A 4D Composite Reinforced along Cube Diagonals with a Small Content of Yarns under Large Shear Deformations

The deformation behavior of a 4D composite reinforced along cube diagonals under large shear deformations is examined. The investigation is based on an applied theory which allows one to perform a macromechanical analysis of composite materials with small volume contents of reinforcing yarns to an accuracy sufficient in practice. Qualitative differences between the properties of such composites under large and small shear deformations are revealed. The evolution of the structural geometry of the deformed composite material is traced.     

Soft elastic shells undergoing large deformations

Soft shells made of elastomers and undergoing large deformations under load are studied. The inverse design problem, non-linear under large deformations, is solved. The results obtained are illustrated on a two-parameter shell of revolution fabricated from a two-constant material. The problems of coupling the biaxial and uniaxial zones of the shell and of designing the composite shell are clarified. Amongst the papers dealing with the theory of soft shells and, generally, under small deformations, /1–7/ merit attention.     

Calculation and Experimental Study of a Two-Way Reinforced Rubber-Cord Composite in Tension

A rubber-cord composite, reinforced in two directions with fibers of polyamide cord, under large tensile deformations is investigated based on calculations of a rubber-cord composite material and on tensile tests of specimens made of the casing of a diagonal truck tire. A method of the experimental tensile testing of rubber-cord composite specimens is described. The calculations are based on the carcass theory of composite materials. The calculated and experimental parameters of the macroscopic strains of the rubber tire cord and of its structure in a deformed configuration are given. The manifestation of edge effects in relation to the reinforcement angle is described.     

Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

The elastic properties of unidirectionally reinforced composite materials under large deformations are studied. The applied model for deformation of materials is based on the structural macroscopic theory of stiff and soft composites, including micro- and macromechanical levels of analysis of composite media. The properties of unidirectional elastomeric composites are studied in tension and shear in the plane of reinforcement. The microscopic fields in the structural components of composites having poorly compressible and compressible matrices are also analyzed. Changes in the parameters of macroscopic deformation of the composites are examined as functions of the loading parameters and initial conditions of the structure. The evolution of the structural changes in deformed composite materials is described.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 29–50, January–February, 1999.     

Numerical modeling of nonlinear deformation and buckling of composite plate-shell structures under pulsed loading

Nonlinear three-dimensional problems of dynamic deformation, buckling, and posteritical behavior of composite shell structures under pulsed loads are analyzed. The structure is assumed to be made of rigidly joined plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Individual structural elements can be made of both composite and conventional isotropic materials. The kinematic model of deformation of the structural elements is based on Timoshenko-type hypotheses. This approach is oriented to the calculation of nonstationary deformation processes in composite structures under small deformations but large displacements and rotation angles, and is implemented in the context of a simplified version of the geometrically nonlinear theory of shells. The physical relations in the composite structural elements are based on the theory of effective moduli for individual layers or for the package as a whole, whereas in the metallic elements this is done in the framework of the theory of plastic flow. The equations of motion of a composite shell structure are derived based on the principle of virtual displacements with some additional conditions allowing for the joint operation of structural elements. To solve the initial boundary-value problem formulated, an efficient numerical method is developed based on the finite-difference discretization of variational equations of motion in space variables and an explicit second-order time-integration scheme. The permissible time-integration step is determined using Neumann's spectral criterion. The above method is especially efficient in calculating thin-walled shells, as well as in the case of local loads acting on the structural element, when the discretization grid has to be condensed in the zones of rapidly changing solutions in space variables. The results of analyzing the nonstationary deformation processes and critical loads are presented for composite and isotropic cylindrical shells reinforced with a set of discrete ribs in the case of pulsed axial compression and external pressure.Scientific Research Institute of Mechanics, Lobachevskii Nizhegorodsk State University, N. Novgorod, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 757–776, November–December, 1999.     

Large deformations of bodies of revolution made of elastic homogeneous and fiber-reinforced materials 1. Torsion of toroidal bodies

Equations of a mathematical model for bodies of revolution made of elastic homogeneous and fiber-reinforced materials and subjected to large deformations are presented. The volume content of reinforcing fibers is assumed low, and their interaction through the matrix is neglected. The axial lines of the fibers can lie both on surfaces of revolution whose symmetry axes coincide with the axis of the body of revolution and along trajectories directed outside the surfaces. The equations are obtained for the macroscopically axisymmetric problem statement where the parameters of macroscopic deformation of the body vary in its meridional planes, but are constant in the circumferential directions orthogonal to them. The equations also describe the torsion of bodies of revolution and their deformation behavior under the action of inertia forces in rotation around the symmetry axis. The results of a numerical investigation into the large deformations of toroidal bodies made of elastic homogeneous and unidirectionally reinforced materials under torsion caused by a relative rotation of their butt-end sections around the symmetry axis are presented.     

