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No 5 (2025)
Articles
Temperature dependences of elastic properties of cubic crystals of simple substances. Review
Abstract
An review of the temperature dependences of the elasticity characteristics of cubic crystals of simple substances is given. It is shown that the general trend is a decrease in elastic modulus E, G and B with temperature due to the weakening of interatomic bonds due to thermal expansion of the crystal lattice. However, there are also anomalous dependencies, such as an increase in the shear modulus G with temperature, observed for BCC crystals of vanadium V, niobium Nb, tantalum Ta and FCC crystals of palladium Pd, platinum Pt. A common feature for the cubic crystals considered, except for BCC chromium Cr, is an increase in Poisson’s ratio n with temperature. The coefficient of elastic anisotropy A also shows a general upward trend, but for some crystals, BCC V, Nb, Ta and FCC Al, local minima are observed, and for BCC Cr and FCC Pd, maxima are observed.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):3-27
3-27
ON HOT FITTING OF A DISK ON A SHAFT TAKING INTO ACCOUNT IRREVERSIBLE DEFORMATION OF THE MATING PARTS OF THE ASSEMBLY
Abstract
The evolution of temperature stresses under the conditions of the assembly process operation of hot fitting a thin disk onto a round shaft is calculated within the framework of the theory of temperature stresses. The materials of the mating assembly parts are considered elastic-plastic with a yield strength dependent on temperature. The moments of time and places of origin of viscoplastic flows in the materials of the assembly elements, the features of the development of plastic regions, their attenuation and collapse are tracked. The level and distribution of residual stresses over the assembly parts are calculated.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):28-48
28-48
The elastic constants of an isotropic medium can have arbitrary values
Abstract
Using the example of the matrix of elastic constants of an isotropic material, it is shown that the Young’s modulus, shear modulus, volume modulus, and Poisson’s ratio can take any real values. In this case, the positive definiteness of the matrix of elastic constants is not mandatory, as is traditionally assumed. The positivity of the specific strain energy also occurs when the matrix of elastic constants is not positive definite. It is sufficient for the invertibility of the relations of Hooke’s law to require the non-degeneracy of the matrix of elasticity constants. Graphs of Young’s modules, volume and Poisson’s ratio depending on the ratio of Lame constants are given.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):49-70
49-70
Development of a complex method of studying filtration, fracturing and sand production processes in gas reservoirs of the Arctic shelf to determine optimal well operation parameters
Abstract
The paper presents the results of a comprehensive study of fracture, filtration and sand production processes in weakly cemented reservoirs of one of the gas condensate fields of the Arctic shelf of Russia. A modified multidisciplinary scientific approach has been developed and implemented, aimed at solving the problems of ensuring safe operation of wells, justifying effective modes of their operation and reducing the sand production risks. The research methods are based on multilateral study of core material properties by means of geomechanical modeling of mechanical and filtration processes in the vicinity of wells, “hollow cylinder” tests to study sand production processes in wells, scanning electron microscopy, micromineralogy, computed tomography and digital core analysis. Special emphasis was placed on the analysis of changes in reservoir structure as a result of sand production processes, taking into account the mineral composition of the matrix and the dislodged sand. Experimental results allowed to determine for the considered field: a) evolution of deformation and filtration properties of rocks in the near-wellbore zone; b) values of critical stresses leading to wellbore wall failure; c) type and nature of rock failure; d) parameters of sand production processes and mechanisms of associated destruction of the reservoir matrix; e) reservoir properties of rocks. Based on the research results, the optimal parameters for safe and efficient well operation have been determined, including allowable drawdowns to reduce the sand production risks and maintain wellbore stability; the nature of well contour failure and the risks of damage to downhole equipment; and the optimal characteristics of downhole filters. The results of this research are intended to contribute to the development of technologies for creating new solutions aimed at improving the efficiency of hydrocarbon production, reducing the risks of sand production and wellbore wall failure, deterioration and breakdown of downhole equipment.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):71-101
71-101
