The work is devoted to a theoretical and experimental study of mechanisms related to plastic strain localization under dynamic loading. A mathematical model that takes into account structural relaxation and thermal softening is built within the framework of the study on the basis of wide-range constitutive equations. The proposed model is capable to adequately describe the deformation of plastic materials (metals and alloys) in the range of strain rates of 102-104 s-1 and in the temperature range from 0 to 0.7 of the melting point. AMg6 aluminum alloy was chosen as a material under study as it is a promising material for mechanical engineering. However, all the obtained results can be applied to a wide class of materials: metals and alloys. The model parameters were identified using experimental data (stress-strain diagrams) at various strain rates and temperatures. The series of original experiments on punching disc-shaped barriers by a cylindrical projectile was carried out to test the constructed model. During the experiment, the impact velocity and the temperature on the back surface of the barrier were measured at the moment of an intense localization of plastic deformation and fracture. The strain rate in the experiment ranged from 500 to 30,000 s-1. As a result of the numerical studies, it was shown that defects play a critical part in during strain localization for AlMg6 alloy at strain rates of less than 104 s-1. Thermal softening begins to make a significant contribution at strain rates above 104 s-1. This theoretical result is also confirmed by the original experiments on the penetration of barriers.

Having analyzed the experimental studies of samples of 12X18H10T stainless steel with a hard (controlled deformation) deformation process including sequences of monotonic and cyclic loading modes, under uniaxial tension-compression and normal temperature, we found some features and differences of isotropic and anisotropic hardening processes under monotonic and cyclic loads. To describe these features in the framework of the plasticity theory (Bondar model) belonging to the class of flow theories with combined hardening, the criterion of changing the direction of plastic deformation and the memory surface allowing the separation of monotonic and cyclic deformations is introduced in the plastic strain tensor space. For the description of transient processes from monotonic to cyclic and from cyclic to monotonic ones, the evolutionary equations are formulated for the parameters of isotropic and anisotropic hardening. The basic experiment, on the basis of which the material functions are determined, consists of three stages, i.e. cyclic loading, monotonic loading and subsequent cyclic up to destruction. The method of material functions identification according to the results of the basic experiment is given. For stainless 12X18H10T steel, the material functions at room temperature were determined on the basis of the basic experiment and the identification method. The comparison of the calculated and experimental results for the stainless steel under rigid loading, was made and consisted of a sequence of five stages: cyclic, monotonic, cyclic, monotonic and cyclic up to destruction, are given. The calculated and experimental kinetics of the stress-strain state throughout the deformation process are compared. Changes in the range and average stress of the cycle at the stages of cyclic stress are analyzed. At these stages there is a landing hysteresis loop. A reliable agreement between the calculated and experimental results was obtained. A sufficiently adequate description by the theory of the processes of change in the kinetics, range and average stress of a cycle under hard loading suggests the possibility of a more adequate description and processes of soft loading, especially in non-stationary asymmetric loading conditions.

In this paper presents a developed method aimed to solve contact axisymmetric problems for limited bodies of revolution from transversely isotropic material which are simultaneously under the action of mass forces. The method involves the development of the energy method of boundary states, which is based on the concepts of spaces of internal and boundary states conjugated by isomorphism, which allows us to establish a one-to-one correspondence between the elements of these spaces. The internal state includes stress tensor components, deformation tensor components and displacement vector. The boundary state includes efforts and moving boundary points and mass forces. The isomorphism of the state spaces is proved, which allows finding the internal state to be reduced to the study of a boundary state that is isomorphic to it. The basis is formed based on the general solution of the boundary value problem for a transversely isotropic body of revolution and based on the method of creating basic displacement vectors while determining the state from continuous nonconservative mass forces. The orthogonalization of the state spaces is carried out, where the double internal energy of elastic deformation is used as scalar products in the space of internal states; in the space of boundary states, the work of external and mass forces is used. Finally, the problem of finding a desired state is reduced to solving an infinite system of algebraic equations regarding the Fourier coefficients. The solution of the contact problem without friction in contacting surfaces for a circular in terms of the cylinder is presented. The material of the cylinder is a transversely isotropic siltstone with the anisotropy axis coinciding with the geometric axis of symmetry. Mass forces act on the body, imitating centrifugal forces of inertia and gravity. Mechanical characteristics have analytical polynomial view. Explicit and indirect convergence patterns of the problem solving and graphical visualization of the results are presented.