Contact formulation of non-linear problems in the mechanics of shells with their end sections connected by a plane curvilinear rod

Starting from the consistent version of the geometrically non-linear equations of the theory of elasticity for small deformations and arbitrary displacements, a Timoshenko-type model that takes account of shear and compression deformations and also an extended variational Lagrange principle, an improved geometrically non-linear theory of static deformation is constructed for reinforced thin-walled structures with shell elements, the end sections of which are connected by a rod. It is based on the introduction into the treatment of contact forces and torques as unknowns on the lines joining the shells to the rods and it enables all classical and non-classical forms of loss of stability in structures of the class considered to be investigated. An analytical solution of the problem of the stability of a rectangular plate, that is under compression in one direction, supported by a hinge along two opposite edges and joined by a hinge with an elastic rod on one of the other two edges, is found using a simplified version of the linearized equations.     

Analysis of Elastomeric Composites Based on Fiber Systems. 4. 3D Composites

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.     

Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures

This paper deals with free vibration analysis of functionally graded composite shell structures reinforced by carbon nanotubes. Uniform and three distributions of carbon nanotubes which are graded in the thickness direction of the structure are considered. The effective material properties are determined via a micro-mechanical model using some efficiency parameters. The equations of motion are developed based on a discrete double directors shell finite element formulation which introduces the transverse shear deformations via a higher-order distribution of the displacement field. Comparison studies are carried out for various functionally graded composite shell structures reinforced by carbon nanotubes in order to highlight the applicability and the efficiency of the proposed model in the prediction of the vibrational behavior of such shell structures.     

On the simulation of textile reinforced composites and structures

This paper presents experimental and numerical methods to perform simulations of the mechanical behavior of textile reinforced composites and structures. The first aspect considered refers to the meso-to-macro transition in the framework of the finite element (FE) method. Regarding an effective modelling strategy the Binary Model is used to represent the discretized complex architecture of the composite. To simulate the local response and to compute the macroscopic stress and stiffness undergoing small strain a user routine is developed. The results are transfered to the macroscopic model during the solution process. The second aspect concerns the configuration of the fiber orientation and textile shear deformation in complex structural components. To take these deformations which affect the macroscopic material properties into account they are regarded in a macroscopic FE model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On certain surfaces of revolution of the second degree

An improvement in the generation of some second-order surfaces of rotation and their construction is presented. In this case, a cube is rotated about one its diagonals to obtain a hyperboloid of one sheet with two duplicate cones on each side.     

Thermoelastoplastic deformation of complexly reinforced shells

The problem on the elastoplastic deformation of reinforced shells of variable thickness under thermal and force loadings is formulated. A qualitative analysis of the problem is carried out and its linearization is indicated. Calculations of isotropic and metal composite cylindrical shells have shown that the load-carrying capacity of shell structures under elastoplastic deformations is several times (sometimes by an order of magnitude) higher than under purely elastic ones; the heating of shells with certain patterns of reinforcement sharply reduces their resistance to elastic deformations, but only slightly affects their resistance to elastoplastic ones; not always does the reinforcement in the directions of principal stresses and strains provide the greatest load-carrying capacity of a shell; there are reinforcement schemes that ensure practically the same resistance of shells at different types of their fastening. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 707–728, November–December, 2006.     

Elastic Wave Propagation in Soft Microstructured Composites Undergoing Finite Deformations

We consider the propagation of elastic waves in soft composite materials undergoing large deformations. The analysis is performed in terms of small amplitude motions superimposed on a deformed state. By consideration of 2D periodic laminates and 3D fiber composites, we find that an applied deformation influences the elastic waves through the change in the microstructure, and through the change in the local material properties. These effects can be significantly amplified by the deformation induced elastic instability phenomenon leading to microstructure transformations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deformation of composites with arbitrarily oriented orthotropic fibers under matrix microdamages

