Relationship between the molecular structure and certain mechanical properties of oriented polymers

The correlations between the molecular structure and intermolecular energy and the fatigue and elastic properties of fibers are considered. It is shown that the maximum of these properties corresponds to an optimal value of the intermolecular energy.Leningrad Branch of the All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 4, pp. 734–735, July–August, 1969.     

Intermolecular interactions in fiber-forming linear polymers and certain of their mechanical properties

Values of the specific volumetric intermolecular interaction energies of a series of linear polymers have been calculated on the basis of data on the interatomic and intermolecular interactions of the functional groups in the polymer molecules. It is shown that the specific volumetric intermolecular interaction energy is closely correlated with the elastic and relaxation properties of the polymers, which makes it possible to predict a series of mechanical properties of chemical fibers.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 790–795, September–October, 1971.     

The contact problem with the bulk application of intermolecular interaction forces (a refined formulation)

A refined formulation of the contact problem when there are intermolecular interaction forces between the contacting bodies is considered. Unlike the traditional formulation, it is assumed that these forces are applied to points within the body, rather than to the surface of the deformable body as a contact pressure, and that the body surface is load-free. Solutions of the contact problems for a thin elastic layer attached to an absolutely rigid substrate and for an elastic half-space are analysed. The refined and traditional formulations of the problem when there is intermolecular interaction are compared. ©2013     

New mathematical model for nonuniform deformation of composites

A new mathematical model is suggested for nonuniform deformation of composite materials valid for arbitrary external load gradients. As a basis stochastic equations are suggested for the statics of an elastic microinhomogeneous two-component material with volumetric forces differing from zero. Expressions are obtained for all coefficients in terms of elastic constants of the components and geometric parameters of the structure.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 310–318, May–June, 1995.     

The potential strain energy of a polymer molecule in nonlinear approximation

The intermolecular interaction mechanism is analyzed, and the results are used to derive a general semiempirical formula for the strain energy of a helical polymer molecule in nonlinear approximation. Formulas are given for the homogeneous straining of specific polymers. The relationship between the elastic constants of the molecule and the final strain is computed.Mekhanika Polimerov, Vol. 3, No. 4, pp. 608–614, 1967     

Stability of linearly viscoelastic bars made from polymer materials of variable cross section

The critical viscoelastic forces for hinged bars made from polymer materials of variable cross section changing in accordance with a power law are obtained. It is shown that these forces are proportional to the critical elastic forces of bars of variable cross section.VMEL "Lenin," Sofia. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 540–546, May–June, 1973.     

Optimal designing of orthotropic cylindrical shells fastened to elastic filler

Conclusions A method has been proposed for optimally designing an orthotropic cylindrical shell rigidly fastened to an elastic and isotropic filler of finite dimensions. The design takes into account simultaneous action of pressure, body forces, and heat on the structure. The optimum design has been calculated for the case of temperature-dependent elastic properties and strength characteristics of the tape. The method allows also for limitation on the strength of the filler. The convergence of the iteration process schematically shown in Fig. 2 is quite fast. Indeed, for the given design variant, the condition of manufacturability (1) is satisfied with a sixfold margin in the third approximation (n=3) already.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 91–94, January–February, 1984.     

Temperature-time dependence of the adhesion strength for polymer — Polymer systems

The temperature — time dependence of the adhesion strength has been studied for polymer systems differing in the thermodynamic compatibility of the substrate and adhesive and in the rate of polymerization of the latter. The fracture-activation energies of these systems have been calculated. It is shown that the temperature — time dependence of the adhesion strength varies depending on whether chemical intermolecular forces are responsible for the strength of the joint.Perm Scientific-Research Institute of Polymer Materials. A. M. Gor'kii Ural State University. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 665–671, July–August, 1968.     

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.     

Estimation of the length distribution of through polymer chains

The contributions of entropy and elastic forces to the tensile modulus of a polymer chain are estimated. The chain length-distribution function in the amorphous region of highly oriented Lavsan is approximately determined from macroscopic stress-strain dependence. It is found that the length distribution has a width of the order of several percent of the length of the amorphous region of the fibril.A. F. Ioffe Physicotechnical Institute, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 922–925, September–October, 1974.     

