Theory of spherofibrous composites. 2. Fundamental equations

Fundamental equations of the theory of spatially reinforced media with a matrix reinforced by spherical particles are proposed on the basis of a linearly reinforced layer and tl.e hypothesis of a longitudinal state. For an arbitrary orientation of the fibers, the generalized elasticity equation for composites was found to contain 21 elastic constants and approximate formulas were derived for their determination.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga. Latvia (October, 1995).Communication 1. see preceding article.A. A. Blagonravov Institute of Mechanical Engineering. Russian Academy of Sciences, Moscow. Russian. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 306–316, May–June, 1996.     

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.     

Shear of orthogonally reinforced spherofibrous composites

The problem of determining the shear characteristics and interphase stress concentration of fibrous composites with spherical inclusions is examined on the basis of a three-phase model. Stress fields caused by diffusion interaction of phases are neglected. The elastic moduli of the composite are investigated and compared with those obtained from a two-phase model. The general formula for determination of the shear modulus of triorthogonally reinforced compsites is derived using previously investigated relationships for averaged stress fields. The matrix of these compsites contained spherical cavities. The dependence of integral characteristics of three-phase composites on their bulk phase concentration was investigated. The stresses between phases were studied as a function of composite structure.A. A. Blagonravov Machine-Science Institute, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, 104–111, January–February, 1997.     

Deformative characteristics of plastics reinforced with high-modulus anisotropic fibers

The independent elastic constants of plastics unidirectionally reinforced with transversely isotropic fibers have been determined. It has been assumed that the distribution of reinforcement in a transverse section of the plastic is regularly rectangular or hexagonal. To determine the transverse elastic modulus and the shear modulus in the plane of reinforcement, a constancy-of-plane-sections hypothesis was used. Values of deformative characteristics determined by the assumed calculational dependences have been compared with the experimental ones for plastics reinforced with graphite fibers.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 631–639, July–August, 1972.     

Elastic constants for a material reinforced in two directions in the planar case

A simplified model is proposed for an elastic material (glass laminate) reinforced in two perpendicular directions. On the basis of an analysis of the cooperation of the reinforcement and the binder in the assumed model, approximate formulas are obtained for the reduced elastic constants of the reinforced material treated as an anisotropic and macroscopically homogeneous body. A slightly different approach to the solution of a similar problem is described in [2, 4]. The formulas obtained are in agreement with the experimental data and the recommendations of other authors.Mekhanika Polimerov, Vol. 3, No. 2, pp. 266–272, 1967     

Elastic constants of glass-reinforced plastics with anisotropic structure

The macroscopic elastic constants of plastics reinforced in one direction are calculated by solving the statistical boundary value problem of the theory of elasticity. The results obtained and the method proposed in [15] are used to compute the macromoduli of GRP with an anisotropic layered structure created by an orthogonal arrangement of unidirectional tapes and to compute the moduli of elasticity of a unidirectional layered material with random deviations of the layers from the direction of preferred orientation.V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR, Sverdlovsk Branch. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 631–637, July–August, 1968.     

Composites reinforced with a system of three straight mutually orthogonal fibers

The effectiveness of reinforcement in direction 3 has been estimated by investigating the mechanical characteristics of two types of three-dimensionally reinforced materials differing with respect to the arrangement of the reinforcement and the fiber content in each direction. The superior transverse stiffness, shear strength, and transverse tensile strength of three-dimensionally reinforced composites based on a system of three mutually orthogonal fibers, as compared with laminated materials, is demonstrated. The theoretical values of the elastic constants, calculated from the relations of [5], are compared with the experimental data.For communication 1 see [5].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1011–1018, November–December, 1973.     

Effect of curvature of the fibers on the elastic properties of unidirectionally reinforced plastics

An approximate method is proposed for determining the reduced elastic constants of reinforced plastics (glass-reinforced plastics) with allowance for the curvature of the reinforcing fibers. All the conclusions relate to plane stress. The results of model tests are presented as confirmation of the theoretical conclusions.Mekhanika Polimerov, Vol. 3, No. 5, pp. 858–863, 1967     

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.     

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.     

Theory of spherofibrous composites. 1. Input relationships: Hypotheses and models

A theory is proposed for fibrous composites with a matrix reinforced with spherical hollow and solid inclusions based on an internal stress field and structural models. The problem solutions are obtained for the fiber-averaged matrix level. The matrix properties are determined assuming a regular distribution of the matrix inclusions. The problem of accounting for the scatter of inclusion properties on the effective composite parameters is examined.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, Latvia (October, 1995).A. A. Blagonravov Mechanical Engineering Institute. Russian Academy of Sciences. Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 291–305. May–June, 1996.     

Electro- and magnetostatics of reinforced polymers

On the basis of previously proposed models of reinforced media with regular structure, a method is developed for determining the electromagnetic fieldand dielectric and magnetic constants of reinforced polymers treated as ideal dielectrics. The solution obtained describes the static electromagnetic field and is suitable for investigating the propagation in reinforced media of electromagnetic waves whose length exceeds the distance between adjacent fibers. The dependence of the macroscopic constants on the orientation and volume content of the reinforcement is investigated.Institute of Mechanics, AS UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1130–1133, November–December, 1968.     

Korn’s Inequalities for Junctions of Elastic Bodies with Thin Plates

We prove the anisotropic Korn inequalities for an elastic junction of a massive body with thin plates clamped along parts of the lateral surfaces. The distribution of the weight factors in the norms under consideration depends essentially on the disposition of the plates, the way they are clamped to the body, and their relative rigidity (as compared with the body).Original Russian Text Copyright © 2005 Nazarov S. A.The author was supported by the Russian Foundation for Basic Research (Grant 03-01-00835).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 876–889, July–August, 2005.     

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.     

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.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.     

Elastic constants of randomly reinforced plastics

A previously developed [4] general method of solving the nonlinear (in the statistical sense) boundary value problem of the theory of elasticity is used to determine the macroscopic moduli of elasticity of randomly reinforced plastics whose structure is simulated by a two-phase microinhomogeneous medium. The macroscopic modulus is represented in the form of a series composed of the sum of the mean value of the modulus and a sequence of corrections that take into account the central moments of the distribution of elastic constants. The limits of convergence of this series are established. The values of the macroscopic moduli for a glass-reinforced plastic obtained by calculation are compared with the experimental data.Mekhanika Polimerov, Vol. 3, No. 2, pp. 259–265, 1967     

A method of estimating the bending strength of reinforced plastics

Various methods of determining the bending strength of reinforced plastics are considered. The reasons for the unreliability of existing standard procedures are analyzed. A new method based on the theory of flexible elastic parts is proposed. The experimental data show that this method gives more reliable results.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Fiberglass, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 355–358, March–April, 1971.     

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.     

Identification of the mechanical characteristics of composite materials from experimental data of shells of revolution

A method is developed for determining the mechanical characteristics of the layer of a shell of revolution made by winding along the geodesic lines. The functions describing the nonlinear elastic behavior of the material are found by analyzing the data obtained from experiments. The equations for unknown parameters and conditions of their solvability in a particular case are obtained.Kazan State Architecture and Civil Engineering Academy, Tatarstan, Russian. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 771–776, November–December, 1998.