Generalized self-consistent method: Modeling and computation of effective elastic properties of composites with composite or hollow inclusions

A new approach to the generalized self-consistent method [1,2] has been developed for problems of the statistical mechanics of composites with composite or hollow inclusions. The approach can reduce the problem of predicting the effective elastic properties of composites to a simpler averaged problem of a single, composite, or hollow inclusion with inhomogeneous elastic surrounding in a homogeneous effective elastic medium. The problem of predicting the effective elastic properties of composites with unidirectional hollow fibers or hollow spherical inclusions are studied by using the new approach.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 173–183, March–April, 1998.     

Contribution to the theory of the elastic properties of amorphous-crystalline polymers

The elastic constants of an amorphous-crystalline polymer are calculated from the known values of the elastic constants of its amorphous and crystalline components.Moscow Lenin Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 213–218, March–April, 1969.     

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.     

Analogues of the Kolosov–Muskhelishvili General Representation Formulas and Cauchy–Riemann Conditions in the Theory of Elastic Mixtures

Analogues of the well-known Kolosov–Muskhelishvili formulas of general representations are obtained for nonhomogeneous equations of statics in the case of the theory of elastic mixtures. It is shown that in this theory the displacement and stress vector components, as well as the stress tensor components, are represented through four arbitrary analytic functions.The usual Cauchy–Riemann conditions are generalized for homogeneous equations of statics in the theory of elastic mixtures.     

Torsional stability of a glass-reinforced plastic cylindrical shell with an elastic core

The problem of the stability of a glass-reinforced plastic cylindrical shell with an elastic core subjected to twisting moments applied to the edges of the shell is considered. As in various other studies [4–6], the glass-reinforced plastic is treated as an elastically orthotropic material. The core is treated as an isotropic elastic cylinder, whose outer surface is bonded to the shell. Expressions for the critical stresses are obtained for an infinitely long shell and a shell of finite length.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1082–1086, November–December, 1970.     

Structural approach to calculation of the effect of moisture on elastic characteristics of organoplastics

Data have been obtained for the structural calculation of the effect of moisture on the elastic characteristics of organoplastics from the properties of components. The distribution of moisture between the fiber and matrix — the components of a unidirectional composite — is considered. The elastic properties of the fiber are determined by an inverse calculation using the experimental dependences of the composite and matrix on moisture. The moisture effect on the properties of the materials is taken into account with influence functions, which differ by more than 25% for various characteristics. The results can be used for calculating the elastic properties of composites with various reinforcement schemes and at the nonequilibrium distribution of the moisture concentration in an actual environment.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 525–530, July–August, 1998.     

Electromechanical strain gage for measuring the deformations of structural plastics

By equipping a multiple-use strain gage based on a metal elastic element, whose natural mechanical stiffness is unacceptably high, with a spring-loaded mechanism forming part of the strain gage itself it is possible to compensate the force developed by the elastic element in the process of deformation.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No.5, pp. 951–953, September–October, 1969.     

Deformation and sliding friction of polyurethane in the presence of a lubricant

The relation between coefficient of friction and elastic and high-elastic strains is investigated with reference to polyurethane subjected to friction in various liquid media. It is shown that a definite relationship between these parameters does exist. The effect of various liquids on the elastic and high-elastic deformation of polyurethane is studied.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, Vol. 5, No. 2. pp. 357–359, March–April, 1969.     

Elastic characteristics of ferrocement reinforced by hexagonal grids

The methods of the structural mechanics of composite materials are used to develop a method for predicting the elastic modulus and shear modulus of ferrocement reinforced with hexagonal woven and stamped grids. The method takes into account the elastic properties of the components and the geometry of the reinforcement.Riga Technical University, LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 182–186, March–April, 1997.     

Numerical model of one possibility of determining the tensor of elastic constants of an anisotropic body

An algorithm for a digital computer is presented which permits calculating the tensor of the elastic constants of a material with any given symmetry on the basis of experimentally measured Young moduli and Poisson ratios for several specimens oriented in unequivalent crystallographic directions. The results of determining the components of the tensor of elastic constants by means of it for a modification of orthotropic reinforced plastic are also given.Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 436–442, May–June, 1973.     

Elastic characteristics of a cement-based composite reinforced with steel grid ribbons

A method is proposed for the estimation of elastic characteristics of a cement mortar orthogonally reinforced with punched steel grid ribbons. The method proposed takes into account the geometry of grids, the distance between ribbons, and the elastic properties of cement mortar and steel.Riga Technical University, Riga, LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 173–180, March–April, 1999.     

