Influence of hydrostatic pressure on the lifetimes of polymers

Under uniaxial tension, the lifetimes of polymers under hydrostatic pressure are longer than under atmospheric pressure. This effect is attributed to a change in the failure mechanism under pressure owing to retardation of the free-radical chain reaction of breakage of the macromolecules under omnidirectional compression.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 207–213, March–April, 1976.     

Dilatometric method of investigating the phase transitions of elastomers in the deformed state

A method is proposed for investigating crystallization and melting processes in vulcanizates in relation to the change of volume of specimens in the compressed or extended state. The method combines the advantages of dilatometry (accuracy of quantitative estimates) and mechanical methods (possibility of acceleration of crystallization associated with orientation of the macromolecules). The vulcanizates are tested under realistic conditions. Vulcanizates of NT Nairit and cis-1,4-polybutadiene have been tested by means of the method described; the crystallization kinetics are shown to depend on the degree of extension and compression of the specimens.Lebedev All-Union Scientific-Research Institute of Synthetic Rubber, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 780–784, September–October, 1970.     

Limiting stresses in spatially reinforced composites with components-having different structural geometries nd elastic properties

A model which is proposed for calculating structural stresses in spatially reinforced composites and an invariant-polynomial criterion for evaluating their limiting values are used to predict the effect of the elastic and strength properties of the components and their relative content on the limiting stress-strain state of composites of different structures. Emphasis is given to tri-orthogonal and 4D cubic structures, in addition to structures with hexagonal and angle-ply fiber reinforcement schemes in the plane and perpendicular to it. The types of composite loading typical of standard tests are examined in separate numerical experiments for shear, tension, compression, and their proportional combination. A computational variant of a criterional estimate of the limiting stresses is substantiated for an anisotropic composite of variable strength. The limiting-stress surface is obtained along with contour maps showing stress isolines as a function of the properties of the components and the geometry of the structure. The maps are suitable for practical use. The cases of maximum resistance to shear, tension, compression, and combination loading of 3D and 4D composites are compared to the analogous cases for two-dimensional structures.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 616–639, September–October, 1995.     

Analitical Description of the Creep of Expanded Polystyrene under Compressive Loading

Data obtained in testing the creep of expanded polystyrene plates in compression are discussed. Power-type and exponential regression equations are used for describing the compression creep curves. Within the limits of data spread, both these equations represent experimental results equally well. A correlation between the creep strain and density, the compressive stress at a 10% strain, and the elastic modulus in compression is revealed for the material investigated.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 525–534, July–August, 2005     

Experimental investigation of the strength of glass-reinforced plastics in biaxial compression in three planes of symmetry

Glass-reinforced plastics (GRP) with fiber (wound) and fabric (hot-molded textolites) reinforcement have been investigated in biaxial compression in the three planes of symmetry. The high strength in biaxial compression in the transverse plane, observed for all the GRP investigated, is explained. A method of investigating the tensile strength of the fiber components of the GRP from the results of testing a unidirectional composite in biaxial compression in the transverse plane is proposed. The possibility of a nondestructive estimation of the strength of GRP in biaxial compression at an arbitrary stress ratio is demonstrated.Translated from Mekhanika Polimerov, No. 1, pp. 63–72, January–February, 1976.     

Finite element construction for simulating delamination of sandwich composite plates and masses

Displacements and transverse normal stresses in sandwich plates and masses have been approximated by the Ambartsumyan iterative approach to constructing mathematical models of the stress-strain state of sandwich structures. A linear distribution of the displacements in the sandwich structure is set up as the first step of the iterative process, while in the subsequent steps the displacement approximations with higher-order polynomials are obtained. The approximation of the compression stresses is based on Hooke's law using the expression of the tangential displacements in the second step and the normal displacements in the third step of the iterative process. Two shear functions are introduced. The finite element is rectangular and has four nodes. The number of degrees of freedom of finite elements is independent of the quantity of the layers that may be orthotropic. The finite element allows us to simulate delamination by a thin low-modulus interlayer. In doing so, the quantity of the layers increases, while the order of the resolving set of equations does not grow. A number of numerical experiments were carried out. It has been shown that the delamination can greatly increase the level of the stresses in the structure. This effect is especially significant for thin structures. The stresses are somewhat lower when taking into account the interlaminar friction.Submitted to the 10th International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 251–263, March–April, 1998.     