On one estimate of the critical value of the J-integral under normal compression around a crack-like defect in a thin adhesive layer
Abstract
On the basis of one- and two-parameter failure criteria of mixed mode loading of I+II crack-like defect of adhesive layer, the critical value of J-integral under normal compression is estimated. The additive decomposition of the J-integral into energy densities and consideration of the sign of hydrostatic pressure are assumed to be valid. It is shown that when the critical value of the J-integral of mode II exceeds significantly the critical value of the J-integral at normal rupture, the critical value of the J-integral at normal compression is much inferior to the analogous characteristic at compression.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):102-108
102-108
Biomechanical Modeling of Osteotomies of the First Metatarsal Bone in Normal and Osteoporotic Conditions
Abstract
Hallux valgus is a widespread pathology. Osteotomy of the first metatarsal bone is the gold standard for its treatment. The success of this surgical intervention depends, among other factors, on the stability of the “bone-fixation” system. Previous studies assessing the biomechanical properties of various first metatarsal osteotomies have examined the influence of osteotomy type, degree of fragment displacement, as well as the number and positioning of screws. In these studies, the biomechanical properties of bone tissue corresponded to normal values of conventionally healthy patients. Older patients are characterized by a high prevalence of osteoporosis. This disease manifests in reduced mineral density and mechanical properties of bone. The effect of osteoporosis on the biomechanical parameters of first metatarsal osteotomy models has not been previously studied. The aim of this work was to evaluate the stability of first metatarsal osteotomies under normal bone density and osteoporotic conditions, as well as to assess the robustness of biomechanical models of the most common osteotomy types to minor variations in screw positioning and bone-cutting plane geometry. For this purpose, 36 biomechanical models of scarf and chevron osteotomies were created, varying screw placement, bone-cutting plane geometry, cortical thickness, and elastic modulus. Finite element analysis was used to assess the stress-strain state of the osteotomy models. Model validation was performed based on natural cantilever bending tests of first metatarsal osteotomies in universal testing machine. The study demonstrated the robustness of scarf and chevron osteotomy models to minor changes in geometric parameters. Chevron osteotomy proved more stable than scarf. Additionally, scarf osteotomy generated significantly higher bone stresses compared to chevron. It was found that even under osteoporotic conditions, both osteotomy types can provide sufficient stability and strength in terms of screw breakage and bone tissue damage.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):109-123
109-123
Shock waves in a one-dimensional semi-infinite hyperelastic rod
Abstract
The excitation of a harmonic wave in a semi–infinite incompressible hyperelastic one-dimensional rod (material according to the Mooney–Rivlin model) leads to the formation and propagation of shock wave fronts arising between half-waves of the initial harmonic wave moving at different speeds. Shock wave fronts lead to the absorption of slow-moving parts by faster ones and, consequently, reduce both kinetic energy and elastic deformation energy with the corresponding release of heat. The explicit Lax–Wendroff difference scheme in combination with the finite element method is used to solve geometrically and physically nonlinear equations of motion.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):124-143
124-143
On the Relationship Between Classical Mathematical and New Physical-Mathematical Theories of Metal Plasticity
Abstract
Currently, there are two theories of metal plasticity in solid mechanics: the classical mathematical theory of plasticity [1, 2] and the physical and mathematical theory of plasticity [3]. Both theories are used to solve applied problems of plasticity, in particular, in the development and improvement of technological processes of metal pressure treatment [5–7]. This paper examines the relationship between the above-mentioned theories. Based on the analysis of the initial postulates and principles, the disadvantages and advantages of the theories for solving problems of theoretical design of technological processes of metal pressure treatment are identified. The analysis allows us to assert that the physical and mathematical theory of plasticity is a more general theory, which includes the mathematical theory of plasticity as a special case and which does not have the disadvantages of the latter. It follows from this that the physical and mathematical theory of metal plasticity is an important scientific achievement in solid mechanics.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):144-161
144-161
On the use of the Stieltjes integral for calculating of mechanical work in relation to adhesive contact
