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Based on a formulated mathematical model, numerical experiments were carried out to study the degradation of permafrost containing ice, accumulations of metastable preserved gas hydrates, and free gas under thermal and saline effects of solutions, taking into account the osmotic effect. Multivariate calculations were used to investigate the patterns and rates of permafrost degradation and methane release. A comparison of some model results with corresponding experimental data showed good agreement.

Based on filtration equations, the problem of CO₂ injection into a viscoelastic porous medium is considered. A two-dimensional problem of deformation of the porous skeleton, taking into account changes in porosity, was studied. For the model system of equations in a thin layer, an exact solution of the initial-boundary value problem was constructed.

The initiation of an inclined edge crack of mixed type (modes I and II failure) in a thin strip of sheet steel under tensile loading is considered. During rolling, an initially isotropic sheet metal typically develops significant anisotropy, characterized by differences in plastic properties along the rolling and transverse directions. The quadratic Hill yield criterion is used to describe plastic anisotropy. The failure process of such materials is described using the modified Leonov-Panasyuk-Dagdale model. Under complex loading, the crack path curves, so the trajectory deflection angle is determined using the force-based integral strength criterion. In the asymptotic representation, stress components near the crack tip account for non-singular terms (T-stresses). To obtain critical failure parameters of a strip with an inclined edge crack, a two-parameter strength criterion is proposed. The parameters in the analytical model are analyzed. Dimensionless geometric parameters of the structure are determined numerically using the finite element method. A system of two nonlinear equations is obtained for the critical length of the pre-failure zone and the critical load under complex stress conditions. Using Hill’s yield criterion, the shape and size of the plastic zone near the crack tip in a plastically anisotropic material are determined.

Results of computations of continuity and stress fields (in the Lagrangian formulation) near the crack front under creep conditions are presented and discussed. Calculations were performed using the finite element method to determine asymptotic distributions of stresses and continuity (damage) near the edge of the cut. For various material constant values, the shape of the damaged material zone under creep developing ahead of the crack tip was determined. Analysis of radial stress distributions obtained from finite element computations shows that the damage accumulation process alters the asymptotic behavior of stresses near the crack tip in a material described by a power-type governing equation. It was shown that, in the absence of damage accumulation, the numerical solution approaches the Hutchinson-Rice-Rosengren asymptotics, whereas accounting for the damage accumulation process affects the stress field near the cut or crack. Using finite-element radial stress and continuity distributions, characteristic sizes of zones dominated by different asymptotics near the crack tip can be determined.

Physical modeling of the forming process of a panel made of AK4-1 (Al-Cu-Mg) alloy under creep conditions at an annealing temperature of T = 420 °C was carried out. The forming process was simulated by tensile creep of cylindrical specimens to various strain values not exceeding 6 %. The tests yielded parameters of the classical Boyle-Norton model for steady-state creep. In accordance with the technological forming process under creep conditions, heat treatment (quenching and aging) was performed to restore the panel’s strength properties. Stress levels for fatigue tests were determined using stepwise cyclic loading with increasing stress amplitude. Tests were stopped upon the occurrence of plastic deformations. A comparison of fatigue resistance characteristics was performed for as-received specimens, specimens stretched under creep, specimens after heat treatment, and specimens with zero creep strain after heat treatment. It was shown that accumulated creep strain exceeding 2 % can reduce the fatigue performance compared to as-received specimens.

The problem of forced bending vibrations of a strip-bar with two cantilevers and a fixed finite-length section on one of the lateral surfaces is addressed. The classical Kirchhoff-Love model is used to describe deformation of the cantilevers, and the fixed section is described by a refined Timoshenko shear model accounting for transverse compression, modified to consider the prescribed displacements of the support element. Kinematic coupling conditions for the fixed section and cantilevers are formulated, and using Hamilton-Ostrogradsky’s principle, equations of motion, boundary conditions, and force coupling conditions for the bar sections are derived. An exact analytical solution is obtained for harmonic forced vibrations under the action of a harmonic transverse force at the end of one cantilever. Numerical experiments were conducted to study forced bending vibrations of a strip-bar made of D16AT duralumin. It was shown that vibrations of the unloaded cantilever are primarily determined by the prescribed displacements of the support element.

Results of studies on the reliability of mathematical modeling of metal plastic flow using the finite element method implemented in various software products are presented. The limitations of the finite element method and their influence on the description of deformation processes occurring during intensive shaping of a workpiece are analyzed. Special attention is paid to the study of regions with complex metal flow. A comparison of mathematical modeling results obtained using MSC Simufact.Forming, Transvalor Forge, SFTC DeForm, and QuantorForm QForm with parameters of actual products is carried out. It is shown that the results of mathematical modeling performed with the mentioned applied software products for complex metal flow studies are sufficiently reliable.

The problem of group classification is solved for equations describing vibrations of a nonlinear elastic plate in a gas flow. Exact solutions of these equations are presented, which can be used as benchmarks for numerical solutions.

This paper presents experimentally obtained shadowgraph images of the shock wave structure in an unsteady supersonic reacting flow of a hydrogen-oxygen mixture, generated by a spherical projectile flying at a velocity exceeding the self-sustained detonation velocity. The conditions for the formation of a stabilized oblique detonation wave, initiated by the high-speed projectile both in free space and in the presence of a wedge surface placed at a certain distance along the projectile trajectory, are determined.

This paper presents a comparative study of the efficacy of fibrous and particulate reinforcement in titanium-matrix composites under high-speed mechanical loading. The structural and phase composition of the synthesized materials is investigated using synchrotron radiation. It is found that, during laser processing, fibrous reinforcing elements dissolve in the titanium matrix to a lesser extent than particulate powder particles. This causes a reduced volume fraction of the resulting secondary phases, such as TiC and Ti₅Si₃C_x when using SiC fibers, as well as TiB and TiB₂ when using boron fibers. It is demonstrated that the use of fibers in the formation of titanium-matrix composite coatings enhances the impact strength of the resulting materials.