An analytical model of high-velocity interaction between a deformable mesh striker (grid) and a semi-infinite deformable barrier, both modeled as rigid-plastic bodies, is proposed. The so-called “normal” impact of the grid against the barrier is considered: it is assumed that at the initial and subsequent moments of time, the grid plane is parallel to the surface of the barrier half-space, and the grid velocity vector is perpendicular to the barrier surface. The dependence of the grid penetration depth on the impact velocity V0 (1÷5 km/s) and the geometric parameters of the grid, which are characterized by a single dimensionless parameter γ (0 ≤ γ ≤ 1) equal to the ratio of the wire diameter to the grid period, is investigated. During the interaction of the mesh striker with the barrier, generally speaking, there are two modes of string penetration into the barrier. The first mode occurs when the plastic deformation zones around the strings do not overlap and the strings penetrate the barrier independently of each other. The second mode occurs when the plastic deformation zones overlap. This mode takes place when the grid aperture is comparable to or smaller than the diameter of the strings from which the grid is woven. The model proposed in this work reproduces both of the aforementioned modes of grid penetration into the barrier, which can be conditionally divided into two intervals using the parameter γ: 0 < γ < γ* and γ* < γ < 1. Within the framework of the adopted model, the value γ* ≈ 0.43 is universal and does not depend on the materials of the grid and the barrier. The calculation results obtained with the proposed model allow estimating the depth of the crater in the barrier formed as a result of the impact. It is shown that with an increase in the parameter γ, the crater depth relative to the grid period increases for 0 < γ < γ* and decreases for γ* < γ < 1. The crater depth relative to the wire diameter decreases with increasing γ, experiencing a sharp drop near γ = γ*. The peak values of the penetration depth relative to the grid period at γ = γ* increase with increasing V0.

The paper presents three approaches for estimating the effective deformation properties of composite materials with a periodic arrangement of inclusion centers and random values of their radii. All the approaches considered in the article for determining the effective deformation characteristics are based on the application of the method of asymptotic averaging of differential equations of elasticity theory with rapidly oscillating coefficients. The size of the inclusions is considered as a random variable with a given distribution law, the main characteristics of which are determined by the methods of probability theory. The approaches for determining the properties of composite materials described in the paper make it possible to obtain not only the average values of the effective characteristics, but also the possible range of their values. It is shown that the symmetry condition of the probability density function for the distribution of the inclusion radius does not imply the symmetry condition of the probability density function for the distribution of the effective components of the stiffness tensor of composite materials with a periodic structure of inclusion centers, i.e., their average values do not lie at the centers of the intervals of their possible values. For layered media, analytical dependencies for determining the effective stiffness tensor were obtained, similar to the dependencies for the averages of a periodic structure.

One possible approach to considering the fracture mechanics of a laminated composite in the low-velocity impact damage zone is proposed. This approach is based on the assumption that upon impact, fragmentation of the matrix of the composite package’s plies occurs, leading to a reduction in its transverse shear elastic characteristics. Unlike isotropic materials, in a laminated composite, transverse shear deformations can significantly affect the stability of the package due to the high anisotropy of its stiffness characteristics in the longitudinal and transverse directions relative to the ply layup plane. As a result of matrix fragmentation, conditions may arise for local loss of stability of the composite in the impact damage region, which will occur predominantly in the shear mode. To substantiate this assumption, a series of computational parametric studies was performed, utilizing available experimental data, the results of which are presented in the article. The studies were conducted using numerical models of the composite. The numerical models were verified by comparing the results of numerical and analytical solutions. Nonlinear calculation methods were used to assess the strength of the damaged zone under post-critical deformation. The research methodology consisted of identifying the degree of influence of the reduction in the transverse shear modulus of the composite package in the damaged zone on its local stability. Parametric studies also included an assessment of the influence of the damaged zone size on its critical buckling stresses. Overall, the results obtained confirmed the validity of the proposed approach to considering the fracture mechanics of the composite in the impact damage zone.

