Requirements to critical elements of transport and logistics systems have been increased due urbanization in the territories of Russia and the world. Bridge bearings, which perceive the vertical and horizontal loads from the bridge span, as well as absorb thermal expansion and contraction, shrinkage, seismic disturbances, etc. refer to such elements. Requirements to strength, durability, wear resistance, operation maintenance-free periods, etc., imposed on the bridge bearing are increasing due to a stable growth of loads on the bridge elements and increase in vehicle fleets. Recently, international and Russian companies have been engaged in development of new polymeric and composite materials, which have improved physical and mechanical, frictional, thermo-mechanical and rheological properties and can be used as a thin layer of sliding bearings bridges. A number of problems are outlined in studying material properties and geometric configuration of bridge bearings in order to rationalize the work of its structure. Three topical problems of solid mechanics are reviewed in the work. This is the identification of qualitative and quantitative patterns of the deformation behavior of modern antifriction polymer and composite materials as relatively thin sliding layers of bridge spherical bearings in order to formulate scientifically grounded recommendations for the selection of the interlayer material regarding the study unit operation. This is an analysis of the influence of the sliding layer material physical and mechanical, frictional, thermomechanical and rheological properties on the structure deformation as a whole and the change in the contact zone parameters, in particular. It is an analysis of the influence of the sliding layer geometric configuration on the structure performance. A significant decrease in the area of full adhesions of the contact surfaces, including up to 0, and the occurrence or increase in the area of the divergence of the contact surfaces (no contact) is observed during frictional contact taking into account the lubrication on the mating surfaces. The surface percentage on which the contact surfaces divergence (no contact) is observed decreases, on average by more than 2 times, if the sliding layer thickness is increased.

The problem of deformation and elastoplastic buckling of shells of revolution with a thick-walled elastic core under combined static and dynamic loading is formulated in a two-dimensional planar formulation based on two approaches: full-scale modeling within continuum mechanics and a simplified formulation based on the hypotheses of the theory of shells of the Timoshenko type and the Winkler foundation. Both approaches allow solving the problems of deformation and stability of non-shallow shells on the basis of Timoshenko's hypotheses, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian coordinate system as a reference one. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the work. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. The nonpenetration conditions are satisfied only in the active phase of the contact interaction; if the contact is broken, they are replaced by conditions on the free surface. In the second approach, the contact interaction of the elastic core with the shell is modeled by the Winkler foundation. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic core, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. Using both approaches, a numerical simulation of epy contact interaction problem of an elastoplastic cylindrical shell with a thick-walled elastic core at a quasi-static uniform external pressure is carried out. The study of the influence of the thickness and initial deflection of the shell, as well as the stiffness and thickness of the core, on the value of the critical pressure and the form of buckling has been carried out. Based on these calculations, a conclusion was made about a wide range of applicability of the Winkler foundation model.

