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Mechanics of Composite Materials (v.37, #3)

Classical and Nonclassical Dynamic Problems of Sandwich Shells with a Transversely Soft Core by V. N. Paimushin (pp. 175-188).
Based on the hypothesis of similarity of transverse displacements in thin-walled sandwich shells with a transversely soft core under dynamic and static loads, refined geometrically nonlinear dynamic equations of motion are constructed in the case of large variations in the parameters of the stress-strain state (SSS) in the tangential directions. For shells structurally symmetric across the thickness and loaded with initial static loads, linearized dynamic equations are derived, which, upon introducing the synphasic and antiphasic functions of displacements and forces, can be used to describe the synphasic and antiphasic buckling forms in the transverse and tangential directions. For nonshallow cylindrical and shallow spherical shells, the nonclassical problems on all possible vibration forms realized at zero indices of variability of the SSS parameters in the tangential directions are formulated and solved. For shallow shells of symmetric structure, the resolving equations are obtained by introducing, instead of tangential displacements and transverse tangential stresses in the core, the corresponding potential and vortex functions.

Keywords: dynamics; sandwich plates and shells; transversely soft core; vibration forms; cylindrical and spherical shells; external pressure; shear buckling form; reduced equations; nonclassical vibration problems; shear vibration form in the core

Application of the Newton Method for Calculating the Axisymmetric Thermoelastoplastic State of Flexible Laminar Branched Shells Using the Shear Model by A. Z. Galishin; V. A. Merzlyakov; Yu. N. Shevchenko (pp. 189-200).
A method for calculating the thermoelastoplastic geometrically nonlinear state of branched laminar shells is elaborated. The method is based on the shear kinematic model for the whole package of layers and on the theory of simple loading processes. The linearization of geometrically nonlinear equations is realized using the Newton method.

Keywords: laminar shells with a branched meridian; thermoelastoplastic state; geometric nonlinearity; Newton method

Arrest of Opening of Two Circular-Arc Cracks with Coalesced Plastic Zones by R. R. Bhargava; S. Hasan (pp. 201-206).
The closure of plastic zones developed ahead of the tips of two unequal hairline arc cracks in an unbounded elastic-perfectly plastic plate is studied. The cracks lie along the circumference of one and the same circle. The rims of the cracks are opened in mode I type deformation by biaxial tension applied at infinity, and consequently plastic zones develop ahead of the tips of the cracks. The tension is increased to such an extent that the plastic zones of both cracks, lying adjacent to each other, are coalesced. To prevent the cracks from further opening, the rim of the plastic zone is subjected to a uniform, constant compressive yield-point stress. The problem is solved using the complex variable technique and the principle of superimposition of the stress intensity factors. The Dugdale hypothesis is used to determined the length of the plastic zones developed. The behavior of each of the parameters, viz. the length of the plastic zone, the crack length, and the intercrack distance effecting the crack closure, is investigated and reported graphically.

Keywords: infinite plate; cirular-arc crack; plastic zone; crack closure; mathematical modeling

The Effects of Poisson Contraction on Matrix Cracking in Brittle-Matrix Composites by Yih-Cherng Chiang (pp. 207-216).
The effects of Poisson contraction on matrix cracking in unidirectional fiber-reinforced brittle-matrix composites are studied in this paper. The fibers, initially held in the matrix by a compressive pressure due to the thermal expansion mismatch, are subjected to frictional slipping over the matrix as soon as a fiber-bridged crack is formed. The friction between the fibers and the matrix is assumed to follow the Coulomb friction law. A shear-lag model, which includes the Poisson contraction and the friction due to the relative fiber/matrix slipping, is adopted to calculate the stress and strain fields in the fibers and matrix. Using the energy balance approach, a relation for the critical matrix cracking stress for propagating of a semi-infinite fiber-bridged crack is derived. The results obtained show that the Poisson contraction has a strong effect on the predicted matrix cracking stress in brittle-matrix composites, especially in composites with a stiff matrix.

Keywords: brittle-matrix composite; matrix cracking; fiber-bridged crack; Poisson contraction; critical stress

Genetic Algorithms Based on a New System of Integral Equations in Identification of Material Constants for Anisotropic Media by E. Zieniuk; W. Gabrel (pp. 217-222).
A hybrid method for solving inverse boundary problems is presented. The method consists in combining the genetic algorithms with a new system of integral equations. The effectiveness of the general idea of the method and its practical application are tested in the identification of material constants for a two-dimensional anisotropic medium.