This work is devoted to constructing an analytical solution to the problem of non-stationary wave propagation in a thin anisotropic plate of large extent. The solution approach is based on the superposition principle and the Green’s function method. Its essence lies in relating the desired solution to the load using an integral operator of the convolution type in spatial variables and time. The kernel of this operator is the Green’s function for the anisotropic plate. It represents the normal displacements in response to the action of a unit concentrated load. The Dirac delta function is used for the mathematical description of the concentrated load. Spatial non-stationary Green’s functions for the Timoshenko anisotropic plate have been constructed for the first time using analytical methods. An elastic medium with a single plane of symmetry, geometrically coinciding with the midplane of the plate, is considered as a model of the anisotropic material. The motion of the plate is considered in a Cartesian coordinate system. At the initial moment of time, the plate is in an unperturbed state. For the solution, integral Laplace transforms in time and two-dimensional integral Fourier transforms in coordinates were used. The Laplace originals of the sought functions were constructed using the second expansion theorem for the Laplace transform. The Fourier originals were constructed using the relationship between the Fourier inversion integral and the Fourier series on a variable interval. The obtained Green’s functions made it possible to represent the desired non-stationary deflection and rotation angles as triple convolutions of the Green’s functions with the function of the non-stationary load. The rectangle method was used to calculate the convolution integral and construct the desired solution. The results of the solution are presented graphically.

A nonlinear two-mode model of self-excitation of vertical-torsional vibrations of a wire in a wind flow in the presence of ice deposits has been developed. Self-excitation of vibrations is interpreted as an instability of the equilibrium state due to the occurrence of a transverse aerodynamic force during twisting of the wire (Magnus effect) and the dynamic coupling of vertical and torsional vibrations. The wire is considered as a heavy flexible thread with averaged characteristics, fixed between two supports of equal height. The tension of the wire is assumed to be constant along the length but variable in time. The static and dynamic components of the total tensile strains are written in a quadratic approximation. The shapes of vertical and torsional vibrations relative to the static equilibrium position are approximated by a quadratic function close to the first partial modes. The equations of wire vibration are written in the form of Lagrange equations of the second kind. The generalized coordinates, measured from the static equilibrium positions, are the changes in the sagitta and the rotation angle of the wire cross-section at the span center. A group of criterion dimensionless parameters of the model is determined, and based on data on the technical characteristics of high-voltage transmission line wires, the practical ranges of their variation are identified. Based on linearized equations, conditions for self-excitation of vibrations are obtained in the form of a dependence of the critical wind speed parameter on a parameter that generally characterizes the possible inertial and geometric characteristics of ice deposits.

The paper investigates the thermomechanical characteristics of modified composites reinforced with fibers on whose surface randomly arranged and intertwined special nanostructures — whiskers — are grown. Such a composite is considered as a transversely isotropic material with an axis of symmetry along the fiber. It is assumed that the composite phases — fiber, whiskerized interphase layer, and matrix — are isotropic materials. The influence of the volume fraction of inclusions in the interphase layer, the thickness of the interphase layer, and the volume fraction of the modified fiber on the effective thermal conductivity of the studied composite is investigated. The effective coefficient of thermal expansion of the interphase layer is also studied. The degree of influence of the whisker volume fraction and the coefficients of thermal expansion of the whiskers and matrix on the effective coefficient of thermal expansion of the interphase layer is assessed. Particular examples are considered where the whiskers are CNTs. The effective thermal conductivity is modeled using a two-stage homogenization procedure. At the first stage, the effective properties of the whiskerized interphase layer are determined. At the second stage, the effective properties of the entire composite are determined using a model of a medium with cylindrical inclusions generalized to a multiphase medium. The effective coefficient of thermal expansion of the interphase layer was studied using Levin’s formula. For the composites under consideration, a simplified relationship between the effective expansion coefficients and the effective elastic moduli is proposed. The paper proposes methods for changing the effective thermal conductivity of the modified composite and the effective coefficient of thermal expansion of the whiskerized interphase layer of the modified composite through the characteristics of microstructural parameters. It was found that modifying the fiber surface with carbon nanotubes makes it possible to increase the effective thermal conductivity of the fibrous composite in the plane perpendicular to the fiber axis by more than 7 times, and in the direction along the fiber axis by more than 1.3 times.