The development of new and improvement of existing modes of thermomechanical treatment of metals and alloys in present conditions is impossible without development of appropriate mathematical models, that allow determining material characteristics during technological processes. Constitutive equations are the core, the main components that determine the quality of such models. Macrophenomenological theories of plasticity relying on processing the results of experiments on macrosamples, have become widespread as such in solving applied problems of solid mechanics. Taking into account the need to describe the memory of processes, the equations of this class have a complicated mathematical structure, require expensive tests (generally speaking, for complex loading) for each material, due to which they are not universal. In the past 15-20 years, constitutive models based on the introduction of internal state variables, of a multilevel approach, and physical theories of inelasticity (plasticity, viscoplasticity) became very popular. Models of this class are focused on describing the evolving structure (including microstructure), which ultimately determines the physical and mechanical properties of materials and constructions. As the physical mechanisms and their carriers are identical for wide classes of materials, the models of this class have significant versatility, including the prediction of behavior of new, not yet existing materials, to study the physical mechanisms of the occurrence of various effects, observed in macro experiments. Hardening is one of interesting effects observed in experiments on complex (including cyclic) loading (as compared to directional loading) of samples, made of various metals and alloys, arising from a significant evolution of the microstructure. Empirical data analysis made it possible to establish that the tendency to manifest this effect is usually experienced by metals and alloys with a low stacking fault energy (SFE). The paper provides a brief analysis of the experimental work and mathematical models describing the response of a material to complex deformation. It is noted that macrophenomenological theories do not allow one to describe in an explicit form the evolution of the microstructure and the carriers of plastic deformation and hardening mechanisms, thus they do not provide an opportunity to explain the physical reasons for the above effects. The purpose of this work is to develop, study and implement a multilevel elasto-visco-plastic model that allows describing the evolution of crystal lattice defects in materials with different SFE under different thermomechanical processing, different strengthening mechanisms at different structural-scale levels. In the framework of constructing a constitutive model, special attention is paid to the development of a submodel, focused on description of the evolution dislocations and barrier densities on slip systems. Kinetic equations for dislocation densities on slip systems make it possible to analyze the nucleation of dislocations due to the activation of Frank - Read sources, annihilation of dislocations of different signs on one slip system, interaction of split dislocations of intersecting slip systems with the formation of barriers. Relations for the description of hardening are given, taking into account the current density of dislocations and barriers. The general structure of the model and the relationship between the parameters of submodels of different levels are considered. An algorithm and a program of implementing the model were developed, the evolution of dislocation densities on slip systems was analyzed, and the intensity of hardening and the formation of barriers on split dislocations were obtained depending on the type of loading.

Thermomechanical behavior of metal-matrix composite materials is investigated. Boron carbide B4C and high-strength aluminum alloy 6061-T6 are used as strengthening particle and matrix materials, respectively. Microstructure of the metal-matrix composite takes into account the complex shape of particles explicitly. Isotropic elastoplastic and elastic-brittle models were used to simulate the mechanical response of the aluminum matrix and ceramic particles, respectively. To investigate the crack initiation and propagation in ceramic particles, a Huber type fracture criterion was chosen that takes into account the type of the local stress state in ceramic materials: bulk tension or compression. The composite material with a single particle of both the really observed in the experiment and ideally round shapes is considered. The influence of the residual thermal stresses arising during cooling of the composite material from the temperature of aluminum recrystallization to the room temperature on the character of plastic strain localization in the aluminum matrix and fracture of carbide particles and on the macroscopic strength of the composite under external tension or compression is studied numerically. Two-dimensional dynamic boundary value problems in the plane-stress and plane-strain formulations were solved numerically by the finite element method using the Explicit module of the Abaqus software package. VUMAT subroutine procedures incorporating the constitutive models were developed and integrated into the Abaqus solver. Based on the results of the numerical simulation, it was concluded that the residual thermal stresses arising during cooling lead to the change in the mechanism of the particle fracture from in-particle cracking to debonding and increase the strength of the composite subjected to tension after the cooling.

The paper deals with mathematical modeling of inelastic behavior and destruction of structural materials (steels and alloys) under simple, complex, isothermal and non-isothermal loads in repeated and long-term exposures to thermomechanical loads. The modeling is carried out on the basis of the applied theory of inelasticity, which belongs to the class of flow theories in combined hardening. The main provisions are formulated and a summary of the main equations of the applied theory of inelasticity is given. The material functions closing the applied theory of inelasticity are determined, and the connection of the defining functions with the material ones is given. Further, the results of some original experimental studies are considered, which are compared with the results of calculations based on the applied theory of inelasticity. In all studies, inelastic deformation is performed under conditions repeated and long-term exposures to thermomechanical loads. Inelastic deformation of AL-25 aluminum alloy samples under uniaxial tension-compression under both isothermal and non-isothermal cyclic loading is considered. Inelastic deformation under complex loading along the two-link polyline deformation paths with different deformation rates under high temperature conditions is studied on tubular 30HGSA alloy samples. Inelastic deformation of tubular stainless steel 304 samples under complex loading at elevated temperatures is considered. Soft cyclic loading is performed along two-link stress trajectories with different fracture angles. At the end of the links of the stress trajectory, exposure is carried out for 8 hours. The results of the calculations based on various theories used in the calculations are analyzed. Inelastic deformation and destruction of samples made of 12X18N9 stainless steel under rigid cyclic deformation under both isothermal and non-isothermal loads is considered. The duration of the loading cycle is 4 minutes, which allowed the effects of healing and embrittlement to appear at a high temperature. There is a significant difference (much higher) in the number of cycles to failure in common-phase and anti-phase modes of changes in force strain and temperature.