Instability at the interface of bodies subjected to high-elastic deformations

The problem of instability at the interface of two elastic half-planes in compression is investigated within the framework of the plane problem of the stability of deformation of compressible and incompressible elastic bodies at finite subcritical strains [1, 2]. The results are obtained for the plane deformation of bodies with an arbitrary form of the elastic potential. Numerical examples are presented for high-elastic bodies with potentials of the Mooney and Treloar types.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 999–1002, November–December, 1971.     

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].Perm State Technical University, Perm, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 785–796, November–December, 1999.     

Creep of orthogonally reinforced spherofibrous composites

Models of composites with three-dimensional structure, a proposed problem solving method, and Rabotnov's creep operators were used assuming purely elastic deformation of the composite along the orientation of the fibers to determine the viscoelastic properties of composites on inclined surfaces in a three-dimensional stressed state. The formulas used in viscoelasticity theory in the elastic region of component deformation lead to results in satisfactory accord with the reported experimental elastic properties of composites with three-dimensional structure.A. A. Blagonravov Mechanical Engineering Institute, Russian Academy of Sciences, Moscow. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 780–786, November–December, 1996.     

Deformation of elastic polyurethanes with a bimodal cellular structure

This article examines the cellular structure and mechanical properties of elastic foamed polyurethanes with a bimodal cellular structure (BFPUs). It is shown that the sizes of the oval cells (3–12 mm) in the elastic foamed polyurethenes that are studied are a tenth of an order greater than the sizes of the polyhedral cells (0.1–0.6 mm). Conversely, for rigid foamed polyurethanes, the polyhedral cells are more than a tenth of an order larger than the oval cells (microcells). The equations of the compression curve of BFFUs are found, and it is established that the deformation of BFPUs is determined by the deformation function of the cellular structure and the viscoelastic properties of the polymer matrix. The deformation functions of the cellular structure and the relaxation properties of BFPUs are determined. It is shown that choosing BFPUs with a cellular structure improves the comfort properties of the foamed material: the softness coefficient increased by 8–19% in the investigated case, while the support coefficient increased by 15–35%.Paper presented at the IX International Conference on the Mechanics of Composite Materials (Riga, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 330–339, May–June, 1996.     

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.     

Modeling the creep stability of plastic shells

The problem of modeling the creep stability of shells is investigated on the basis of the strain compatibility, equilibrium and physical equations, and the boundary conditions. The mechanical similarity of physically nonlinear elastic and elasto-hereditary materials is examined in detail. The concept of an elastic potential and Volterra-type integral relations with increasing multiplicity are employed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1059–1063, November–December, 1969.     

Variation of the instantaneous modulus of elasticity of certain types of plastics under long-time static loads

The variation of the elastic characteristics of polymeric materials tested to destruction under long-time static loads has been investigated. Experiments on polymethyl methacrylate, KAST-V glass laminate, and Soviet and Finnish polyester glass-reinforced plastics under constant and intermittent (with "recovery") static tensile loads have shown that their elastic characteristics vary with the loading regime, the type of material, and the stress level. In a number of cases the value of the modulus of elasticity falls by 25–35%. This is attributed to the reduction of the effective cross section of the specimen as a result of damage accumulation.All-Union Correspondence Structural Engineering Institute, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 430–435, May–June, 1971.     

Elastic displacements of a cement-based composite beam reinforced with punched steel grids

Using Mohr's method, a procedure is proposed for calculating the elastic displacements of a cement-based composite beam reinforced with punched steel grid ribbons. The approach proposed takes into account a possible asymmetry of the structure, the geometry of grids, and the elastic properties of cement mortar and steel.Riga Technical University, Riga, LV-1047, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 181–186, March–April, 1999.     

Dynamic stability of axisymmetrically heated glass-reinforced plastic cylindrical shells bonded to elastic cylinders

The dynamic stability of glass-reinforced plastic shells subjected to the action of a longitudinal pulsating force and an external, uniformly distributed load is examined. The shells are orthotropic, and their elastic properties are temperature-dependent and vary over the thickness of the wall. It is assumed that the elastic cylinder forms a Winkler foundation. Three boundary conditions are investigated.Moscow Institute of Chemical-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 331–337, March–April, 1972.