The oxidation resistance of a coating on a C/C-SiC composite substrate, formed by the slurry-fusion method from a powder mixture in the ZrSi2-MoSi2-ZrB2-Si system, has been investigated. Oxidation resistance tests were carried out under conditions of interaction with a high-speed air plasma flow up to 2200°C. The performance of the coating is ensured by the formation and evolution during operation of a heterogeneous oxide film based on borosilicate glass modified with zirconium, which is an effective barrier to oxygen diffusion, contributing to the passivation of oxidation processes. An increase in operating temperatures above 1750-1800°C leads to the evaporation of the glass phase from the surface and the formation of a porous thermal barrier layer based on ZrO2 containing secondary phases Mo/MoO2, Mo3Si, and Mo5Si3. The temperature gradient observed across the coating thickness promotes partial retention of the glass phase in the inner layers due to a decrease in vapor pressure, which slows down oxygen diffusion into the material. The temperature-time limits of performance, mass loss characteristics, catalytic activity, emissivity of the coating, as well as the main factors limiting the effectiveness of its protective action were determined.

The elastic-plastic deformation of a thin adhesive layer by elastic arms of a DCB specimen, corresponding to normal fracture loading, is considered. The thickness of the adhesive layer is included in the variational equilibrium condition as a linear parameter. Based on finite element analysis, the influence of the linear parameter on the tendency for the formation of irreversible deformation regions and the value of the J-integral was investigated. A square element with side length equal to the linear parameter is defined as the structural element of the layer. Two adhesives with different mechanical properties are considered. It is shown that for an adhesive with pronounced plastic properties in the pre-fracture state, two zones of plastic deformations with different signs of hydrostatic pressure, separated by an elastic region, are observed. The zone with positive hydrostatic pressure is localized at the tip of the crack-like defect, and its size, like the size of the secondary region, is related to the linear parameter. As the linear parameter decreases, the region with negative hydrostatic stress approaches the plastic region with tensile stresses. For a quasi-brittle adhesive, a plastic region with negative hydrostatic pressure is not formed. At the same time, the formation and localization of a plastic region with tensile stresses at the tip of the crack-like defect is observed from a certain value of the linear parameter. A decrease in the linear parameter leads to a decrease in the size of the plastic region with positive hydrostatic pressure. In the plastic regions, there is a practical coincidence of the two principal stresses of the layer acting in directions orthogonal to the fracture. It is shown that the value of the J-integral in the critical state exhibits computational convergence as the linear parameter decreases. The elastic-plastic solution in a layer of finite thickness leads to a larger J-integral value compared to the elastic solution, which is due to the influence of dissipation. The linear parameter tending to zero eliminates the difference in the corresponding J-integral values.

The paper investigates the rheonomic behavior of rubber used in tires in the breaker under quasi-static loading with a constant speed. Based on the experiments conducted, it is concluded that viscous properties should be taken into account even for sufficiently slow quasi-static loading. The reason is a jump in speed at the beginning of loading. Such loading is realized in an experiment called a puncture test. The essence of this test is to measure the force depending on the penetration depth of an indenter as it is inserted into an inflated tire in the radial direction until rupture or contact with the wheel rim. Loading in such a test occurs quite slowly. It can quite be considered quasi-static. Thus, the conducted study of the rheonomic behavior of breaker rubber and the rubber-cord layer of the breaker is of interest from an applied perspective. Two models were used to approximate the experimental results. The first is a generalized Maxwell model, the second is its modification based on the idea of a reference curve. The material constants of the models under consideration were obtained. The use of the Maxwell model did not lead to a sufficiently accurate description of the measured stress-strain diagrams for different strain rates. However, it is shown that the stress-strain diagrams are well approximated using a model based on a reference curve. To analyze the effect of viscosity on the development of plate deflection, the problem of cylindrical bending was solved numerically. It was found that under slow loading, the deflections differ significantly depending on the loading rate, both when using the geometrically linear model and the geometrically nonlinear model.