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The creep rupture strength of tensile bars in an aggressive environment is studied analysis. The time to rupture of the bars is analyzed as function of the shape of their cross section. It is shown that the influence of the aggressive environment on the creep rupture strength of the bars is determined by the diffusion of its elements into the bar material, resulting in a decrease of its creep rupture strength. The diffusion of the aggressive environment into the bar is studied using an approximate method of solving the diffusion equation taking into account the motion of the diffusion front. Bars with different cross-sectional shapes are considered using Rabotnov kinetic theory. It is shown that under the same tensile stress, the bar with a circular cross-section has minimum time to failure.

It is shown that, in the planar case, the system of constitutive equations of the linear elasticity theory should contain five independent equations. n the classical theory, only three equations are formulated, while the other two are contained in implicit form in the postulate of diffeomorphism, which the assumption of smoothness of the displacement field. A closed elasticity model is constructed without the assumption of diffeomorphism, and it contains a structural parameter having a dimension of length. It is shown that, in a static version, macrodeformations depend on stresses and the second derivatives of stresses by the coordinates, while there is dispersion of longitudinal and transverse waves in the dynamics.

The generalized rheological method is used to construct a mathematical model of small deformations of a porous media with open pores. Changes in the resistance of the material to external mechanical impact at the moment of collapse of the pores is described using the Mises~--- Schleicher strength condition. The irreversible deformation is accounted for with the help of the classic versions of the von Mises - Tresca - Saint-Venant yield condition and the condition that simulates the plastic loss of stability of the porous skeleton. Within the framework of the constructed model, this paper describes the analysis of the propagation of plane longitudinal compression waves in a homogeneous medium accompanied with plastic strain of the skeleton and densification of the material. A parallel computational algorithm is developed for the study of the elastoplastic deformation of the porous medium under external dynamics loads. The algorithm and the program are tested by calculating the propagation of plane longitudinal shock waves of compression and cylindrical cavity of in an infinite porous medium. The calculation results are compared with exact solutions, and it is shown that they are in good agreement.

This paper presents the results of a study of the shapes of axisymmetric bodies with minimum penetration resistance and maximum depth of penetration into the plastic soils. Optimum shapes of bodies of revolution of predetermined length and cross-sectional radius with generatrices represented by line segments are obtained by a modified method of local variations. The problem is solved using a binomial quadratic model of local interaction, including inertial and strength terms containing constant and Coulomb frictions. The resistance forces and the depth of penetration of cones and the obtained bodies of optimal shape are determined at different penetration velocities.

A mathematical model is developed for an inhomogeneous thermoelastic prestressed half-space consisting of a stack of homogeneous functionally graded layers rigidly attached to a homogeneous base.аEach component of the inhomogeneous medium under an initial mechanical stress and temperature.аConsistent linearization of the constitutive relations of nonlinear mechanics of a thermoelastic medium is performed using the theory of superpositionа of small deformations on finite deformations with the inhomogeneity of the medium taken into account.аIntegral formulas for studying dynamic processes in inhomogeneous prestressed thermoelastic media are derived.

The effect of a small added mass on the frequency and shape of free vibrations of a thin shell are studied using shallow shell theory. The proposed mathematical model assumes that mass asymmetry even in a linear formulation leads to coupled radial bending vibrations. The interaction of shape-forming waves is studied using modal equations obtained by the Bubnov-Galerkin method. Splitting of the bending frequency spectrum is found which is caused not only by the added mass, but also shell wave-formation parameters. The ranges of the relative lengths and shell thicknesses are determined in which the interaction of bending and radial vibrations can be ignored.

An electromagnetic viscoelastic problem is solved for piecewise-homogeneous plates. The problem is reduced to solving a sequence of problems of electromagnetoelasticity with complex potentials. General representations of approximation functions for multiply connected domains and the boundary conditions for their determination are given. An analytical solution of the problem for a plate with one inclusion and an approximate solution to the plate with a finite number of inclusions are obtained. The change in the electromagnetoelastic state is investigated numerically as a function of time, the properties of the plate and inclusion materials, and the distance between the inclusions.

The influence of hydrogen on the strength and ductility of 30KhGSA and EI659 steels in quasi-static and shock-wave tests was studied experimentally. The sensitivity of the steels to hydrogenation in air under normal pressure or in hydrogen at a pressure of 25 MPa was determined from the results of tests of samples in the initial state and samples pre-hydrogenated at a temperature of 773 K and a hydrogen pressure of 50 MPa for 24 h. It is found that EI659 steel doped with tungsten and vanadium is less sensitive to to hydrogen than 30KhGSA steel doped with manganese and chromium.

A mathematical model is proposed which describes the interrelated processes of unsteady elastoplastic deformation of stacks of woven metal wire meshes and wave processes in pore gas in a two-dimensional axisymmetric approximation. The nonlinear equations of the dynamics of two interpenetrating continua are solved numerically using a modified Godunov scheme. The problem of explosive loading of a multilayer shell with an internal permeable deformable layer is solved. The results of numerical solutions are compared with experimental data. The influence of the gas-permeable layer on the shell deformation is determined.

The effect of the position of a passive porous coating on natural disturbances in a hypersonic boundary layer is studied experimentally. The experiments are performed in the flow around a sharp cone aligned at a zero angle of attack with the free-stream Mach number M_∞ = 5,8, stagnation temperature T₀ = 370±5 К, and unit Reynolds numbers Re_1∞ = 2,6 x 106, 4,6 x 106, 6,6 x 106, and 10⁷ m^-1. The wave characteristics of the boundary layer are calculated with the use of the linear stability theory for flow parameters corresponding to experimental values. A comparison of experimental and predicted results shows that the presence of a porous coating in the region where the second mode is unstable leads to reduction of its amplitude at the measurement point, whereas the presence of a porous coating in the region of second mode stability leads to enhancement of the amplitude.