Acoustic anisotropy is a consequence of anisotropy of the mechanical characteristics of a solid. In metals, it is associated with microstructural anisotropy of mechanical characteristics, internal mechanical stresses and strains, including residual stresses and plastic deformations. Sensors measuring acoustic anisotropy do not require complex preparations of a metal surface, therefore it is easy to measure which makes it possible for measurement results to be used to quantify stresses and strains in metals based on the magnitude of phase shifts of the shear wave velocities of the orthogonal polarization. Acoustic anisotropy is one of the manifestations of the phenomenon of changes in the elastic properties of an acoustic medium caused by mechanical stresses and deformation (acoustoelastic effect). This makes it possible to use the effect of acoustic anisotropy for the development of quantitative methods of acoustic tensometric measurements, as well as methods of non-destructive testing, which enables effective quality controls and diagnostics of the residual life of structures and machine parts. The article describes the history of the discovery and theoretical substantiation of the acoustoelastic effect and the quantitative relationship of acoustic anisotropy with stresses and deformations, starting with the pioneering works of the twentieth century. The way of forming the theory based on nonlinear mechanics of continuous media is shown. The third part of the article is concerned with an overview of the current state of research. An analysis is presented of experimental works on the measurement of acoustic anisotropy in low- and high-carbon steels, aluminum alloys, as well as in composites and other structural materials. Special attention is paid to a review of studies on the relationship between acoustic anisotropy and plastic deformations and the applicability limitations of the acoustic method. It also provides a list of the main applied results related to the measurement and use of acoustic anisotropy to control the blades of compressors and gas turbine engines, pipe steels, welded joints, etc. A review is given of the main publications on system analysis and generalization of theoretical and experimental scientific results obtained by domestic and foreign researchers in the field of studying the acoustic anisotropy of metallic structural materials under conditions of uniaxial and complex stress states, plastic deformation, thermomechanical loading and fatigue fracture is given.

Within the framework of a multilevel mathematical model to describe the evolution of functional disorders of the human organism under the influence of environment factors, a mathematical model of the "meso-level" of the human respiratory system is developed. The article is deals with the development of the meso-level model - the formulation of a constitutive model to describe the airflow in a porous lung medium. Human lungs filled with small airways and alveoli, with air contained in them, are modeled by an elastically deformable saturated porous medium enclosed in an internal chamber with varying volume (movable walls). Conceptual and mathematical statements are presented. Air movement in the deformable porous medium of lungs is described by ratios of the mechanics of deformable solid body and filtration theory. As an element of this sub-model an analytical solution is obtained for an auxiliary geometrically linear problem of the all-round compression of an elastic thin-walled hollow sphere filled with air to determine the rate of mean stress of the two-phase medium of the lungs, taking into account the interaction between the lung tissue and the air contained in the lungs. To confirm the hypothesis on the acceptability of a linear solution of an auxiliary problem for large deformations, a similar problem was numerically solved in a geometrically nonlinear formulation. The results show that the obtained analytical solution is in satisfactory agreement with the solution of a similar problem in a nonlinear formulation both for calm and deep breathing, which indicates the possibility of using the former in the construction of the considered sub-model.

