Solution of boundary-value problems of the statics of layered elastic bodies with nonrigid contact between the layers

A technique is proposed for solving three-dimensional problems of the stress-strain state of cylinders, spheres, and shallow elastic bodies with a rectangular projection which are composed of laterally nonhomogeneous anisotropic layers with nonrigid contact between the layers. The solution of the corresponding many-point boundary-value problem is reduced to solving a number of two-point problems by a known numerical apparatus. Solution results are reported for the strain of a three-layer spherical shell with slipping layers.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 62–68, 1985.     

Wave-field asymptotics in the problem of diffraction by a planar junction of thin layers and boundary-contact conditions

The problem of diffraction by a planar junction of thin layers covering a perfectly conducting substratum is considered, and its asymptotic solution is constructed. The wave field in the vicinity of the junction of the layers is described by a function of the boundary layer. Based on the asymptotics obtained, the generalized impedance boundary condition, which simulates thin layers, and the contact conditions are derived. The uniqueness of the solution of a model problem is discussed. Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 157–171. Original Translated by M. A. Lyalinov.     

Simulation of Electrolytes in the Modeling of Batteries

Calculating the cell voltage of a lead-acid battery requires the solution of a complex multiphysical problem including electrochemical reactions on the electrode surfaces and diffusive transport in the enclosed electrolyte. Recently, the authors proposed a new electrolyte model with a thermodynamically correct coupling of mechanics to the diffusive transport. In the analysis of that model, formal asymptotic expansions were applied to handle sharp interface layers. Here, we use this analysis to formulate a simplified model for a lead-acid battery such that it is not necessary to resolve the layers numerically, but instead there are jump conditions at double layers imposed. The cell voltage is then derived using Butler-Volmer Formula. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the geometry of the structure on the strength distribution of multilaminate tridirectional reinforced plastics

Conclusion The proposed analytical method makes it possible to predict the strength distribution of an LRP of the type [0/±]_s from its structure (the geometry of the packet, the number of layers, and the strength properties of the layers) in a plane stress state. Allowance is made for the random character of the strength properties of the layers, which makes it possible to evaluate the reliability of the LRP for both determinate and random loading. A criterion was formulated for the optimum design of the structure of an LRP with respect to ensuring maximum reliability for specific loading conditions. We also evaluated the effect of the parameters of the structure and the characteristics of the plane stress state on reliability. According to the results of a numerical analysis performed with the above-developed structural model of the failure of an LRP — with allowance for the random character of the strength properties of the layers — the imbalance of the laminated packet which occurs during failure can be ignored. The method used to predict the strength distribution of the LRP, involving determination of the strength distribution law of an RSE and subsequent examination of the loading of parallel-connected RSEs, is promising for other reinforcement schemes as well.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 805–812, September–October, 1988.     

Homogenization of the equations of state for a heterogeneous layered medium consisting of two creep materials

A mathematical model that describes the joint motion of periodically alternating layers of two isotropic creep materials is considered. It is assumed that all layers are parallel to one of the coordinate planes and the thickness of any two adjacent layers is ε. For this model, the corresponding homogenized model for ε → 0 is constructed, which describes the behavior of a homogeneous creep material.     

Effect of liquid media on the deformation of the surface layers of a polymer-metal pair in sliding friction

The relation between the high-elastic component of polyurethane deformation and the deformation of the surface layers of metals has been investigated for sliding friction in various media. The surface layers of polymer and metal are plastically deformed. There is a certain correlation between the coefficient of friction and the amount of deformation.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 147–149, January–February, 1970.     

The stress state of the finite cylinder with the circular cracks

The axysimmetrical torsion problem for a finite cylinder with an arbitrary quantity of the cylindrical layers is solved. The cylinder is weaked by the parallel circular cracks in the first internal layer. The stated boundary valued problem problem is reduced to the system of the integro-duferential equations solving with the help of the orthogonal polinomials method. The stress intensity factors (SIF) are obtained. The dependences of SIF values from the cracks' sizes, their location, and ratio of the layers' shear moduluses are concretized for the case of the two layers. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of random irregularities of the creep of reinforced layered plastics

