Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

The problem of interaction of a plane time-harmonic SH-wave with an elastic fiber of quasi-square or quasi-triangular cross section, when an interface crack is present between an infinite elastic matrix and the fiber, is considered. The modified null-field method taking into account the asymptotic behavior of the solution at crack tips is exploited for obtaining numerical results. The effects of fiber shape, fiber/matrix material combination, debonding (crack size), and direction of wave incidence on the scattering amplitude in the far zone are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 245–254, March–April, 2008.     

Method for studying fracture of bodies with a cylindrical cavity and a coaxial cylindrical crack of finite length under axial compression

The fracture of elastic materials with a cylindrical cavity and a coaxial cylindrical crack near the surface during uniform compression of the medium along its axis is studied using a nonclassical criterion approach associated with a mechanism for local loss of stability near the defect. A solution technique is proposed which makes it possible to reduce the three-dimensional axially symmetric linearized problem to a system of linear homogeneous equations to be solved numerically. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 76–83, 1999.     

On the influence of the distance between edges of cracks on brittle fracture

We study the influence of the shape of a hole (cavity or crack) in an elastic plane on brittle fracture. We use a modified method of solving macrocrack problems. The results obtained are generalizations of known problems. One figure. Two tables. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 26–30, 1991.     

Fracture of a piezoelectric fiber/elastic matrix composite

A piezoelectric fiber/elastic matrix system subjected to axially symmetric mechanical and electric loads is considered. The fiber contains a penny-shaped crack located at its center perpendicularly to the fiber. By using the Fourier and Hankel transforms, the problem is reduced to the solution of an integral equation. Numerical solutions for the crack tip fields are obtained for various crack sizes and different fiber volume fractions. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 301–318, May–June, 2006.     

Stability of the wave equations on a tree with local Kelvin–Voigt damping

In this paper we study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at the vertices of the tree, exponential/polynomial stability are proved. Our results generalize the case of single elastic string with local Kelvin–Voigt damping in Liu and Rao (Z. Angew Math Phys 56:630–644, 2005), Liu and Liu (Z. Angew Math Phys 53:265–280, 2002).     

The stressed state of a transversally isotropic body with inner elliptic crack. A linearly varying pressure on the surface of the crack

An exact solution to the problem of the distribution of stresses in a transversally isotropic elastic body with inner elliptic crack is given. An assumption that the linearly varying pressure acts on the surface of the crack is made. The intensity coefficients of stresses at the vertex of the crack are found. Bibliography: 5 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 79, 1995, pp. 117–124. Original     

Local near-surface buckling of a system consisting of an elastic (viscoelastic) substrate,a viscoelastic (elastic) bond layer,and an elastic (viscoelastic) covering layer

Within the framework of a piecewise homogenous body model and with the use of a three-dimensional linearized theory of stability (TLTS), the local near-surface buckling of a material system consisting of a viscoelastic (elastic) half-plane, an elastic (viscoelastic) bond layer, and a viscoelastic (elastic) covering layer is investigated. A plane-strain state is considered, and it is assumed that the near-surface buckling instability is caused by the evolution of a local initial curving (imperfection) of the elastic layer with time or with an external compressive force at fixed instants of time. The equations of TLTS are obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary-form perturbation technique. A method for solving the problems considered by employing the Laplace and Fourier transformations is developed. It is supposed that the aforementioned elastic layer has an insignificant initial local imperfection, and the stability is lost if this imperfection starts to grow infinitely. Numerical results on the critical compressive force and the critical time are presented. The influence of rheological parameters of the viscoelastic materials on the critical time is investigated. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operator. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 771–788, November–December, 2007.     

Wedging of an elastic wedge by a rigid plate under conditions of contact with detaching

We consider a problem of wedging of an elastic wedge by a rigid plate along an edge crack that is located on the axis of symmetry of the wedge and reaches its vertex. The detachment of the crack faces from the surfaces of the plate is taken into account. Using the Wiener–Hopf method, we obtain an analytic solution of the problem. The size of the detachment zone, the stress intensity factor, the distribution of stresses on the line of continuation of the crack and in the contact domain, and circular displacements of the crack faces are determined.     

Modeling the scattering processes on a crack in an elastic plate with the help of a zero-range potential

The problem of flexural wave scattering on a finite crack in elastic plate is considered. The zero-range potential is suggested as a model of a short crack. Bibliography: 2 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 11–16, 1990. Translated by I. V. Andronov.     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

Investigation of the prefracture zone at the tip of a mode I crack reaching a nonsmooth interface of an elastic media

We perform calculation of the initial prefracture zone at the tip of a mode I crack that reaches a nonsmooth interface of two dissimilar elastic media at its corner point by the Wiener–Hopf method. The zone is modeled by a line of normal displacement fracture on a crack continuation. Expressions for the length of the prefracture zone and the potential energy accumulated in it are obtained. Their numerical values are compared with the corresponding values for the prefracture zone in a bonding material on the interface of the media, on the basis of which we draw a conclusion on the possible direction of development of the zone.     

