The strength of a square plate with a central crack at normal separation was studied within the framework of the Neuber–Novozhilov approach using a modified Leonov–Panasyuk–Dugdale model using an additional parameter, the diameter of the plasticity zone (width of the pre-fracture zone). As a model of a deformable solid body, a model of an ideal elastic-plastic material with a limiting relative elongation was chosen. This class of materials includes, for example, low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. In the presence of a singular feature in the stress field in the vicinity of the crack tip, it is proposed to use a two-parameter discrete integral strength criterion. The deformation fracture criterion is formulated at the tip of a real crack, and the force criterion for normal stresses, taking into account averaging, is formulated at the tip of a model crack. The lengths of real and model cracks differ by the length of the pre-fracture zone. The constitutive equations of the analytical model are analyzed in detail depending on the characteristic linear dimension of the material structure. Simple formulas suitable for verification calculations for the critical breaking load and the length of the pre-fracture zone are obtained. Numerical modeling of the propagation of plasticity zones in square plates under quasi-static loading has been performed. In the numerical model, the updated Lagrangian formulation of the equations of mechanics of a deformable solid body is used, which is most preferable for modeling the deformation of bodies made of an elastic-plastic material at large deformation. The plastic zone in the vicinity of the crack tip is obtained by the finite element method. The results of analytical and numerical prediction of plate fracture under plane deformation are compared. It is shown that the results of numerical experiments are in good agreement with the results of calculations using the analytical model of fracture of materials with a structure under normal separation. Diagrams of quasi-brittle and quasi-ductile fracture of a structured plate are constructed.

To select rational parameters of the process of hybrid additive manufacturing of structures made of structural metal alloys and stainless steels, mechanical characteristics capable of serving as indicators of material quality were determined. The most advanced technologies of additive manufacturing by wire-arc surfacing (plasma, plasma arc with a melting electrode, including cold metal transfer) with layer-by-layer forging with a pneumatic impact tool and subsequent heat treatment were used. Aluminum-magnesium alloy AlMg5, titanium alloy Ti-6Al-4V, austenitic stainless steels 12Cr18Ni10Ti (AISI 321) and AISI 308LSi have been studied. Samples were cut from the blanks created by additive manufacturing – blades for standard tests for static uniaxial tension and cylinders for high-speed compression tests by the Kolsky method on a Hopkinson split bar. According to the registered and processed stress–strain curves for all materials, standard strength and ductility characteristics and the Johnson – Cook law of deformation and speed hardening were determined. For a correct assessment of the mechanical properties of additively produced materials, these tests were also carried out for each of them in the form of annealed rolled products. It is established that to compare the efficiency of various technological parameters of additive manufacturing, it is advisable to use static tensile strength and uniform elongation to rupture, having the smallest statistical variation. It was also found acceptable to approximate the Johnson – Cook law of the deformation curves of each of the studied materials according to averaged data, including various technological modes. Certain mechanical characteristics seem to be necessary for the search for effective modes of hybrid additive manufacturing and numerical calculation of various elastic-plastic problems in a dynamic formulation for the studied materials for design and technological needs.

The article is devoted to solving the urgent problem of improving the method of nondestructive testing of the condition of non-rigid road clothes. In addition to the previously developed approach to determining the mechanical parameters of materials of structural layers of nonrigid road coverings based on solving the inverse coefficient problem of restoring operational elastic modules providing specified displacement fields, an approach was developed that allows determining the parameters of energy dissipation in the structure of multilayer road pavement based on the correction of dynamic hysteresis loops recorded in the field and calculated using mathematical model of dynamic VAT. The article presents the results of numerical simulation of dynamic hysteresis loops for two different variants of multilayer structures. The possibilities of correcting the shape of hysteresis loops and their area by varying the tangents of the energy loss angles in layers of a multilayer medium and the elastic modulus of a homogeneous half-space are shown. The complex correction of the elastic modulus values of the structural layers of road clothes and the calculated loops of dynamic hysteresis made it possible to fully take into account the processes of energy attenuation at a distance from the point of application of the load. During the correction, it was found that the values of the elastic modulus of the road layers and the tangents of the loss angles in them have a complex effect on the areas of dynamic hysteresis loops and the nature of energy attenuation at a distance from the point of application of the load. At the same time, the elastic modulus of the underlying half-space is not limited in thickness to the greatest extent on the area of dynamic hysteresis loops (which led to an increase in the elastic modulus of the underlying half-space from 120 and 150 MPa for road construction variants with a reinforced and non-reinforced base to 170 and 160 MPa, respectively), and a decrease in the dissipated energy at a distance from the point of application This is primarily due to the tangent of the angle of energy loss in the half-space. The obtained values of the tangents of the loss angles are obviously related to the patterns of energy dissipation at the boundaries of the contacting layers of the pavement, and also take into account all possible anomalies and delaminations in the calculated structures. Within the framework of this article, calculated hysteresis loops on the surface of the pavement were obtained for the first time, the deformation energy was calculated based on their areas, and the possibility of their comparison with those registered experimentally was proved.