The ultrasonic non-destructive testing is widely used in different civil and engineering applications as one of the most effective and convenient method of structural health monitoring. It is necessary to have a reliable mathematical model simulating scattering caused by defects and inhomogeneities in order to apply effective ultrasonic methods. Modern composite materials used in manufacturing have a laminated structure; therefore it is important to detect damages occurrence located between two materials. Scattering caused by interface cracks can be investigated using the boundary integral equation (BIE), the method which is analytically oriented. The unknown function of the crack opening displacement in the BIE is expanded in terms of orthogonal polynomials. Then the integral equation is projected onto a set of polynomials. Regularization of the hypersingular BIE using the Bubnov-Galerkin scheme is obtained through a repeated integration on the crack faces. This paper uses the BIE method to derive an asymptotic solution describing the elastic wave diffraction by the strip-like crack located at the interface between two dissimilar elastic half-spaces. The Fourier transformation of Green's matrix is applied to obtain a scattered field. Asymptotic representations of the equation kernel around zero and at infinity are derived with the assumption that the crack size is much less than a wavelength of an incident wave. The Bubnov-Galerkin scheme is used to obtain the frequency dependent asymptotic solution of BIE which has a wider accuracy frequency range than the existing quasi-static solution. A good agreement of the derived asymptotic solution with the numerical solution is shown for different materials of the considered structure. The asymptotic solution allows increasing the BIE method potency by reducing the computational cost of integrals. It can also be used to describe dynamic damaged interfaces in the Bostrom-Wickham model's term.

The paper examines general shells supported from the incurvity side by a cross-sectional ribbing directed parallel to coordinate lines. Ribs’ position on a shell is set using ordinary bar graph functions so that the rib and shell contact is arranged along the strip. A mean shell surface shall be considered as a coordinate surface. Geometrical nonlinearity and transverse shears are considered; and the shell is considered to be shallow. Forces are expressed via stress function in the mid-surface of the shell in such a way that the first two equilibrium equations are fulfilled identically. Shell deformation is expressed via this function. Introduction of ribs by means of ordinary bar graph functions does not cause difficulties for expression of deformations using forces with the consequent insertion to moments, since ordinary bar graph functions may be also used in denominator, this is not applicable for delta-function (when positions of narrow ribs are set using delta-functions). Mixed equations are established starting from the minimum of shell energy deformation functional. At that, except for equilibrium equations, the variational procedure allows obtaining the third equation of strain compatibility in a shell mid-surface for ribbed shells too. Curvature and torsion change functions are registered in the same way as for Kirchhoff-Love model considering transverse shears. Mixed form equations are given for ribbed shells of the general form and for the Kirchhoff-Love model. For ribbed shallow shells, an algorithm for their solution has been developed and the results of calculating their stability for a different number of reinforcing ribs are given.

In dynamic calculations of thin-walled structures, an account of nonlinear viscoelastic properties of material plays an important role in a reliable assessment of the strength capability of structures. In this regard, in the mechanics of a deformable rigid body, much attention is paid to the description of nonlinear material properties and the methods to solve specific problems for various thin-walled structures under static and dynamic loads. Thin-walled structures such as plates and shells often play the role of a bearing surface, to which lining, fasteners, various instrument assemblies and other structural elements are attached. In dynamic calculation, the attached elements having an inertial character are considered as additional mass rigidly connected to the systems and concentrated in points. The effect of concentrated mass is introduced using the Dirac delta function. In this paper, a mathematical model has been constructed, a solution method has been proposed, and a computational algorithm has been developed for the problem of oscillations of a viscoelastic plate carrying concentrated mass, with account of physically nonlinear strain of material under different conditions of fixing the plate contours within the Kirchhoff-Love hypothesis. The physical relationship between stresses and strains, with account of nonlinearity, is taken in the form of the Boltzmann-Volterra integral model, where the weakly singular Koltunov-Rzhanitsyn kernel is taken in calculations as the relaxation kernel. Discretization on spatial variables has been conducted by the Bubnov-Galerkin method, and non-decaying systems of integro-differential equations (IDE) with respect to time function of the problem have been obtained in a general case. To solve the IDE, a numerical method was proposed based on the use of quadrature formulas, which eliminate the features in the relaxation kernel. A unified computational algorithm to determine the deflection of a viscoelastic plate with concentrated masses has been developed.