Abstract
A procedure for regularization of the Stieltjes integral in the case of a common breaking point for integrand functions is described. Using this procedure, it is possible to determine the Stieltjes integral, which represents mechanical work in accordance with the energy conservation law. The physical validity of the obtained results is confirmed by a number of examples. In particular, the regularization procedure makes it possible to calculate the energy dissipated during an abrupt change in the state of the elastic suspension.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):162-184
162-184
On elastic-plastic deformation of a rectangular plate on a cylindrical surface under normal loading
Abstract
In the approximation of the cylindrical bending model, a solution is obtained for the problem of elastic-plastic deformation of a thin plate bent along a cylindrical surface, taking into account the resulting longitudinal forces, under boundary conditions of the rigid or generalized elastic fixation type. When describing the plate, standard Kirchhoff–Love kinematic hypotheses were used, which made it possible to reduce the problem to a system of ordinary differential equations. A numerical solution is obtained for this system for rigid and generalized elastic fixation conditions.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):185-205
185-205
A COMPREHENSIVE APPROACH TO THE SEISMIC ANALYSIS AND DESIGN OF REINFORCED CONCRETE BUILDINGS AND STRUCTURES
Abstract
This paper presents a modern comprehensive approach to the analysis and design of reinforced concrete buildings, taking into account soil-structure interaction (SSI) under seismic loading. As a case study, the approach was applied to the seismic analysis of a five-story reinforced concrete building. The external seismic impact was defined using a three-component accelerogram corresponding to a magnitude-9 earthquake. The interaction between the building and the soil foundation was implemented through an SSI interface (soil-structure interaction). To eliminate the influence of wave reflections from the boundaries of the finite soil domain, a perfectly matched layer (PML) was employed. The reinforced concrete structures were modeled using a method that combines solid elements for concrete with beam elements for reinforcement. The simulations were performed using distributed computing technology on a high-performance computing cluster. A study of the failure mechanisms of the structure was carried out. A comparative analysis was conducted between the input accelerogram at the free surface of the soil and the acceleration recorded at the building’s foundation slab. With appropriate adaptation and the use of high-performance computing systems, the proposed methodology can be applied in engineering practice to improve the reliability of seismic analysis of reinforced concrete buildings.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):206-226
206-226
Computer simulation of the stress-strain state of a concrete gas pipeline in a swamp with compensators installed at its ends
Abstract
The technologies of construction and major repairs of main pipelines provide for the replacement of pipes with anchor devices and reinforced concrete weights with three-layer pipes consisting of a steel pipe, an outer continuous weighting reinforced concrete coating and an insulating layer located between them. This three-layer pipe is designated as a concrete-coated pipe in scientific and technical literature. When such pipes are used in difficult natural and climatic conditions, they float. Floating sections of the gas pipeline are classified as emergency and are taken out of operation. In this article, the problem of the stress-strain state (SSS) of a gas pipeline section in a swamp is stated and solved using the finite element method after the following changes were made to its design: pipes with reinforced concrete weights are replaced with concrete-coated pipes; G-shaped compensators are installed at the ends of the gas pipeline section in the swamp. For a section of the gas pipeline in a swamp, at the ends of which compensators have not yet been installed, the limit values of the operating parameters were found that determine the change in the shape of the pipe bend, in which the deflection arrow becomes directed upwards, and it can lead to the gas pipeline floating up. In the flooded underwater part of the gas pipeline section in a swamp with compensators installed at its ends, when the pipe bends, the deflection arrow remains directed downwards, there are no prerequisites for its floating up. The gas pipeline along the entire length of the section is stretched in the longitudinal direction, while in the flooded underwater part there is a uniform stretching of the pipe. At the ends of the calculated section, the values of the tensile-compressive stresses of the pipe in the longitudinal direction are determined from the longitudinal forces specified by the boundary conditions.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.. 2025;(5):227-260
227-260