The present research is devoted to the development of the theoretical foundations of nondestructive acoustic method for identifying inhomogeneous prestress fields in a hollow cylinder, depending on the probing loading type. A linearized model of steady oscillations of an elastic body in the presence of an inhomogeneous prestress field of arbitrary nature is considered in the standard and weak formulations. On the basis of this model, we formulate a problem for a cantilever-clamped prestressed hollow cylinder that performs steady axisymmetric vibrations under three types of probing loading. A corresponding weak formulation of the problem in the cylindrical coordinate system is presented, in which six independent components of the prestress tensor are taken into account. At that, a case of prestress fields obtained by applying some initial mechanical external static load is considered. In the presence and absence of prestresses of various types, amplitude-frequency dependences are analyzed, and resonant and natural frequencies are found in a wide frequency range. Numerical calculations were carried out using the FEM on a non-uniform grid; mesh refinement is carried out in the vicinity of the boundary points, where the type of boundary conditions changes. Based on the numerical solution of an auxiliary set of direct problems, seven types of prestress fields are constructed, differing in the types of initial loading, most often encountered in practice. To assess the possibility of implementing the procedure for reconstructing prestresses of each of the considered types, a sensitivity analysis was additionally performed, which showed that for some prestress types there are frequencies and types of probing loading for which the presence of prestress is practically not manifested. The sensitivity analysis performed made it possible to implement the optimal method of probing loading when solving the inverse coefficient problem. The statement of the new inverse problem on the restoration of arbitrary inhomogeneous prestress fields in the considered finite hollow cylinder is formulated. When restoring the prestress of a given structure, the inverse problem is reduced to finding a set of parameters from an ill-conditioned algebraic system, which was studied with the help of the A.N. Tikhonov regularization method. Additional data for solving the inverse problem was obtained on the basis of probing both via a single load and via combined probing modes. It has been found that it is most effective to use a combined loading mode and use a sufficiently wide frequency range when selecting sounding frequencies. The results of computational experiments on the reconstruction of six components of the prestress tensor are presented and analyzed, and recommendations are proposed for choosing the optimal modes of acoustic sounding.

In the deformable solid mechanics, there are concepts associated with continuum points (displacements, relative elongations, shifts) and a set of continuum points – an elementary volume (mass, energy, stresses). The role of such volume in the mechanics of composite materials is played by the representative volume element (RVE).This concept was first introduced by R. Hill (1963). Modern authors use the W.J. Drugan, J.R. Willis (1996) formulation. Based on the analysis of the RVE concept, we formulated its essential features: RVE is the minimum possible sample for numerical tests to determine the effective material parameters of the composite; under any RVE loading, its macroscopic stress-strain state is uniform. Its significance for the mechanics of composite materials is revealed: the existence of RVE for a composite is a criterion for applying the effective modulus theory to the analysis of its stress-strain state; the dehomogenization of a stressed-state composite material at a point is a solution to the micromechanics problem of the RVE stress-strain state determination; the characteristic size of RVE limits the size of the sampling grid in the numerical study. An iterative algorithm for constructing a representative volume of a periodic structure composite and its effective material thermoelastic characteristics is proposed. It is shown that the geometric shape of such a composition is a rectangular parallelepiped. The RVE construction algorithm for periodic compositions is extended to the composites statistically uniformly reinforced with continuous fibers. A method for modeling such materials with a following regular structure is suggested described: in the section perpendicular to the fibers, fiber centers should be located at the vertices of regular triangles. Examples of constructing RVE and thermoelastic material characteristics of specific compositions are given. The calculation results are compared with the data obtained using certified software products.

