polimerov, Vol. 2, No. 1, pp. 52–59, 1966     

Structural susceptibility of strength characteristics of polystyrene under uniaxial stretching

The structural susceptibility of the strength characteristics of polystyrene under uniaxial stretching and under test conditions with = const and v_elong = const was studied at 20–100°C. The low structural susceptibility of the durability and durability-equation parameters is due to a change in the elementary fracture volume at different test conditions. It was proposed to characterize the degree of participation of chemical and intermolecular forces by the value U₀/.Moscow Technological Institute of Meat and Milk Industry. Translated from Mekhanika Polimerov, No. 6, pp. 979–984, November–December, 1974.     

Sufficient conditions for uniform convergence on layer-adapted meshes for one-dimensional reaction–diffusion problems

We study convergence properties of a finite element method with lumping for the solution of linear one-dimensional reaction–diffusion problems on arbitrary meshes. We derive conditions that are sufficient for convergence in the L_∞ norm, uniformly in the diffusion parameter, of the method. These conditions are easy to check and enable one to immediately deduce the rate of convergence. The key ingredients of our analysis are sharp estimates for the discrete Green function associated with the discretization. AMS subject classification 65L10, 65L12, 65L15     

Study of the prefracture states of rigid polymers 1. Forced high-elastic deformation

It is shown that in the process of extension specimens of a rigid unoriented polymer — polyethylene terephthalate — go over into the oriented state before failure. Various cases of transition to the oriented state are considered: with the formation of a neck and deformation bands, with and without loss of continuity. The degree of molecular orientation of the specimens and their fracture conditions are estimated.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 8–14, January–February, 1976.     

A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O(h⁴+τ⁵). It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.