Entropy principle in the theory of creep and long-time strength of polymeric materials

The possibilities of applying thermodynamic methods in the theory of creep and long-time strength are considered. General principles are employed to construct creep equations for certain types of media and to formulate a criterion of long-time strength.Translated from Mekhanika Polimerov, No. 1, pp. 113–121, January–February, 1971.     

The laws and methods of Il'yushin in the mechanics of deformable bodies and media

Certain of the important laws and methods of Il'yushin relating to the mechanics of incompletely elastic deformable bodies and media are discussed.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 36–40, January–February, 1971.     

The conditions for the existence of a temperature - time analogy

The conditions are formulated for the existence of a temperature-time analogy in stationary temperature fields for hereditary viscoelastic media which are described by Volterra equations of the second kind with a singular relaxation kernel. A time transformation has been found for a nonstationary temperature field which results in the heredity equation becoming invariant with respect to temperature.The M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 2, pp. 217–222, March–April, 1970.     

General criteria of the strength of isotropic media

The limit surfaces of isotropic materials are considered in the invariant spaces of the stress tensor. The general requirements that must be met by limit surfaces are formulated. A three-invariant strength criterion for isotropic media sensitive and insensitive to hydrostatic pressure is given in general form. The convenience of analyzing strength criteria in the two-dimensional space of the base invariants of the stress tensor is demonstrated.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 251–261, March–April, 1971.     

Correspondence principle and the method of approximations for certain nonlinear hereditary media

Problems for two classes of nonlinear hereditary media are reduced by integral transforms to problems of the nonlinear theory of elasticity. An approximation of the elastic solution that makes it possible to solve the formulated problems for nonlinear hereditary materials is demonstrated in the case when the viscoelastic problems reduce to problems of the theory of small elastoplastic strains with active loading.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 66–73, January–February, 1971.     

Theoretical prediction of the properties of multicomponent reinforced materials

On the basis of a generalization of previously considered models of reinforced media solutions are constructed for problems of determining the effective parameters and internal stress, temperature, and electromagnetic fields with application to multicomponent reinforced materials. Special attention is paid to the construction of approximate relations for calculating the reduced characteristics of multicomponent materials from the given properties of the components, by means of which the problem of predicting the physical properties of new multiphase materials may be solved. The approximate equations for determining the parameters of two-component media of the oriented glass-reinforced plastic type, obtained by various authors, follow from these relations as a special case.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 4, pp. 646–654, July–August, 1969.     

Solution of the second boundary value problem for one variant of the nonclassical theory of elasticity

The existence and uniqueness of the solution of the second boundary value problem of the nonclassical theory of elasticity describing the behavior of media with memory are investigated.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 88–91, January–February, 1971.     

Smooth convex limit surfaces in the space of symmetric second-rank tensors

Equations are proposed to describe smooth (regular) convex hexagonal and triangular curves in the deviatoric plane. The equations are used to construct smooth convex limit surfaces for media whose properties are arbitrarily anisotropic. The results supplement the findings in [A. Lagzdin' and A. Zilauts, Mekh. Kompozitn. Mater.,32, No. 3, 339–349 (1996)], where the third invariant of a tensor was introduced into the limit-surface equation by means of singular deviatoric curves.Institute of Polymer Mechanics of the Latvian Academy of Sciences, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 171–181, March–April, 1997.     

Statistical theory of elasticity of reinforced plastics with internal stresses of shrinkage origin

The statistical boundary value problem of the theory of elasticity of macrohomogeneous composite media in the natural (unstressed) starting state is extended to media with internal stresses of shrinkage origin. It is established that the moduli of elasticity of the composite do not depend on the magnitude of the shrinkage stresses. The conditions, under which shrinkage of the resin in materials of the glass-reinforced plastic type does not lead to warping, are determined. Applications of the results to the computation of structural reliability characteristics are noted.Kirov Ural Polytechnical Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 4, pp. 676–681, July–August, 1970.     

Estimation of the error of approximation of the analytic solution of problems for nonlinear viscoelastic materials

Estimates are given for the error of approximation of the solution of problems of nonlinear viscoelastic media, for which the nonlinear elastic solution depends analytically on the material characteristics, the body and surface forces, and on the boundary displacements. From the integral estimates particular estimates are derived for viscoelastic materials in cases when the nonlinear elastic solution is majorized by a geometric progression or the sum of products of geometric progressions.Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, No. 5, pp. 827–834, September–October, 1971.     