The use of C60 fullerites to create films on the surface of a solid substrate can be used not only to create coatings, but also to modify the surface layer of the substrate, which from a practical point of view can be in demand in such sectors of the economy as machine and instrument engineering. To analyze the process of formation of fullerite films on the substrate surface, a computer experiment was carried out, but the behavior of not a single fullerite or fullerene, as it was implemented in previous works of the authors, but a significant number of C60 fullerites deposited in the modeling area over a certain time interval and forming a "flow" was modeled. The substrate of the solid was an iron crystal Fe(100). The substrate temperature in the study was kept constant at the following values – 300 K, 700 K, 1150 K. The initial parameters of each individual fullerite were determined stochastically within the specified limits. The software package used to conduct the described computer experiment was – LAMMPS. The interaction of the atoms of the system with each other, during the simulation, was determined by the multiparticle potential (MEAM is a modified submerged atom method). The main result of the conducted computer experiment is that it was possible to simulate the deposition of C60 fullerites with the formation of a film on a solid substrate. The main regularities of the interaction of fullerite as a whole and fullerenes forming it, both with the substrate and with other fullerites forming the film, were revealed. And the analysis of changes in temperature and potential energy of the system, both during the deposition of fullerites and after its completion, allows us to talk about the stability of the resulting fullerite – substrate system.

A physically non-linear Maxwell-type constitutive relation with two material functions for nonaging elasto-viscoplastic materials is studied analytically in order to examine the set of basic rheological phenomena that it simulates, to enclose its application field, to obtain necessary phenomenological restrictions which should be imposed on its material functions and to develop identification and validation techniques. Characteristic features of loading-unloading-recovery curves family produced by the model with two power material functions (with four parameters) under loading and unloading at constant stress rates and subsequent rest are analyzed in uni-axial case and compared to general properties of stress-strain-recovery curves produced by the constitutive relation with two arbitrary (increasing) material functions (theorems 1 and 2). Their dependences on loading rate, maximal stress and material functions exponents are examined. Power functions are the most popular in creep models, elastoviscoplasticity, polymer rheology, hydrodinamics of non-newtonian fluids and simulation of superplastic flow. The analysis reveals several specific properties of theoretic loading-unloading-recovery curves produced by power model with four parameters that can be employed as the model applicability indicators which are convenient for check using test data of a material. They should be checked in addition to general applicability indicators for the Maxwell-type constitutive relation with two arbitrary material functions. A number of effective calibration procedures for the model in the class of power material functions are developed. They are more rapid and effective than general identification techniques for two arbitrary material functions developed previously. The first procedure employs a pair of stress-strain curves at different stress rates, the second one is based on a pair of loadingunloading- recovery curves with various maximal stress values and loading rates and the third one needs only one loading-unloading-recovery curve. The explicit expressions are derived for four material parameters via test data. They enable separate and direct evaluation of the material parameters without error accumulation. Identification techniques versions are considered and their advantages and shortcomings are discussed. The ways to minimize the error using additional tests are proposed.

The electro-mechanical properties of a ferroelectric film of barium strontium titanate (BST) film located on a silicon substrate depend on applied external strain. A significant dependence is observed for concentrations close to values, where a phase transition for the ferroelectric film occurs. A model of single-crystal BST film near the phase transition under uniaxial strain is studied by the thermodynamic theory of phase transitions. The material properties of the film obtained by the model are used for numerical study of the excitation of Rayleigh’ acoustic waves on the surface of the film-substrate heterostructure. Shifting the extrema of S-parameters, characterizing the efficiency of excitation of surface acoustic waves, is shown under the applied strain. The change of S-parameters for the first three resonances determined principally by the geometry of the interdigital electrodes is presented. The largest shift of resonant frequency is observed in a case of the second resonance that corresponds to Sezava wave.