Viscoelastic deformations of a thick-walled cylinder under prolonged exposure to gravitational stresses

A method is presented for the calculation of the stress-deformed state of an infinitely long viscoelastic thick-walled cylinder, enclosed in an elastic casing and exposed to gravitational stress in equilibrium with a system of concentrated forces, applied to the casing. The problem is solved by analyzing the flat deformation of the annular region under the influence of mass forces and unknown reactions on the outer surface, and by determining the stress-deformed state of the casing ring exposed to distributed normal and tangential loads, and to a system of concentrated forces. The solutions are then compared on the basis of compatibility of the deformations and equality of the stresses. Integral transformations are used in the calculations and an example is cited.S. Ordzhonikidze Aviation Institute, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 846–853, September–October, 1972.     

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.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

State of stress of a hollow viscoelastic cylinder whose material properties depend on temperature

The state of stress of a long thick viscoelastic cylinder enclosed in an elastic shell is examined. The inner boundary recedes; body forces, internal pressure, and a uniform nonstationary temperature field are considered. The material properties depend on temperature; time-temperature superposition does not hold. A singular kernel is taken as the influence function. An approximate solution is found in displacements and stresses. A numerical example is presented.M. V. Lomonosov, Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 86–94, January–February, 1970.     

Optimal material orientation of nonlinear orthotropic materials

The problems of optimal material orientation are studied in the case of orthotropic elastic materials. It is assumed that the stress-strain relation (material behavior) is nonlinear and can be described by a transcendental relation including a logarithmic function. The orientation of the material is established from the condition that the elastic energy density attains its maximal (or minimal) value.Tartu University, Estonia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 335–346, May–June, 1999.     

State of stress of flexible plastic shells with an opening

The state of stress of flat flexible shells with an opening is investigated with allowance for the viscoelastic properties of the material. The equilibrium equations and boundary conditions are written in finite-difference form. A nonlinear system of algebraic equations is solved by successive approximations. A method of accelerating the convergence of slowly converging iteration processes is proposed. The effect of the viscoelastic properties of the shell material on its state of stress is investigated with reference to the example of a polymethyl methacrylate shell. The variations of the ring moment and ring forces at the free edge of the shell are plotted for various moments of time, load values, and flatness parameters. It is shown that as soon as the viscosity factor begins to take effect, the state of stress and strain of the shell changes sharply; the concentration of forces and moments increases in the flexible viscoelastic (as compared with the elastic) shell.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1071–1075, November–December, 1973.     

Quasistatic anti-plane motion in the simplest theory of nonlinear viscoelasticity

We consider a very simple model in the framework of differential viscoelastic materials which are isotropic and incompressible. In this model the Cauchy stress tensor is split in an elastic part and a dissipative part. The elastic part is derived from a strain-energy density function only of the first invariant of the Cauchy–Green strain tensor. The dissipative part is like the Navier–Stokes equations: linear in the stretching tensor with a constant viscosity parameter. For this model we provide some time and spatial estimates in the quasistatic approximations for the equations governing anti-plane shear motions. Several explicit examples for specific form of the strain energy are produced. Our results impose analytical restrictions on the mathematical properties of the strain energy to ensure a physical behavior in the creep and recovery experiments. Moreover, we show polynomial decay for the spatial behavior in the class of stress-hardening (or strain-stiffening) materials. For stress-softening materials a Phragmen–Lindelof alternative is proved.     

Deformation and fracture of polymers

On the basis of experimental research it is suggested that in polymers under load two physically different kinetic processes — deformation and fracture — develop simultaneously. Their rates depend on different components of the stress tensor; accordingly, the relation between these rates can be experimentally controlled. It is suggested that these processes involve the overcoming of physically different potential barriers and that their elementary events embrace essentially different activation volumes. Deformation involves the overcoming of the forces of intermolecular interaction, and fracture, with the rupture of the main chains.Review of work carried out in the Materials Laboratory of the A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR.A. F. Ioffe Physico-Technical Institute, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 95–106, January–February, 1975.     

Analysis of the vibrational spectrum of crystalline polypropylene

The effect of intermolecular interactions on the skeltal vibration frequencies of the isotactic polypropylene crystal active in the IR spectrum is theoretically estimated. A simplified model of the molecule is employed. The Kitaigorodskii potential function is used for the intermolecular atom—atom interactions. The results are given in the form of a frequency table.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 205–211, March–April, 1971.     

Vibrations of a viscoelastic cylinder with an elastic shell

The nonlinear vibrations of a viscoelastic cylinder with an elastic shell subjected to two harmonic forces are investigated using the averaging scheme described in [3, 4]. Nonresonance, resonance, and subharmonic vibrations are examined. It is shown that the presence of viscosity in the system leads to a single stationary equilibrium position for which the stability conditions are given.V. I. Lenin Tashkent State University. Translated from Mekhanika Polimerov, No. 4, pp. 691–697, July–August, 1973.