The state of stress of an anisotropic half-plane with an elliptic inclusion

One solves the problem of the determination of the state of stress in an anisotropic half-plane in the presence of an elliptic inclusion of the same material, subjected to a preliminary strain. This problem is equivalent to the problem of the determination of the state of stress in a half-plane, due to a thermal patch, coinciding with the inclusion domain. The solution of the problem is given in complex potentials. The case of an orthotropic half-plane with a circular inclusion is considered in detail. The results are illustrated by graphs.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 79–86, 1987.     

A generalized constitutive equation for creep of polymers at multiaxial loading

Summary This paper introduced a unified formulation for generalized deformation models including load dependent effects (2nd order effects). It is given in more detail for stationary creep of isotropic, orthotropic, and anisotropic material behavior. A further generalization of the introduced 6-parameter constitutive equation is possible by coupling creep and damage. These generalizations include the classical theory of creep damage [13]. The proof of the proposed theory is given in [20–22] for special cases with a reduced number of material parameters. The results of calculations show a good agreement with results from multiaxial tests.Dedicated to our colleague and friend Vitauts Tamus on the occasion of his sixtieth birthdayPublished in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 723–733, November–December, 1995.     

Nonaxisymmetric thermal stress state of laminated rotational bodies of orthotropic materials under nonisothermic loading

A procedure for numerical investigation of nonaxisymmetric temperature fields and the elastic stress-strain state of laminated rotational bodies of cylindrically and rectilinearly orthotropic materials under nonisothermal loading is proposed. The deformation of orthotropic materials is described by the equations of anisotropic elasticity theory. The equations of state are written in the form of Hookes law for homogeneous materials, with additional terms which take into account the thermal deformation, changes in the mechanical properties of materials in the circumferential direction, and their dependence on temperature. A semianalytic finite-element method in combination with the method of successive approximations is used. An algorithm for numerical solution of the corresponding nonlinear boundary problem is elaborated, which is realized as a package of applied FORTRAN programs. Some numerical results are presented.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 731–752, November–December, 2004.     

Method of estimating the strength of glass-reinforced plastic shells

A combined method of estimating the strength of glass-reinforced plastic shells in the plane stress is described. The method consists in a combination of destructive and nondestructive methods of determining the necessary starting characteristics for use with a criterion of the strength of orthotropic materials in the form of a fourth-degree polynomial.Ritm Scientific-Production Association. Central Scientific-Research Institute of Shipbuilding Technology, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 571–573, May–June, 1972.     

Variant of the geometrically nonlinear theory of anisotropic shells with allowance for transverse shear

A very simple variant of the geometrically nonlinear theory of anisotropic shells with allowance for the high compliance of the material in transverse shear is proposed. From this theory there follow, as a special case, the equations for an isotropic shell; these differ from the relations of [2] with respect to terms of the order of the ratio of the thickness of the shell to the radii of curvature small as compared with unity. The equations obtained are used to solve the problem of the stability of orthotropic shells of revolution relative to the starting axisymmetric state of stress.Translated from Mekhanika Polimerov, No. 5, pp. 863–871, September–October, 1969.     

Large deflections and rigidity of a long cylindrical orthotropic glass-plastic panel subjected to intermittent-uniform loads

Large deflections and the stability of a long slanting orthotropic cylindrical panel, subjected to an external pressure uniformly distributed over a section of the panel width, are discussed. Relationships are used, taking into account lateral-shift deformation and normal stress _z. A closed-loop solution is obtained by means of generalized functions. A numerical evaluation has been made to assess the error of Kirchhoff's hypothesis. Similar solutions, taking into account the lateral-shift deformation are presented in [4, 5] for cases involving continuous uniform pressure and local linear loads.Kazan Physicotechnic Institute, Academy of Sciences of the USSR. Translated from Mekhanika Polimerov, No. 5, pp. 829–837, September–October, 1972.     

Applied theories of the plasticity of porous, “unequally strong,” and anisotropic media. 2. Basic results

Conclusions We obtained practically convenient modifications of the theory of flow and TSEPD [3] for porous and anisotropic media with different strength. These qualities are taken into account with the aid of the respective stress and strain intensities. The fundamental hypotheses are confirmed by verification in known experiments with polymer and composite materials. As an example we examined elastoplastic tension of an anisotropic specimen and the limit state of an internally loaded disk, both made of materials with the mentioned qualities.Communication 1, see [2].Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 426–432, May–June, 1986.     

Experimental investigation of the propagation of longitudinal stress waves in optically active polymeric rods

A photoelastic technique has been used to investigate the propagation of longitudinal stress waves in free rods. The experiments have made it possible to establish the mechanism of stress wave formation under impulsive loading, explore the dynamic state of stress of the rod, and estimate the effect of the inelastic resistance of the material.B. E. Vedeneev All-Union Scientific-Research Institute of Hydroengineering, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 68–75, January–February, 1970.     

Analysis of the state of stress of cylindrically orthotropic rings subjected to concentrated loads

The state of stress of rings of different thickness with high degrees of anisotropy ²=E/E_r, ²=E_gq/G_r is analyzed on the basis of the solution of the plane problem for a cylindrically orthotropic body. The accuracy of the stress determination in accordance with approximate theories of bending of curved bars is estimated. The radial tensile stresses that develop when rings are bent by concentrated loads are calculated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 445–452, May–June, 1976.     

