Abstract— The general representation of a symmetric isotropic tensor-function of the second rank in three-dimensional space, depending on two tensor arguments of the second rank, is investigated. This representation includes eight scalar material functions of ten invariants of dependent tensors, including four joint invariants. The tensor function is interpreted as the constitutive relation of an isotropic

Abstract— The article deals with flows of the perfectly plastic compressible media for stress states corresponding to the facets of a piecewise linear yield criterion. Similar flows are observed, in particular, in loosely bonded Coulomb–Mohr media for plane strain states. It is assumed that the intermediate principle stress has no effect on the yielding or transition to the limit state. Under these

Abstract— The article deals with some problems of the theory of elasticity for domains bounded by non-concentric circles by taking into account surface effects such as surface elasticity and surface stresses. The solutions are obtained by expanding variables written in a bipolar coordinate system into Fourier series. The values of surface stresses and stress concentrations that are of our interest

Abstract— It is proved in the article that the recently revealed cracks of a new type, which have a different mechanism of destruction of the medium than the Griffith cracks, cannot be obtained as a result of the convergence of the sides of the wedge-shaped cavity in the plate. Thus, cracks of a new type are obtained as a result of the virtual convergence of the lateral sides of a rectangular cavity

Abstract— A model of planar oscillations of a plane region in the presence of prestress fields is formulated. Various formulations of two-dimensional inverse problems on the restoration of the preliminary stress state are presented. Methods and algorithms for solving the stated inverse problems are proposed and discussed.

Abstract— In this paper, asymmetric equations for an elliptical boundary layer in the vicinity of the conditional front of Rayleigh surface waves, which occurs in shells of revolution under shock end impacts of normal type are constructed. The technique of asymptotic derivation of these equations, based on the use of the symbolic Lurie method and the introduction of special coordinates that distinguish

Abstract— The flexural rigidity of a thin elastic multilayer plate with transversely isotropic layers is considered. If the rigidity of the layers is very different, the classical model based on the hypothesis of a straight normal is not applicable and the effect of lateral shear must be taken into account. Two models for taking into account the effect of transverse shear for a multilayer plate are

Abstract The paper discusses the dynamic propagation of cracks in brittle materials under various loads. The crack propagation is studied under both quasi-static and the shock-pulse loading conditions. Particular attention is paid to the dependences characterizing the crack propagation and having a non-stationary character. Thus, for the case of crack propagation under quasi-static loading, the crack

Abstract— The titanium alloy Ti–6Al–4V with strongly nonequilibrium α- and β-phases has been studied for the first time. For this, it was subjected to cross-helical rolling (CHR) at T = 1000°C (above the polymorphic transformation temperature), and then quenched in water in order to partially preserve vanadium in the α-phase, and aluminum in the β-phase. Under active uniaxial tension, the non-equilibrium

Abstract— The indentation of a rigid cylinder with a flat base into a viscoelastic layer situated without friction on a rigid base is considered. The interaction process consists of two stages: indentation of a cylinder at a constant speed to a certain depth and its further holding in this depth. The mechanical behavior of a viscoelastic layer is described by equations of linear viscoelasticity with

Abstract— For viscoelastic materials, a generalization of the elementary Maxwell model to the case of finite deformations is investigated using the one-parameter set of Gordon-Showalter objective derivatives. Using the obtained constitutive relations, we consider the problems of simple shear, uniaxial tension-compression, and shear vibrations given by the sawtooth function. It is shown that the obtained

Abstract— For an elastic isotropic incompressible material of general form, a number of exact solutions have been found about large torsional and tensile–compressive deformations of a solid circular cylinder, taking into account distributed dislocations. Explicit formulas are obtained that determine the effect of dislocations on the dependences of the torque and longitudinal force on the twist angle

Abstract— One of the urgent problems of mechanics is the study of the regularities of thermomechanical processes that affect the formation of microdefects in dislocation-free silicon single crystals both at the stage of their growth from the melt by the main industrial technology called the Czochralski method, and in subsequent heat treatment technologies of the wafers cut from them. This requires

Abstract— A mathematical formulation and an algorithm for its numerical implementation are presented, intended to study the aeroelastic stability of cylindrical shells of arbitrary cross-section. The problem is solved in a three-dimensional formulation using the finite element method. The reliability of the results obtained is confirmed by comparison with the known solutions for circular shells. The

Abstract— Axisymmetric and non-axisymmetric in-plane vibrations of thin radially growing disc are considered in the frame of the Kelvin–Voigt model of linear viscoelasticity. The main focus of the research is on asymptotic behavior of solutions to the model. Mixed boundary value problems are formulated and converted into standard form by means of time dependent coordinate transformation. The boundary