Steady-state vibrations of a thin two-layer plate with delamination

We consider the problem of harmonic vibrations of a thin two-layer plate with horizontal crack. The problem is solved with the help of the null-field approach. The influence of the shape of the crack contour on the amplitude-frequency characteristics of plate vibrations is investigated. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 83–89, April–June, 1998.     

Stability for the Timoshenko Beam System with Local Kelvin-Voigt Damping

In this paper, we consider a vibrating beam with one segment made of viscoelastic material of a Kelvin-Voigt （shorted as K-V） type and other parts made of elastic material by means of the Timoshenko model. We have deduced mathematical equations modelling its vibration and studied the stability of the semigroup associated with the equation system. We obtain the exponential stability under certain hypotheses of the smoothness and structural condition of the coefficients of the system, and obtain the strong asymptotic stability under weaker hypotheses of the coefficients.     

A biodegradable polymer nanocomposite: Mechanical and barrier properties

The preparation of an environmentally friendly nanocomposite based on plasticized potato starch and unmodified montmorillonite clay is described. Data on the influence of montmorillonite concentration on the mechanical properties of the materials obtained are reported. The effective elastic constants of the nanocomposites are calculated. The calculation results are compared with experimental data. The influence of montmorillonite content on the moisture permeability is also investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 61–76, January–February, 2008.     

Dynamics of a bridged crack in a discrete lattice

The paper addresses a problem of partial fracture of a latticeby a propagating fault modelling a crack bridged by elasticfibres. It is assumed that the strength of bonds within thelattice alternates periodically, so that during the dynamiccrack propagation only weaker bonds break, whereas the strongerbonds remain intact. The mathematical problem is reduced tothe functional equation of the Wiener–Hopf type, whichis solved analytically. The load–crack speed dependenceis presented, which also has implications on the stability analysisfor the bridged crack propagating within the lattice. In particular,we address the evaluation of the dissipation rate, which isfound to be strongly dependent on the crack speed. In this latticemodel, our results also cover the case of the supercriticalcrack speed.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Stability analysis of CFRP-wrapped concrete columns strengthened with external longitudinal CFRP sheets

The external confinement by CFRP wrappings is a very efficient method to increase the load-carrying capacity of round concrete columns. Nevertheless, the serviceability of such columns under loads exceeding the strength of unconfined concrete is limited by different factors. One of them is the reduced stability of the columns due to the significantly reduced tangent elastic modulus inactive loading. To increase the critical load of buckling instability of concrete columns, an additional longitudinal composite reinforcement can be used. In this paper, the stability and strength of concrete columns confined by circumferential wrappings and strengthened with a longitudinal external CFRP reinforcement are studied. Plain and confined columns of length 300 and 1500 mm were tested. Theoretical predictions show that the additional longitudinal reinforcement is efficient in improving the stability of confined columns in the region of moderate slenderness. The prediction for the ultimate strength and stability of the columns coincides rather well with experimental results. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 295–308, May–June, 2005.     

A fibre microbuckling model for predicting the notched compressive strength of composite sandwich panels

Cohesive-zone models have been successfully applied to predicting the damage from notches in engineering materials loaded intension. They have also been used to determine the growth of fibre microbuckling from a hole in a composite laminate under compression. The usual strategy is to replace the in elastic deformation associated with plasticity or microbuckling with a line crack and to assume some form of stress-displacement bridging law across the crack faces. This paper examines recent published experimental data for notched glass-fibre epoxy/honey comb sand wich panels loaded in uniaxial compression. A plastic fibre kinking analysis and a linear softening cohesive-zone model are used for the prediction of the unnotched and open-hole compressive strength and the theoretical results are found to be in a good agreement with experimental data. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 73–84, January–February, 2007.     

A study of the perturbed stress state of a closed cylindrical shell with a system of part-through transverse cracks

We study the elastic equilibrium of a closed infinite circular cylindrical shell with a system of surface cracks of identical length and depth. We use the method of singular integral equations together with the modeling of solid matter in the plane of a part-through crack by irregularly distributed “line springs”. We conduct a numerical analysis of the variation of the relative stress intensity factor at the center of a crack as a function of the parameters of a crack and the number of cracks. We study cracks located on both the interior and exterior surface of the shell. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 63–65.     

Nanocomposites based on a styrene-acrylate copolymer and organically modified montmorillonite 1. Mechanical properties

The preparation of polymer nanocomposites by mixing a solution of a styrene-acrylate copolymer with a suspension of organically modified montmorillonite in dimethyl formamide is described. Seven different compositions with organomontmorillonite content from 0 to 7 wt.% were prepared and tested. Results of their X-ray diffraction analysis are presented. Data on the influence of organomontmorillonite content on the tensile stress-strain curves, elastic modulus, strength, and ultimate elongation of the nanocomposites are obtained. The concentration dependences of elastic properties of materials with differently oriented platelike nanoparticles is analyzed by using an algorithm elaborated for stepwise calculations of elastic constants with account of the features of structural hierarchy of intercalated and exfoliated nanocomposites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 375–388, May–June, 2006.