Stability of laminar shells having a viscoelastic binder

Conclusions 1. In loading with a force whose value lies between the long-term and instantaneous critical values, a loss of shell stability by rupture takes place at a certain time after loading. This time is naturally taken as the critical one.2. Numerical estimates show that the level of the initial irregularities has a very great effect on the magnitude of the critical time. Therefore, in a theoretical estimate of the critical time it is necessary to take account of them as accurately as possible.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 277–282, March–April, 1978.     

Stability and bound-exceeding elastic and viscoelastic response of composite materials having a negative-stiffness phase

We show that a composite material with one phase having negative bulk and Young's moduli (and therefore being unstable by itself) can be stable overall under dead traction boundary conditions if the encapsulating phase is sufficiently stiff. We also show experimental evidence that appropriate tuning of the negative-stiffness phase can lead to bound-exceeding elastic and viscoelastic overall material response. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polarization tensors and effective properties of anisotropic composite materials

In this paper, we present a systematic scheme for derivations of asymptotic expansions including higher-order terms, with estimates, of the effective electrical conductivity of periodic dilute composites in terms of the volume fraction occupied by the inclusions. The conductivities of the inclusion and the matrix may be anisotropic. Our derivations are based on layer potential techniques, and valid for high contrast mixtures and inclusions with Lipschitz boundaries. The asymptotic expansion is given in terms of the polarization tensor and the volume fraction of the inclusions. Important properties, such as symmetry and positivity, of the anisotropic polarization tensors are derived.     

Numerical identification of properties of particle-reinforced composite materials

The paper deals with numerical identification of the average elastic properties of particle-reinforced composite materials. The finite element method for the determination of deformation energy of the characteristic volume element was used. In earlier analytical investigations, an approximation function of the averaged elastic properties of the composite was derived. An identification procedure allows the estimation of the unknown approximation parameters from numerical experiments. The obtained functions describe precisely the numerical data for any relationships between constituents of the material.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Computer Analysis of Structures, Riga Technical University, Riga PDP-1658, Latvia. Institute of Materials Science, Department of Materials Science, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 383–390, May–June, 1998.     

On the three-dimensional stability loss problems of elements of structures of viscoelastic composite materials

Up to now, numerous problems of the stability loss for elements of structures made from composite materials have been investigated in the framework of the three-dimensional linearized theory of stability (TDLTS). It follows from the analysis of these investigations that the TDLTS was mainly applied to the design of elements of structures made from time-independent materials. For the solution of these problems for viscoelastic materials in the framework of the TDLTS, the dynamic investigation method and the critical deformation method are recommended in many references. However, it is known that a very reliable and frequently used approach for viscoelastic materials is the approach based on the study of the growth of insignificant initial imperfections in elements of structures with time. Taking into account the above-mentioned, an approach based on the growth of the initial imperfection for the investigation of the stability loss problems of elements of structures made from viscoelastic composite materials in the framework of TDLTS is proposed in the present paper. The composite material is modeled as an anisotropic, viscoelastic solid with averaged mechanical properties and all investigations are made on the strip simply supported at the ends.Yildiz Technical University, Dept. Math. Eng., 80750, Besiktas-Yildiz, Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 761–770, November–December, 1998.     

Asymptotic evaluation of effective complex moduli of fibre‐reinforced viscoelastic composite materials

We propose an asymptotic approach for the evaluation of effective complex moduli of viscoelastic fibre‐reinforced composite materials. Our method is based on the homogenization technique. We start with a non‐trivial expansion of the input plane‐strain boundary value problem by ratios of visco‐elastic constants. This allows to simplify the governing equations to forms analogous to the complex transport problem. Then we apply the asymptotic homogenization method, coming from the original problem on multi‐connected domain to the cell problem, defined on a unit cell of the periodic structure. For the analytical solution of the cell problem we apply the boundary perturbation technique, the asymptotic expansion by a distance between two neighbouring fibres and the method of two‐point Padé approximants. As results we derive uniform analytical representations for effective complex moduli, valid for all values of the components volume fractions and properties.     

Dynamic properties of wing panels made of composite materials

The dynamic characteristics of an elastic wing panel made of composite material are investigated in relation to the transient processes in a gas flow. The problem is solved using the geometrically nonlinear equations of shallow orthotropic shells and the numerical methods of linearized nonsteady aerodynamics. The displacements are determined by a finite-difference method and the aerodynamic load intensity by means of a model of a thin lifting surface. The numerical results are presented in the form of graphs reflecting the laws of deformation of the middle surface of the panel and pressure distribution and their development with time. Curves characterizing the motion of individual points in relation to the parameters reflecting the anisotropic properties of the panel are also constructed.Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 662–669, July–August, 1974.     

Natural vibrations of composite viscoelastic cylinders

Free damping spatial and axisymmetrical vibrations of short cylinders consisting of elastic and viscoelastic layers are considered. A numerical study is made of the dependence of natural frequencies and damping coefficients on the ratio of geometric cylinders.Translated from Dinamicheskie Sistemy, No. 5, pp. 55–58, 1986.     

Near-surface failure of layered viscoelastic materials

Within the framework of a piecewise homogeneous body model, with the use of exact equations of the geometrically nonlinear theory of viscoelastic bodies, the distribution of near-surface self-balanced normal stresses in a body consisting of a viscoelastic half-plane, an elastic locally curved bond layer, and a viscoelastic covering layer is investigated. A method for solving the problem considered by employing the Laplace and Fourier transformations is developed. Numerical results for the self-balanced normal stresses caused by a local curving (imperfection) of an elastic bond layer upon tension and compression of the body mentioned along the free face plane are presented and analyzed. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operators. A macroscopic failure criterion is proposed, and the validity of this criterion is examined.     

Damping properties of soft viscoelastic materials for certain combinations of a planar stress distribution

The results of experimental studies of the energy scattering by soft, viscoelastic materials with certain combinations of a planar stress distribution, established by the superposition of a cyclic shear on tension-compression, are given. Special graphs were used for evaluating the damping properties of the materials, i.e., lines of equal damping, which enabled the equivalent uniaxial stress to be found for each combination of planar stress distribution, which produced the same specific scattering of energy. It is shown that the use of the superposition principle for calculating the mechanical losses in a planar stress distribution from experimental data obtained in uniaxial cyclic loading leads to large errors.Volgogradskii Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 999–1005, November–December, 1972.