Abstract— The article considers the problems of calculating the durability of orthotropic polygonal plates, described in the framework of the Kirchhoff theory and subjected to acoustic action with a wide spectrum, taking into account the effects of sound re-emission. A hybrid numerical-analytical method for solving the problem is proposed, based on the determination of the eigenmodes and vibration

Abstract— The unsteady vibrations of a simply supported Timoshenko beam are investigated by taking into account the mass transfer under the action of a distributed transverse load. To formulate the problem, the Timoshenko beam model obtained using the d’Alembert principle from the elastic diffusion equations for a continuum is used. To solve the obtained problem, the integral Laplace transform in time

Abstract— To obtain the heat equation, the first and second laws of thermodynamics and the consequences from them, which are obtained from the requirement that the laws are independent in the sense of choosing the inertial reference frame, are used. To write the second law of thermodynamics, the Clausius-Duhem inequality has been used. In this article, the derivation of the heat equation from the laws

Abstract The problem of stretching a plate with a central or lateral crack is considered. The previously obtained solution, which determines the stresses in the plate in the vicinity of the central crack, is used to predict the load at which plastic deformation appears in the plate with a lateral crack. The Mises condition is used as a criterion for plasticity. The calculation results are compared

Abstract The results of testing of three rods made of different alloys for creep and long-term strength under normal or tangential stresses, which change once or repeatedly in time, are presented. The kinetic theory of Yu. N. Rabotnov was used as a basis for modeling the obtained data. As a result, a good agreement was obtained between the theoretical characteristics of creep and long-term strength

Abstract A model of fracturing of an interface between dissimilar materials in the presence of a section of weakened bonds between materials is considered. Such a section is modeled by a crack, between the faces of which adhesion forces act, depending on the crack opening. The size of the interaction zone of the crack faces (bridged zone) can change during the crack growth and is not small compared

Abstract The article contains an analysis of the kinetics of brittle fracture processes during compression of a two-scale porous medium, in which a larger scale is associated with a system of holes. This work is a continuation of studies of fracture structures during compression. Within the framework of the project, experiments were carried out on samples of porous brittle model material (gypsum) containing

Abstract A complex form of Hooke’s law for an anisotropic body is given, which made it possible to write down the previously known relations obtained in the simplest way. The structure of the matrix of elastic parameters and six linear invariants, which play a key role both in the connection of the stress-strain state and in the structure of the matrix of elastic parameters, have been determined. It

Abstract— A problem on identification of multiple cracks in a rod by means of eigenfrequencies of transverse vibrations is considered. The cracks are modeled by weightless rotational springs. It has been proven that cracks can be uniquely identified using three spectra corresponding to three different types of boundary conditions. A numerical method for assessing fracture caused by cracks has been

Abstract— The axisymmetric wave propagation is investigated in coaxially layered isotropic functionally graded cylinders with different mass and stiffness properties of the layers. Exact solutions of the governing equations of the wave propagation in the cylinders exist only for isotropic, transversely isotropic and piezoelectric transversely isotropic cylinders. In the case of the functionally graded

Abstract To describe the propagation of acoustic surface waves in an anisotropic layer, a six-dimensional complex formalism is introduced, a Hamiltonian is constructed, an analogue of the Rayleigh dissipative function, and an exponential fundamental matrix. Dispersion equations are obtained for a multilayer plate with different conditions on the boundary surfaces. Examples of the application of the

Abstract The problem of wave generation on the surface of a liquid layer lying on an elastic half-space is considered. The generation source is located in an elastic medium. The joint system of equations of the theory of elasticity in a half-space and the theory of waves in a liquid is solved. On the basis of the previously obtained simplified solution of the dispersion equation for the water mode

Abstract A combined model of the phase-structural deformation of shape memory alloys is proposed, within the framework of which the inelastic deformation of these materials can change, both due to phase transformations and due to structural transitions. The model of the development of deformations due to the structural transition uses the concept of a loading surface, isotropic and translational hardening

Abstract— An analysis properties of the constitutive relations of the theory of deformation for physically nonlinear materials with properties depending on the type of stress state is carried out. These relations take into account two forms of nonlinearity, one of them is associated with the nonlinearity of the deformation diagrams and another one is associated with the change in these diagrams depending