Propagation of elastic waves in certain composites

Conclusions 1. Relationships have been obtained for determining nine elastic characteristics of orthotropic composite materials from the properties of the starting components and the assigned reinforcement scheme.2. Formulas are given for calculating the propagation velocity of three types of elastic flat waves for an arbitrary direction in one of the planes of elastic symmetry of a uniform orthotropic material.3. It has been shown that the velocity of the first arrival of a packet of ultrasonic vibrations which is recorded in an experiment is equal to the velocity of motion of the wave front in a limitless medium even for rather thin (5–10 mm) fiberglass-plastic specimens with unidirectional or cross-reinforced schemes.4. The dependences of elastic properties and rates of propagation of elastic vibrations on direction which are calculated theoretically from the properties of the starting components and the reinforcement scheme agree satisfactorily with experimental results.Translated from Mekhanika Polimerov, No. 3, pp. 531–536, May–June, 1978.     

Transient creep of glass-reinforced plastic

Short-time (up to 30 min) creep tests on SVAM glass-fiber orthotropic material at 20°C have shown that it is subject to creep even at room temperature. At the same time, the behavior of this material in creep is observed to be markedly anisotropic.Mekhanika Polimerov, Vol. 1, No. 2, pp. 47–54, 1965     

Antiplane deformation of an orthotropic body with a crack and elliptical cavities

A study was made of the stress distribution in an anisotropic body with a tunnel crack and one or two elliptical cavities. Examined as special cases were problems for a body with cavities and edge cracks with one or two sides, a body with cavities connected by a narrow slit, and a body with two or three longitudinal-transverse cracks. It is shown that anisotropy of the material has a substantial effect on the SIF and stresses around the cavities.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 61–66, 1988.     

Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

Experimental determination of the concentration of stresses and strains around a circular hole in a glass-reinforced plastic specimen

The results of experimental studies on the concentration of stresses and strains at a circular hole in a glass-reinforced plastic specimen, involving the use of the photoelastic coating method, are given. The effects of the anisotropy of the material, of ratio of the hole diameter to the width of the model, and of the load level on the magnitude of the stress and strain concentration factor are indicated.Translated from Mekhanika Polimerov, No. 1, pp. 159–163, January–February, 1972.     

Stress analysis for a rectangular thick plate of a composite material with a spatially locally curved structure under forced vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially locally curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of the parameters of local curving on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three-dimensional FEM modelling.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 779–790, November–December, 2004.     

Temperature dependence of the strength of a woven composite in a plane state of stress

Conclusions On the basis of an analysis of test results obtained by typical patterns of simple momentary quasistatic loading at various temperatures within the 20–150°C range, we have found a family of strength surfaces for a woven organic plastic material in a plane state of stress in the reinforcement plane. These experimentally found strength surfaces can be approximated by the equation of a second-degree surface. It has been established that the range of safe states of stress in the stress space narrows nonuniformly with rising temperature; namely, this narrowing is accompanied by a shift of the center and a reorientation of the axes of the strength ellipsoid. We have revealed and described the temperature dependence of the components of the strength surface tensors involved in the strength criterion. The data can be used for predicting the strength of a composite material under consideration when the latter is subject to simple quasistatic loading patterns in the three-dimensional (₁₁, ₂₂, ₁₂) stress space in the reinforcement plane within a given test range of temperatures.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 452–457, May–June, 1978.     

Crosslinked polychlorostyrene as an optically sensitive material for photoelastic stress analysis

The photoelastic properties of chlorostyrene-ethylene glycol dimethacrylate copolymers have been investigated. Thanks to the high segmental polarizability anisotropy of chlorostyrene and the possibility of regulating the crosslink density in the crosslinked polymer, these materials possess high optical sensitivity combined with a broad range of moduli of elasticity at the "freezing" temperature.Institute of High-Molecular Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 554–556, May–June, 1969.     

Bäcklund Transformation and Dressing Chains for the Landau–Lifshitz Equation

We use the dressing method for the Landau–Lifshitz equation and the breeding procedure to obtain a modified Landau–Lifshitz equation. We find the Darboux transformation (the dressing) for the integrable Landau–Lifshitz equation of the anisotropic magnet. We find the Bäcklund transformations and dressing chains.     

Compliance tensor for an elastic material reinforced in two directions

The relations for all the independent components of the elastic compliance and stiffness tensors of an elastic material reinforced in two directions are examined on the assumption that it is a continuous, macroscopically homogeneous, anisotropic (orthotropic) medium. The results obtained are used to construct illustrative curves and are compared with certain experimental data.Mekhanika Polimerov, Vol. 2, No. 3, pp. 372–379, 1966     

Use of plastics as model materials in the photoelastic method of stress analysis

The suitability of various plastics for use as model materials in the photoelastic method of stress analysis is briefly reviewed. The photoelastic properties of a series of optically sensitive plastics are examined. It is shown that the wide range of properties possessed by these materials makes them suitable for the photoelastic solution of various problems.Mekhanika Polimerov, Vol. 2, No. 3, pp. 440–445, 1966