Keywords: anisotropic medium; identification problem; genetic algorithm

Analysis of Elastomeric Composites Based on Fiber Systems. 4. 3D Composites by V. M. Akhundov (pp. 223-236).
The elastic properties of 3D elastomeric composite materials under large deformations are considered. The investigation is based on the structural macroscopic theory of stiff and soft composites. The results of micro- and macromechanical analyses of composite materials with compressible and poorly compressible matrices are presented. The character of interaction between the fibers of various reinforcing systems in these matrices is revealed. The deformation characteristics of the composites in tension and shear are presented as functions of their orientation and loading parameters. The evolution of the configuration of a composite material with a compressible matrix during loading is traced.

Keywords: 3D composites; elastomeric composite materials; 3D reinforcement; large deformations; calculation of micro- and macrostresses; matrix-reinforcement interface; compression; tension; shear; stable deformation; deformation curves

Fundamental Solutions of Electroelasticity Equations for a Piezoceramic Layer in R3 by A. Fil'shtinskii (pp. 234-237).
Coupled electroelastic fields in a piezoceramic layer under the action of force and electric sources are determined analytically. The Fourier coefficients of the displacement and electric potential vectors and of the stress tensor are expressed in terms of the Macdonald cylindrical functions in a closed form. The solutions obtained can be used to consider the boundary-value problems of electroelasticity for a piezoceramic layer with tunnel heterogeneities.

Keywords: piezoceramic layer; fundamental solution; mixed boundary conditions; stress tensor

On a Representative Volume in the Micromechanics of Particulate Composites by O. Vinogradov (pp. 245-250).
A rectangle filled with closely packed spheres of random size and properties is considered as a micromechanical model of a two-phase particulate composite. A numerical simulation is used to determine the effective mechanical properties of the assembly and their scatter as a function of the number of spheres. It is shown that, in a system with relatively small number of particles (up to 300), the scatter of Young's modulus decreases with the system size. However, the rate of the scatter decrease becomes smaller with growing size of the system, so that the convergence to zero most likely takes place at infinity.

Keywords: particulate composite; micromechanical model; representative volume; Young's modulus; scatter

Features of the Formation of Composite Materials in Anisotropic Liquid Systems with Elongated Suspended Particles by E. Yu. Taran; Yu. V. Pridatchenko; V. A. Gryaznova (pp. 251-256).
The equations of rotational motion of nondeformable spherical and axisymmetric elongated particles and a rheologic equation for stresses in arbitrary gradient flows of dilute suspensions of such particles in an anisotropic carrying fluid are obtained within the framework of a structural-phenomenological approach. As a rheologic model of the suspension-carrying fluid and a hydrodynamic model of the suspended particles, we use the Ericksen simple anisotropic fluid and a symmetric triaxial dumbbell, respectively. The constitutive equations obtained are used to study the effect of anisotropy of the carrying fluid on the dynamics of suspended particles and on the rheologic properties of suspensions in a simple shear flow. A stationary orientation of the elongated suspended particles under the action of hydrodynamic forces is discovered. The possibility of applying this phenomenon to the formation of composite materials is discussed.

Keywords: dilute suspension; anisotropic carrying fluid; stress; dynamics of suspended particles; simple shear flow

Cellulose-Based Composite Films by J. P. Borges; M. H. Godinho; A. F. Martins; A. C. Trindade; M. N. Belgacem (pp. 257-264).
The mechanical and optical properties of cellulose-based composite films are investigated.It is shown that the use of toluene diisocyanate as a coupling agent and Avicel fibers as reinforcing elements give films with the highest mechanical characteristics. Using differential scanning calorimetry, it is also found that the glass transition temperature T g of all the materials studied is below the room temperature and that the T g increased with cross-linking and introduction of Avicel.

Keywords: composite films; cellulose fibers; structure; glass transition temperature; mechanical properties

Effect of the Rounding Radius of Supports on the Accuracy of Determining the Interlayer Shear Modulus of Reinforced Plastics from Short-Beam Bending Tests by A. O. Shcherbakova; S. B. Sapozhnikov (pp. 265-270).
The accuracy of determining the elastic constants of reinforced plastics is estimated based on bending tests of short beams using the results of a numerical experiment with known elastic constants of the specimen material. Several combination variants for the initial values of the shear modulus and support radius are considered. It is shown that the calculation error of the shear modulus is considerably higher than that of the elastic modulus A decrease in the shear modulus increases the accuracy of its determination. The radius of supports affects this accuracy insignificantly.

Keywords: glass-fiber-reinforced plastics; short beams; elastic modulus; shear modulus; transverse bending; experimental determination; numerical experiment; contact deformations; sliding down from supports

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