Abstract— The article provides a brief overview of studies on crystalline materials with negative Poisson’s ratio (crystalline auxetics) with cubic anisotropy. It has been demonstrated that 1/4 part of all cubic crystals has auxetic properties. Even more auxetics are found among chiral nano/microtubes with cubic cylindrical anisotropy. It has been established that chiral nano/microtubes made of cubic

Abstract Cylindrical grid shells made of modern composite materials by automated continuous winding that have a high degree of weight perfection and are widely used in aerospace engineering are considered. The problem of using such structures as deep-submergence vehicle bodies operating not under external pressure is discussed. The problem of optimal design of cylindrical grid shells based on the criterion

Abstract— The main focus of this study is to investigate the dynamic responses of a simply supported bridge structure in terms of displacement, speed, and acceleration subjected to vehicles traveling at different speeds. The interaction between a bridge and the vehicles moving on it is a coupled, dynamic problem. Conventionally, most research has been focused on the dynamic or impact response of the

Abstract The problem of refined modeling of ultrafine rods, which arose in connection with the need to explain the known experimental data on the significant dependence of the bending stiffness of such ultrathin structures on their thickness if the thickness becomes very small, commensurate as some authors believe with the characteristic dimensions of the material microstructure, is considered. To

Abstract The use of effective approximations that increase the rate of convergence of numerical results when constructing a finite element model of bearing layers for a more accurate layer-by-layer analysis of the stress-strain state of three-layer irregular cylindrical shells is considered. It is believed that the carrier layers are sufficiently thin and rigid, and two-dimensional finite elements

Abstract A design scheme is considered: a cylindrical shell, which is loaded concentrated through the frame. A classical mathematical model is used for the adopted calculation scheme. Based on the mathematical model, the initial problem is analytically solved and an effective algorithm for multiparameter solution of the corresponding boundary value is constructed. The results of a quantitative analysis

Abstract A spatial non-stationary contact problem with moving boundaries of the interaction region for a thin elastic cylindrical shell and an absolutely solid impactor bounded by a smooth convex surface is considered. A closed mathematical formulation is given and a system of resolving equations is constructed. The latter is based on the spatio-temporal integral equation resulting from the principle

Abstract— The influence of morphological features of nanocomposites based on a polymer matrix and graphene oxide on the effective elastic and electrically conductive properties is studied. The concept of a representative volume element (RVE), the geometry of which is modeled explicitly using specified parameters, is used. A method for analyzing the specific conductivity of a RVE that is based on graph

Abstract— In the present article, we argue a choice of a modifier (filler) for an epoxy binder, namely, carbon nanotubes. The solid-state epoxy adhesive obtained by modification is a 3-phase nanocomposite, where the matrix is epoxy resin, the filler is nanotubes, and the contact layer is the domain of the epoxy resin, molecules of which have been undergone conformation. Next, the effective deformation

Abstract Many features of dynamic fracture caused by shock-wave action are most pronounced under spalling conditions, i.e., when an intense wave pulse is reflected from a free boundary. Therefore, such material tests are one of the main ways to study the fracture processes occurring in a solid under ultrafast dynamic stress. Nevertheless, the geometrical characteristics of the fracture zone formed

Abstract The paper considers differential equations in partial derivatives of an elliptic type with variables, piecewise-smooth coefficients, depending on the coordinates (initial equations). It is shown that the solution of the original equation can be represented as an integral equation through the solution of the accompanying equation with constant coefficients of the same type. This representation

Abstract The problems on determining the design fatigue resistance characteristics of materials and structural elements by using methods of the statistical theory of fatigue failure similarity are considered. The results of vast number of fatigue tests conducted by various researchers and research and production enterprises for samples of different sizes, models and full-scale parts have been subjected

Abstract An elastic inhomogeneous coating is considered for which a simplified deformation model is proposed in the framework of the concept of an asymptotically thin layer. Based on such a model for an inhomogeneous coating, a solution of the contact problem in the presence of intermolecular interaction is constructed and the wear kinetics for the thrust sliding bearing is calculated. It is shown

Abstract— An approach to calculating the stress-strain state during axisymmetric deformation of domes and bottoms by synthesizing two stress states, namely, momentless and edge effect is generalized to the case of arbitrary deformation of cylindrical and conical shells. It is proposed to construct the stress state on the basis of approximate equations describing the so-called elementary stress states:

Abstract An analysis of the properties of the constitutive equations of the theory of plasticity for porous media using Green’s yield criterion is carried out. It is shown that this criterion is one of the possible yield criteria for materials with plastic properties depending on the type of stress state, with the only difference being that the coefficients depend on the porosity parameter. Therefore