Optimal Control and Filtering of the Reproduction Law of a Branching Process

A finite horizon control problem for the reproduction law of a branching process is studied. Some examples with complete information are tackled via the Hamilton–Jacobi–Bellman equation. A partially observable control of the cardinality of the population using the information given by the splitting process is formulated. Though there is correlation between the state and the observations and the observation process has unbounded intensity, a Girsanov-type change of probability measure can be set and the filtering equation for the unnormalized conditional distribution (the Zakai equation) can be derived. Strong uniqueness for the Zakai equation and, as a consequence, also for the Kushner–Stratonovich equation is obtained. A separated control problem is introduced, in which the dynamics are represented by the splitting process and the unnormalized conditional distribution. By the strong uniqueness for the Zakai equation, equivalence between the partially observable control problem and the separated one is proved.     

High-precision modeling of deformation of laminated structures

Precise three-dimensional solutions for homogeneous, two- and three-layer plates of symmetric and nonsymmetric structure over their thickness with orthotropic layers in transverse symmetric and antisymmetric loading normal to the surface of the plates are given. It is shown that the character of stressed states under flexural (antisymmetric) and nonflexural (symmetric transverse compression) loading differs greatly. It is noted that the known refined continual models, which take into account the transverse shear and compression, are all essentially flexural and therefore cannot describe the nonflexural deformations well. In particular, continual shear models in symmetric pressure loading lead to zero solutions. A refined nonflexural continual model of deformation of sandwich plates in bilateral symmetric compression is constructed. The general order of resolving differential equations for continual models does not depend on the number of layers. Approximation functions of the transverse coordinate are obtained with the help of well-founded hypotheses. A high-accuracy variant of the flexural continual model is proposed for antisymmetric loading with account of shear and transverse normal strains, as well as a version combining both models mentioned. A method of precise satisfation of all the constitutive relations for the layers, including the conditions of their contact, is proposed, whereas in the known continual models the dependence between the transverse normal stress and strain is satisfied only integrally, or else the Poisson effect is neglected.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 13–28, January–February, 1999.     

Method of constructing shock compression diagrams for foam plastics

A method is proposed for constructing shock compression diagrams for foam plastics based on experimental determination of the residual deformation of a specimen after impact with a rigid obstacle. An approximate diagram is obtained for expanded polystyrene PS-1 of initial density 0.21 g/cm³, and the dynamic yield strength is estimated.Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 566–568, May–June, 1973.     

Terminal defects in crystalline polyethylene

Conclusions 1. Possible modes of transverse movement of terminal defects in crystalline polyethylene have been investigated for the three-dimensional case. It has been found that the probability of aggregation of two columns of monovacancies by means of their transverse movement decreases rapidly with increase in the initial distance between defects.2. The process of decrease in volume of a column of vacancies during compression has been investigated. A dependence of the degree of compression of a vacancy on the angle between the external force and the plane of zigzag of the chain has been found.3. Three positions of stable equilibrium of doubling of the three-dimensional model of polyethylene containing a series of vacancies have been observed during loading of the simple shear type.For Communication 1, see [1].Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 588–595, July–August, 1978.     

Effect of cellular structure on the mechanical properties of plastic foams

A generalized equation for the compressive stress-strain diagrams of plastic foams is derived on the basis of a 14-faced model of the cell. The results obtained make it possible to predict the polymer base and type of cellular structure required to obtain a foam with predetermined mechanical properties in compression. The calculated values are shown to be in satisfactory agreement with the experimental data.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 4, pp. 594–602, July–August, 1970.     

Experimental investigation of the stability of glass-reinforced plastic cylindrical shells subjected to long-term axial compression

The results of an experimental investigation of circular cylindrical glass-reinforced plastic shells under long-term axial compression are reported. The experimental method and the experimental apparatus are described. The initial irregularity functions and their evolution during loading and in time at various values of the compressive loads are investigated. The spread of the critical times at a given load level is studied together with the dependence of the critical time on the compressive load. The behavior of the shell after unloading and under alternating loading and unloading is considered. The correlation between the buckled shapes resulting from long-term compression and the initial irregularity functions is examined.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 710–713, July–August, 1973.     