The authors investigate the creep of inhomogeneous materials consisting of a large number of stiff orthotropic elastic layers alternating with layers of linear isotropic viscoelastic material. The elastic layers are assumed to be almost plane; the functions describing the irregularities (curvature) form a random field. The averaged characteristics of the medium are found together with the variation of the averaged displacements and strains in time. An analogous problem was previously considered in [1, 6] on the assumption that the binder layers are elastic. The present paper is based on the equations of [1] and the elastic-viscoelastic correspondence principle [4]. When the correlation scales of the irregularities are small as compared with the dimensions of the body and the characteristic distances over which the averaged parameters of the stress-strain state vary appreciably is considered in detail. A relation is established between the creep functions for simple cases of the state of stress and the parameters characterizing the properties of the components, the properties of the random field of initial irregularities, etc. The development of perturbations with different wave numbers is investigated. The theory is used to describe the creep of reinforced layered plastics.Mekhanika Polimerov, Vol. 2, No. 5, pp. 755–762, 1966     

Determination of the optical density of human coronary arterial walls

Conclusions 1. The greatest thickness is found for the segment of a coronary artery adjacent to the myocardium; this effect is observed even in a neonate.2. At a young age, the greatest thickness is found for the middle and outer wall layers of both coronary arteries.3. In individuals reaching age 40 and having atherosclerosis of the major branches of the cardiac arteries, the walls of both coronary arteries become thicker due to the inner and middle layers, but the thickening of the individual layers is most pronounced in the wall of the left coronary artery.4. The method of optical densitometry relative to stained histological sections of the vascular wall may be used for the relative determination of the densities of tissues and their distributions over the individual wall layers.5. The optical density of elastic tissue of the walls of the coronary arteries reaches a maximum in the third decade of life in the human and decreases after age 40 (especially in the distal segment of the left coronary artery).6. The optical density of the total connective tissue in the walls of the left coronary artery increases with increasing age, especially in the distal segment of this artery. In youth, the optical density of connective tissue is greater in the wall of the right coronary artery, but with increasing age this density decreases markedly.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–318, March–April, 1978.     

Technological aspects of the study of the mechanical properties of the human abdominal aorta

Conclusions 1. It was experimentally established that upon the monoxial stretching of individual layers of the abdominal aorta, the tensile strength and tangential elasticity modulus upon breakage are higher in the atherosclerotic layer. The deformative properties are higher in the uninjured layer.2. With increasing age, the capacity for deformation and the tensile strength of both layers of the wall of the abdominal aorta decrease.3. The technique developed for determining the resistance to separation into layers of the wall of the abdominal aorta indicates that the bonding strength of the layers of the aorta depends on the stage of atherosclerosis and increases with advancing stages of the atherosclerotic process.Report presented at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.N. É. Bauman Moscow Higher Technological School. Translated from Mekhanika Polimerov, No. 4, pp. 693–698, July–August, 1977.     

The kinetics of some structural changes in the surface layers of polymers during friction

It is established that in sliding friction there is a change in the dimensions of the elementary crystalline regions and the degree of crystallinity of the surface layers of polymers. The laws governing these structural changes in the surface layers of PTFE in relation to the conditions and time of polymer-metal contact are given. The results supplement and refine existing concepts on the mechanism of friction involving polymers.Mekhanika Polimerov, Vol. 1, No. 6, pp. 114–119, 1965     

Dynamic method of determining the mechanical characteristics of the surface layer of polymers

A thin polymer film is treated as a three-layered plate, the inner layer being characterized by the bulk and the outer layers by the surface properties of the polymer. Using the equations describing the vibrations of a cantilever element of rectangular section, the authors propose formulas for the thickness, modulus of elasticity, and mechanical loss factor of the surface layer. The mechanical characteristics of the surface layers of PMM and nitrocellulose have been determined by electromagnetically exciting and photometrically recording vibrations in film specimens of varying thickness.Institute of the Chemistry of High-Molecular Compounds, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 548–550, May–June, 1969.     

Finite expressions for the characteristic matrices of weakly curved elastic layers

The propagation of two-dimensional waves in cylindrical and spherical, homogeneous, elastic layers is investigated. For these layers finite formulas are found for the characteristic matrices. Comparison of these matrices and use of asymptotic representations for the Hankel functions make it possible to derive expressions in the case of weakly curved elastic layers. The expressions obtained correspond to analogous formulas in the form of matrix series.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 156–169, 1981.     