Abstract The article considers two problems, one of which is related to the engineering direction, devoted to the study of the resources of bearings with coatings that have received a certain defect. The second relates to the mechanics of natural phenomena and is associated with the phenomenon of subduction. Subduction is the process of moving oceanic lithospheric plates under the continental in the

Abstract The relations of the mathematical model for studying the stress-strain state of structurally anisotropic panels made of composite materials are given. The mathematical model of the reinforcing element is clarified under conditions of one-sided contact with the skin. The influence of panels manufacturing technology is taken into account: residual temperature stresses and prestressing of reinforcing

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AbstractThe axisymmetric torsion of a layer of incompressible Mooney–Rivlin material placed between two rigid coaxial cylindrical surfaces is considered. It is assumed that the ends of the cylinder are fixed to avoid axial displacement and the cross-sections orthogonal to the axis of symmetry do not distort during deformation. In this case, the material points move along arcs of circles with an angular

AbstractThe present article deals with a solution of an analogue of the Prandtl problem on compression and drain (spreading) of a perfectly rigid plastic material in an asymptotically thin spherical layer by taking into account inertial effects. Various compression modes that characterize the transition from a quasistatic process to a dynamic one are considered.

AbstractThe present article claims that by preliminary heat treatment (thermal annealing) of polystyrene in a fixed state at a temperature of 60°C, a slight increase in its light stability can be achieved.

Abstract–A rectangular plate pivotally mounted on two opposite edges is considered. It is shown that one of the plate fastenings at the other two edges is determined up to a permutation of the fastenings at these edges uniquely from five natural frequencies. It is also shown that four eigenfrequencies for such a recovery is not enough. The corresponding counterexample is given. It was previously shown

AbstractIn this work, the evolution of dispersion relations of 2D asymmetric phononic crystals in the low-frequency range is introduced and discussed. Two phononic crystal structures are proposed and calculated using Finite Element method. The first one is a thin plate from PDMS with a circular one-side stubbed from tungsten and the other is a thin plate in the X-shape from rubber and tungsten. The

AbstractBased on the layer-by-layer analysis approach, the construction of a model of two types of finite elements (FE) of natural curvature (two-dimensional FE of the momentary bearing layers and three-dimensional FE of the filler) is considered for refined investigation of the stress-strain state (SSS) in layers of three-layer generally irregular shells of revolution of double curvature.The presented

AbstractWe study the dynamics of a gimbal-mounted gyroscope, which has a vertical external gimbal axis and is equipped with a synchronous electric drive that rotates a gyroscope (electric motor rotor). A mathematical model of the electric motor that includes differential equations for electric currents in the rotor windings is used. Both friction and control torques on the gimbal axes are assumed to

AbstractCurrently, various structural components have coatings of different purposes that are multilayer or gradient structures. During operation these elements are often subjected to compressive loads, as a result of which sometimes the upper part of the coating is delaminated. To analyze this process, we use a simplified model of infinite structure, namely, a modified beam approximation that takes

AbstractA continuum model is proposed and a system of equations is constructed to describe the processes of destruction of a solid. In the framework of the model, a decaying solid is considered as a heterogeneous medium consisting of two phases—solid and gaseous. Based on the analysis of the energy balance equation, in which its surface component is taken into account, the regularities of the onset

AbstractIn a non-standard setting, motion with respect to the center of mass of a spheroid with a cavity filled with a fluid of high viscosity is considered. The moment of forces acting on the body from the side of a viscous fluid in the cavity is determined by the technique developed in the works of F.L. Chernousko. As a result of original asymptotic and numerical calculations, solutions are obtained

AbstractThe present article deals with the problem on constructing a guaranteeing time of a given control beginning for a shock isolator protecting an object on a movable base from impacts acting on this base. The initial moment of control action can either be ahead (anticipation) or lag behind (delay) the moment of the disturbance beginning. It is assumed that the shock shape is unknown, but its duration

AbstractIn the framework of the model of M.A. Lavrentiev, the effect of internal elastic and dissipative forces on the rotational motion of the planet in a central gravitational field in a circular orbit is studied. The averaged equations of the rotational motion of the planet are derived. The stability of plane rotations is investigated. The analysis of the evolution of rotational motion depending

AbstractIn the framework of the theory of large deformations, a solution is obtained for the deformation of a material with nonlinear elastic, plastic and viscous properties located in the gap between two rigid coaxial cylindrical surfaces. The outer surface remains stationary, and the inner rectilinearly moves with variable speed. With uniformly accelerated surface motion, initially irreversible strains