In the present work, a model of nonlinear deformation of stochastic composites under microdamaging is developed for the case of a composite with orthotropic inclusions, when microdefects are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by triaxial arbitrarily oriented ellipsoidal inclusions with orthotropic symmetry of the elastic properties. It is assumed that the process of loading leads to accumulation of damage in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic modules in the case of orthotropic components are taken as basic relations. The fracture criterion is specified as the limiting value of the intensity of average shear stresses acting in the intact part of the material. On the basis of the analytic and numerical approach, we propose an algorithm for the determination of nonlinear deformation properties of the investigated material. The nonlinearity of composite deformations is caused by the finiteness of deformations. By using the numerical solution, the nonlinear stress–strain diagrams are predicted and discussed for an orthotropic composite material for various cases of orientation of inclusions in the matrix.     

Analysis of elastomeric composites based on fiber-reinforced systems. 1. Development of design methods for composite materials

A method for calculating the elastic properties of fiber-reinforced composites is discussed. The method is based on the structural macroscopic theory for reinforced media [1, 2], which can be used for analysis of stiff and soft composites. As a measure of the elastic properties of composites, the parameters of macroscopic deformations of the base system of Cartesian coordinates are used, with the axes oriented in a certain direction relative to the general reinforcement and loading field. The corresponding macrostresses in the loaded composites are found by a solution of the microboundary problem for a composite macroelement with sides parallel to reinforcement planes of the system. The microboundary-value problem is multiply connected and is formulated based on the information about the homogeneous field of macroscopic displacements specified by the parameters of macroscopic deformation. The problem is solved using the local system of coordinates whose axes are directed along some of the reinforcement trajectories.State Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 733–745, November–December, 1998.     

Calculation of deformations in nanocomposites using the block multipole method with the analytical-numerical account of the scale effects

Local scale effects for linear continuous media are investigated as applied to the composites reinforced by nanoparticles. A mathematical model of the interphase layer is proposed that describes the specific nature of deformations in the neighborhood of the interface between different phases in an inhomogeneous material. The characteristic length of the interphase layer is determined formally in terms of the parameters of the mathematical model. The local stress state in the neighborhood of the phase boundaries in the interphase layer is examined. This stress can cause a significant change of the integral macromechanical characteristics of the material as a whole if the interphase boundaries are long. Such a situation is observed in composite materials reinforced by microparticles and nanoparticles even when the volume concentration of the inclusions is small. A numerical simulation of the stress state is performed on the basis of the block analytical-numerical multipole method with regard for the local effects related to the special nature of the deformation of the interphase layer in the vicinity of the interface.     

Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite

In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates.     

Deformations of pressure vessel domes in asymmetric winding

The deformation of pressure vessel domes in asymmetric winding with the use of two families of yarns is accompanied by shear deformations and torsion. For the case of large deformations, a system of equations for describing the stress-strain state of an asymmetrically reinforced netlike shell of revolution loaded with an internal pressure is obtained. It is shown that the shear deformations depend on the deformations of both the yarn families and the deformations of meridians and parallels of the shell. As an example, the dome of a pressure vessel in a deformed state is calculated for an initial equilibrium shape determined on the assumption that the yarns are inextensible. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 425–432, July–August, 2006.     

Applied model of a round cylinder reinforced with systems of yarns at large tensile,inflation, and torsional deformations

Equations for a round cylinder weakly reinforced with systems of yarns and subjected to large tensile, inflation, and torsional deformations are presented. Since the degree of filling is small, the model of uniaxial stress state is assumed. The fibers are aligned with spirals on cylindrical surfaces and with radii in the transverse and meridional sections of the cylinder. The equations are obtained in the macroscopically unidimensional statement for the case of cylindrically symmetric strains. Numerical results are given for twisted hollow rubber cylinders reinforced with polymer yarns in the axial and radial directions. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 237–256, March–April, 2007.     

Polymer morphology and strength characteristics in the presence of large and small deformations

An investigation of the strength characteristics of polychloroprene under the action of a chemically active agent and of polypropylene under the action of a physically active agent, as well as of polychloroprene and polyurethane in both the brittle and highly elastic states in the absence of an aggressivemedium showed that the strength properties of polymers in the small-deformation region are a function of the degree of crystallinity or spherolite size and do not depend on these parameters in the high-deformation region. The influence of the degree of crystallinity on strength characteristics at small deformations and the absence of this effect at large deformations were also demonstrated with pressed specimens having the granular structure typical of real rubbers.Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov No. 2, pp. 222–225, March–April, 1972.