Structure-sensitive liquid flowable compositions based on polyvinyl alcohol and silicotungstic acid

Conditions of the formation of structure-sensitive liquid flowable media based on 1.5 and 10% aqueous solutions of polyvinyl alcohol containing silicotungstic acid and water-soluble carboxy-methylcellulose in the form of its potassium salt (Na-CMC) are examined. Rheological, optical, and dielectric relaxation methods revealed the formation of several types of interpolymer complexes in the examined liquid flowable media. This leads to the formation of associates and an increase in the molecular mobility of the macromolecules and their fragments. The structure and properties of the complexes depend on the composition of the media as well as the method of introducing polyacids. It was found that it was possible to control the structure of such solutions by applying a mechanical of magnetic field. The compositions obtained can be used for producing anisotropic light-, electric-, and heat-sensitive film materials, as well as sensors of different types.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of General and Inorganic Chemistry, Belarus Academy of Sciences, Minsk, Belarus. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 413–424, May–June, 1998.     

Method of solving quasistatic boundary value problems of viscoelasticity for media with time-varying properties

It is shown that, if certain conditions are satisfied, the solution of a viscoelastic mixed boundary value problem can be obtained from the solution of the corresponding elastic problem by substituting time operators for the body and surface forces or given displacements. A similar assertion is also proved for media with time-varying properties. The applicability of the method to the theory of shallow flexible viscoelastic shells is demonstrated.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, No. 6, pp. 987–993, November–December, 1969.     

Surface buckling of a layered medium

The surface buckling of a layer-reinforced medium with the layers arranged at right angles to the surface is investigated on the basis of Bolotin's theory of layered media. The critical load is determined and the buckling mode studied. By means of a simplified approach simple expressions are obtained for the critical loads corresponding to surface buckling.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 648–654, July–August, 1973.     

Some problems of the correlation theory of structurally inhomogeneous elastic media

The correlation theory of random functions is used to describe structurally inhomogeneous elastic media with randomly distributed inhomogeneities. Expressions are obtained for the elastic moduli of averaged layered, fibrous and granular media.Mekhanika Polimerov, Vol. 2, No. 3, pp. 365–371, 1966     

Load transmission in layered materials

Load transmission in reinforced plastic heterogeneous media is investigated on the basis of the equations of the theory proposed in [1–3]. The stress distribution problem is solved for a layered half-space with loads applied to one of the "hard" layers in the plane of that layer. Simplified stress formulas are presented. The corresponding error is estimated by working a numerical example. The results are compared with the corresponding problem of the theory of elasticity for a homogeneous orthotropic body.Mekhanika Polimerov, Vol. 4, No. 2, pp. 322–327, 1968     

Construction of a phenomenological theory of fracture of anisotropic media

The theory of fracture proposed in [1] is extended to anisotropic media.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 634–644, July–August, 1971.     

Basic equations of the theory of reinforced media

The author derives the basic equations of the theory of composite elastic media obtained by reinforcing some elastic medium with a large number of linear or planar elastic elements with high strength and deformation resistance. The argument is based on macrostructural considerations. The stress-strain state of each of the reinforcing elements is considered with allowance for interaction with the matrix material. In addition, the "smoothing" principle introduced in [1–3] is applied. This corresponds to approximating the reinforced medium with some equivalent quasi-homogeneous anisotropic medium.The case of a fibrous medium in which the reinforcing elements are rods or filaments [4] is discussed in detail. Allowance for moment effects leads to equations analogous to the equations of the Voight-Cosserat moment theory and its later generalizations. Similar equations are obtained for the case of laminated media, where the reinforcing elements are membranes or plates. On the basis of the viscoelastic analogy [7], the equations of the theory of reinforced media are extended to include the case in which the matrix and/or reinforcing materials are linear viscoelastic.Mekhanika Polimerov, Vol 1, No. 2, pp. 27–37, 1965     

Wear resistance of cured epoxy-novolac compositions

It has been established that changing the elasticity of rigid crosslinked epoxy-novolac block copolymers changes the friction mechanism and wear characteristics. The optimal conditions for obtaining block copolymers with the greatest wear resistance have been determined. The results of testing epoxy novolacs in neutral and alkaline media are presented.Leningrad Lensovet Technological Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1107–1109, November–December, 1969.     

Thermal conductivity of reinforced media

On the basis of a model of an inhomogeneous body a solution is obtained for the problem of the temperature field and thermal conductivities of reinforced media, whose structure is formed by a doubly periodic system of n hollow cylinders of arbitrary diameter with the space between filled by a homogeneous medium. The thermophysical characteristics of the components are assumed given.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 749–751, July–August, 1968.     

Effect of liquid media on the deformation of the surface layers of a polymer-metal pair in sliding friction

The relation between the high-elastic component of polyurethane deformation and the deformation of the surface layers of metals has been investigated for sliding friction in various media. The surface layers of polymer and metal are plastically deformed. There is a certain correlation between the coefficient of friction and the amount of deformation.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 147–149, January–February, 1970.