Measurement of the strength of plastics in high-speed compression

A previously developed [1] method of determining the strength of plastics in high-speed compression is extended to the temperature range –196° to +150°C. Dynamic strength data have been obtained for epoxy-polyester and polyvinyl butyral resins and glass-fabric reinforced plastics based on these resins in the indicated temperature range.Mekhanika Polimerov, Vol. 1, No. 5, pp. 34–38, 1965     

On the difference in the moduli of elasticity of polyamides subjected to different kinds of deformation

Experiments to determine the moduli of elasticity of polyamides (kapron) in tension and compression are described. A substantial difference in these characteristics was detected. The modulus of elasticity in tension is 0.75–0.80 of the value of the modulus in compresion. This difference is explained by the textural characteristics of the polyamides. The use of values of the modulus of elasticity obtained by testing specimens in tension to determine the stiffness of parts working in compression give overestimated strain values.Mekhanika Polimerov, Vol. 1, No. 4, pp. 47–51, 1965     

Fracture of plates,the compression of which is accompanied by cracking

The appearance of fracture shapes, analogous to fractures in the shape of a "Chinese lantern" in rectangular plates has been discussed, the compression of which is accompanied by cracking. It has been shown that one or two cracks can appear when rectangular hinged plates are subjected to compression. An arbitrary number of cracks can be formed when a cylindrical shell is subjected to compression.Paper presented at the 9th International Conference on the Mechanics of Composite Materials, Riga, October (1994).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 326–329, May–June, 1995.     

Load bearing capacity of multilayered sectional tubular rods made of composites

Conclusion We investigated the load bearing capacity of a new class of tubular rods made of composites, viz., peripherally and radially sectional. It was discovered that under conditions of tension, compression, bending, and combined loading by compression and torsion the number of macrolayers, strengthening by a carcass or external lagging have practically no effect on the rigidity and strength of peripherally and radially sectional rods. The nature of failure of sectional and monolithic rods is the same. Ways were shown of increasing the load bearing capacity of the rods under consideration with the object of bringing their mechanical properties up to the level of monolithic rods by improving the technology of assembly and by using high-strength film glues.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 85–92, January–February, 1990.     

Experimental investigation of the strength of anisotropic materials in biaxial and triaxial compression

It is proposed that the strengths in uniaxial and uniform biaxial compression in the direction of the axes of symmetry be used as parameters. The applicability of a strength criterion in the form of a fourth-degree polynomial to glass-reinforced plastics in biaxial compression in the plane of reinforcement and the transversal plane and to wood in triaxial compression has been experimentally confirmed.S. M. Kirov Leningrad Forest Engineering Academy. Translated from Mekhanika Polimerov, No. 6, pp. 991–996, November–December, 1973.     

Practical and flexible pattern matching over Ziv–Lempel compressed text

We address the problem of string matching on Ziv–Lempel compressed text. The goal is to search for a pattern in a text without uncompressing it. This is a highly relevant issue to keep compressed text databases where efficient searching is still possible. We develop a general technique for string matching when the text comes as a sequence of blocks. This abstracts the essential features of Ziv–Lempel compression. We then apply the scheme to each particular type of compression. We present an algorithm to find all the matches of a pattern in a text compressed using LZ77. When we apply our scheme to LZ78, we obtain a much more efficient search algorithm, which is faster than uncompressing the text and then searching it. Finally, we propose a new hybrid compression scheme which is between LZ77 and LZ78, being in practice as good to compress as LZ77 and as fast to search as LZ78. We show also how to search for some extended patterns on Ziv–Lempel compressed text, such as classes of characters and approximate string matching.     

Theory of the biomechanism of fractures of the diaphysis of long tubular bones

A new theoretical basis is proposed for the biomechanism of fractures of the diaphysis of long tubular bones resulting from bending deformation. Bone damage is shown to result from the concentration of maximum tensile stresses on the tension side and shear stresses in the compression zone. The origin of fan-shaped cracks and oblique fractures, occurring individually or in combination, is explained in these terms.Altai State Medical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 318–322, March–April, 1971.     

Creep of linear unoriented polymers in tension,compression, and torsion

The creep of polymethyl methacrylate, polystyrene, and polyethylene in tension, compression, and torsion has been investigated over a broad interval of temperature below the glass transition point. It is shown that the creep criterion changes depending on the temperature. This is associated with changes in molecular mobility.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 24–28, January–February, 1970.