Currently, developments of the so-called Smart-constructions are relevant as they enable a real-time monitoring of changes in required values. Smart designs are widely used in the construction, automotive and aerospace industries. Technologies of creating products from polymer composite materials make it possible to introduce various sensors directly into the structure of a material, thereby create systems monitoring the state of structures. The most recommended for such implementation are fiber-optic sensors, which have a number of advantages over other sensors (luminescent, strain gauge, piezoelectric ones). However, when introducing the fiber-optic sensors, there is a number of difficulties, which are primarily associated with fragility of the optical fiber and lead to the breakdown of fiber-optic lines. As a result, it is necessary to develop a Smart-layer that will protect the optical fiber leads and will not significantly change the physical and mechanical characteristics. This paper aims to determine the stiffness and strength characteristics of samples made of polymer composite materials: reference samples, samples with embedded fiber-optic sensors, samples with embedded Smart-layers. In this work, a Smart-layer is understood as a coating that protects the fiber-optic sensors at the stage of implementation into a structure. The paper considers the following configurations of the Smart-layer: polymer reinforced mesh, polyamide and polyurethane layer. We analyzed and compared the influence of the embedded optical fiber and various configurations of the Smart-layer in the composite structure on the physicomechanical characteristics of the samples obtained under quasi-static loading (tension, compression, and interlayer shear). For a more detailed analysis of using the fiber-optic sensors and various configurations of the Smart-layer, the corresponding loads were simulated to assess their mechanical behavior. Based on the obtained physical and mechanical characteristics, a specific configuration of the Smart-layer was selected and justified for further researches.

The article discusses an approach to creating structural elements by forming periodic structures in the structure, developed based on the results of topological optimization. In the article, a metamaterial is understood as a structure with a complex internal periodic organization of strength elements, the details of which are significantly smaller than the typical dimensions of the final structural product. In this paper, the analysis is devoted to panels with a filler based on periodic structures to achieve the required mechanical characteristics. The transition from the results of the topological optimization is carried out on the basis of engineering analysis, taking into account the particularities of loading, fastening and operational effects on the structure. The use of topology optimization makes it possible to determine the distribution density of periodic structures in the material and to shorten the design cycle of a conventionally optimal design. As a first step solution, authors consider panels based on sandwich panels with the pyramidal fillers. Their application is considered in the aircraft, shipbuilding and construction industries. As basic technological solutions, efficient technologies are proposed - laser radiation sources and a high degree of automation. With these technologies, efficiency and costs of testing and certification of manufacturing are reduced in comparison to the standard approaches, when results of the topology optimization are made using expensive additive manufacturing. The proposed elements make it possible to reduce the metal consumption while achieving the same rigidity and strength of the structure. Another advantage of the proposed structures is their modularity and the ability to optimize the panel filling density without significantly changing the manufacturing process and design. As an application, we considered the possibility of creating a large-span panel for civil constructions, which is characterized by high specific loads with a significant span length (20 m).

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

Aluminum-fiber-reinforced plastics (GLARE) are promising aviation materials with increased characteristics of specific stiffness and strength, fatigue strength, impact resistance, and residual strength after impact. Nowadays, GLARE are used for making elements of the fuselage of the long-haul passenger aircraft Airbus A380, as well as some other elements of aircraft structures. The results of experimental studies of eigenfrequencies and damping coefficients of three-layer beams made with face sheets of five-layer GLARE and with a core made of polyimide foam are presented. The tests were performed using the method of free bending vibrations of cantilever samples. The dynamic parameters of the three-layer beams were calculated based on the analysis of amplitude-frequency characteristics obtained by the fast Fourier transform method. Mechanical characteristics of GLARE and filler samples are preliminary determined in static and dynamic tests. The damping factor of the core is determined by the dynamic mechanical analysis method. The core shear modulus is determined by measuring the flexural rigidity of manufactured three-layer beams in a quasi-static three-point bending test. Based on a comparison of the design data and the results of the experiments, it is shown that in dynamic tests, the flexural rigidity of three-layer specimens is reduced in comparison with the estimated values, which may be due to the peculiarities of changing the characteristics of the foam core under dynamic loading. The value of the damping factor of GLARE samples was ~0.02, the foamed core was ~0.08 and three-layer beams were ~0.067 in the range of vibration frequency up to 60 Hz.