It is known that non-compact materials (porous, powdery, with defects in continuity) are much less resistant to shear than to hydrostatic compression. The effect of dilatancy in such media causes a change in density during shear deformation. For compact materials, a process of lateral extrusion (or equal-channel angular pressing) is known. The ECAP realizes a stress state close to a pure shear in the deformation zone (as opposed, for example, to direct extrusion, where a simple shear is realized). It can be expected that ECAP process for non-compact materials is less energy consuming and leads to a more intensive consolidation of the frame material than hydrostatic compression. In particular, ECAP can be considered as one of the methods of extracting the fluid from a porous medium (oils from vegetable raw materials, water from soils, etc.). This paper is devoted to modeling of such processes. We consider the plane problem of stationary plastic deforming of a material in the region of junction of slot channels. The cross section of the deformation region is an annular sector. We assume that the material is irreversibly compressible and obeys the elliptic Green type yield condition. One of the walls of the channel is permeable to fluid. We consider the fluid filtration in the pores. We use a number of model assumptions. The motion of the frame material particles is a flat azimuthal in a cylindrical coordinate system. The mechanical characteristics of the material vary slightly in accordance with small changes in density. The intraporous pressure is small in compare with the stressed state of the skeleton material and does not have a significant effect on the process of plastic flow. A rigid-plastic analysis was performed and the exact solution of the mechanical part of the problem was obtained. The exact solution of the fluid filtration problem in case of a constant filtration coefficient is obtained. The solution is the intraporous pressure field. When using these results one can determine the two-dimensional vector field of the fluid velocity and the total discharge of flow. In case of a non-constant filtration coefficient, the problem is reduced to integrating the boundary value problem of anisotropic thermal conductivity with a special case of anisotropy, for which a number of exact solutions are known.

Additive technologies make it possible to manufacture products using a layer-by-layer synthesis, thus obtaining products of complex shapes. When solving a complex problem of numerical modeling of additive technological processes, it is necessary to describe various thermomechanical phenomena with high accuracy. The most effective in this regard is the use of a combination of capabilities of specialized software systems and the development of unique algorithms for them, taking into account the maximum possible number of process parameters. The paper considers the calculation algorithm of non-stationary temperature fields and stress-strain state of the structure in the process of its creation by 3D welding of wire materials developed and implemented using the ANSYS Mechanical package in the APDL language. In particular, this model takes into account the non-stationary radiant transfer of thermal energy of the welding arc to the surface of the product. The review highlights three of the most commonly used methods for modeling material deposition, i.e. the so-called element birth, sleeping element (quiet element) and hybrid activation (hybrid activation). It is shown that in order to ensure greater efficiency of calculations, it is necessary to use the principle in which successive steps of melting and even layers are grouped together for a subsequent simultaneous activationn. In the presented model, the task is divided into the boundary problem of non-stationary thermal conductivity and the boundary problem of thermomechanics of the stress-strain state, which are uncoupled. To solve them we applied the technology of killing and the subsequent birthing of a part of the material, implemented with the ANSYS package. Verification of the developed numerical algorithm aimed at solving the three-dimensional problem of the arc surfacing of wire materials was carried out by a comparison with the results of the experimental tests on D16 aluminum alloy samples. To describe the elastoplastic behavior of the alloy, the BISO model of bilinear isotropic plasticity with a temperature dependence of yield strength was used. A good consistency of the calculated data with the experiment was shown. The effect was studied on the level of the residual distortion of such process parameters as exposure time to the next layer, the motion path of the slicer, ambient temperatures. It is shown that the latter parameter is the most effective way to reduce residual shape deviations, but requires high thermal stability of equipment and accuracy of arc energy control.

The aim of this study is to develop a new analytical approach to calculation of effective properties of elastic heterogeneous media based on multipoint approximations of solutions of stochastic boundary value problems. Prediction of macroscopic properties of heterogeneous media is associated with the need for a reliable description of their microstructural behavior, including the interaction between individual components. A number of analytical and numerical approaches have been developed to evaluate the effective properties of structurally inhomogeneous media. However none of them makes it possible to calculate the effective properties of such media with an absolute accuracy. One of the main limitations is imposed by taking into account the features of the microstructure of the medium, such as orientation, size, shape and distribution of inclusions, as well as the features of influence of the matrix on inclusions. In this paper, multipoint approximations of solutions of boundary value problems are used to calculate the effective characteristics, in which it is necessary to employ higher-order correlation functions, which allows to take into account the multiparticle interaction of microstructural elements with a higher extent. Analytical expressions for the calculation of the effective properties of structurally inhomogeneous media using multipoint higher-order approximations of solutions of stochastic boundary value problems in elastic formulations are obtained. A numerical comparison of the calculation results of relative effective characteristics of porous inhomogeneous polydisperse media with spherical inclusions of different volume fractions is performed. For the numerical solution of the integral-differential equations, a global adaptive strategy is applied in conjunction with the multidimensional integration rule and the IMT variable transformation rule to handle the singularity of the Green’s function. Some conclusions are made on the effectiveness and limitations of the proposed approach.