Numerical methods for the modeling of the magnetization vector in multiferroic heterostructures

Multiferroic heterostructures are commonly used to obtain electro-magnetic coupling effects. Thereby, the ferroelectric layer is used to control the magnetization in the ferromagnetic layer. The coupling between the layers is obtained by the mechanical coupling between the layers, which have well-defined interfaces. Within this contribution we use phase field models to define the polarization and magnetization in the ferroelectric and ferromagnetic layers, respectively. A coupling between polarization/magnetization and strains in each layer in combination with coherent deformations at the interface yields an electromagnetic coupling within the entire heterostructure. Numerical formulations for the interpolation of the polarization vector are well-defined in the literature. However, the establishment of a consistent numerical formulation for the ferromagnetic layer, where the length of the magnetization vector has to be constant, remains a difficult task. We propose a new numerical approach for the consistent treatment of the ferromagnetic layer and provide numerical simulations which illustrate the electromagnetic coupling effect. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation

In the present article an investigation is presented into the stability of an electro-statically deflected clamped–clamped micro-beam sandwiched by two piezoelectric layers undergoing a parametric excitation applying an AC voltage to these layers. Applying an electrostatic actuation not only deflects the micro-beam but also decreases the bending stiffness of the structure, which can lead the structure to an unstable position by undergoing a saddle node bifurcation. Utilizing an appropriate AC actuation voltage to the piezoelectric layers produces a time varying axial force, which can play the role of a stabilizer exciting the system parameter. The governing equation of the motion is a nonlinear electro-mechanically coupled type PDE, which is derived using variational principle and discretized, applying Eigen-function expansion method. The resultant is a Mathieu type equation in its damped form. Using Floquet theory for single degree of freedom system the stable and unstable regions of the problem are investigated. The effects of viscous damping and electrostatic actuation on the stable regions of the problem are also studied.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Calculation of rigidly clamped circular plates in the statement of the problem on contact interaction in a two-layer package

The use of a mechanicomathematical model of bending of thick transversely isotropic plates is illustrated, where the plate is divided in an arbitrary number of equally thick conditional layers. This model allows one to approximately reduce the problem of determination of stresses and displacements in the thick plate to a corresponding contact problem for a bent pack age of layers. The axisymmetric bending of a rigidly clamped package consisting of two plates rigidly fastened together is considered. The results of numerical calculations are presented, which are compared with those obtained within the framework of a refined bending model of plates (with account of transverse compression and shear) and of the Timoshenko model, as well as in the statement of the three-dimensional theory of elasticity. The accuracy of satisfying the boundary conditions in each model is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 93–108, January–February, 2007.     

Relationship between acoustic emission and development of the damage zone in the interlaminar fracture of fiber composites

A study is made of unidirectional carbon-fiber-reinforced composites with both thermosetting and thermoplastic matrices. Experimental data on acoustic emission for unidirectional fiber composites with a crack is presented in the form of an exponential dependence of the number of AE signals on the stress-intensity factor. The increase in the size of the damage zone across the layers of the composite turns out to be linearly dependent on loading time (and, thus, on K_lc), in contrast to the usual quadratic dependence along the layers.Presented at the IX International Conference on the Mechanics of Composite Materials (Riga, October 1995).Institute of High-Molecular-Weight Compounds of the Russian Academy of Sciences (St. Petersburg).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 792–796, November–December, 1995.     

Generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures

The feasibility of using a generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures has been examined. Using this method, the problem is reduced to solution of simpler special averaged problems for composites with single inclusions and corresponding transition layers in the medium examined. The dimensions of the transition layers are defined by correlation radii of the composite random structure of the composite, while the heterogeneous elastic properties of the transition layers take account of the probabilities for variation of the size and configuration of the inclusions using averaged special indicator functions. Results are given for a numerical calculation of the averaged indicator functions and analysis of the effect of the micropores in the matrix-fiber interface region on the effective elastic properties of unidirectional fiberglass—epoxy using the generalized self-consistent method and compared with experimental data and reported solutions.Perm State Technical University. Translated from Mekhanika Kompozitmykh Materialov, Vol. 33, No. 3, pp. 289–299, May–June, 1997.     

Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements

In the paper, the bending stiffness and strength of multilayer structural elements in relation to the mechanical properties of layers and their number layout and sizes are investigated and the corresponding correlations are established. It is found that the most rational structure of a multilayer element in bending is a symmetric three-layer structure formed from two materials with the thickness of the core less than the half-thickness of the element. The values of normal stresses in the layers of a multilayer beam in bending depends on its bending stiffness and the position of layers relative to the neutral axis. The influence of the number of layers on the stiffness of the structural element and on the magnitude of normal stresses is insignificant.