The values of elastic wave propagation velocities in isotropic and anisotropic materials largely determine the time of elastoplastic deformation and fracture of solids under impact loading. The features of elastic wave propagation in elements made of anisotropic auxetic materials characterized by negative Poisson’s ratio values are considered. In anisotropic materials, the velocities of elastic wave propagation depend on the direction; in the presence of negative Poisson’s ratio values in continuous solids, there are Poisson’s ratio values in perpendicular directions that significantly exceed the limit of 0.5. Using the finite element method in a dynamic formulation, the impact loading of plates, compact cylinders, and thin cylinders made of single-crystal zinc against a rigid wall is simulated in a three-dimensional formulation. The deformation modeling of bodies was carried out using tetrahedral finite elements, traditionally used in armor-ballistic problems. The features of elastic wave propagation processes in bodies from thin cylinders to thin rods with a continuous change in shape factors determined by the ratio of cylinder height to its diameter are shown. The influence of the sign of the Poisson’s ratio in an anisotropic material on the coefficients of restitution of a body impacting a rigid wall is considered. Parametric studies of the influence of the absolute value of the negative Poisson’s ratio on the coefficient of restitution after impact against a rigid wall are conducted. The difference in wave propagation processes when changing the symmetry axes of the zinc single crystal relative to the symmetry axes of the cylinders is shown. To minimize the number of characteristics affecting the longitudinal wave propagation process, it is convenient to conduct research on anisotropic materials, since density does not vary, only Young’s moduli and Poisson’s ratios are variable. It is shown that the longitudinal wave propagation velocity depends on one pair of Poisson’s ratios measured in the plane perpendicular to the propagation direction, while deformation in this plane is determined by another pair of Poisson’s ratios, which is important for auxetic materials.

This article presents an approach to solving coupled problems of wave interaction in the ground with an obstacle, where a segment of a cylindrical shell is used as the obstacle. The ground motion was modeled using an elastic medium model, and the Kirchhoff-Love shell was taken as the obstacle model. A cylinder infinite along its own axis is considered. During the solution, the ground motion was considered, surface influence functions for it were found, as well as displacements and stresses in the incident harmonic cylindrical wave that directly affected the obstacle. Since wind screens having the same shape as the incident wave possess the most effective vibration-absorbing properties, a cylinder segment was considered as the obstacle. The contact conditions were taken as equality of displacements of the medium and the obstacle. The main task was to determine the displacements at any point in the ground after the wave passed the obstacle. One of the problems in solving this class of problems is finding an analytical solution for the fixation conditions of the vibration-absorbing obstacle other than hinged ones. To solve this problem, the method of compensating loads was used, which allows satisfying any boundary conditions corresponding to various real methods of fixing vibration-absorbing screens. Thus, the solution of the problem was divided into three stages. At the first stage, the motion of the cylindrical shell under the influence of a cylindrical harmonic wave was specified. At the second stage, the motion of the elastic medium and the cylindrical wave induced in it was studied. Next, the coupled problem of wave-obstacle interaction in an elastic medium was solved. The solution was obtained for a complete cylindrical shell. Then, displacement influence functions were determined, and based on the method of compensating loads at cylinder points corresponding to the boundaries of the vibration-absorbing screen, the boundary conditions were satisfied. As an example, boundary conditions corresponding to rigid clamping were considered.

Resonant vibrations of a circular symmetric three-layer sandwich plate under the action of an axisymmetric harmonic annular load are investigated. For thin load-bearing layers, the classical Kirchhoff hypotheses are adopted, according to which the deformed normal to the middle surface of the layer is incompressible, remains straight and perpendicular to it. The core is considered light and thicker. During its deformation, the normal also remains incompressible and straight but ceases to be perpendicular to the middle surface, i.e., it obeys the Timoshenko hypothesis. The plate temperature is assumed to be uniform and varying with the ambient temperature. Its influence on the elastic parameters of the layer materials is taken into account. A general system of differential equations for transverse isothermal vibrations of an asymmetric circular three-layer plate is used, which is also valid in the considered case. For the investigated sandwich plate, it is simplified and reduced to two equations regarding the plate deflection and additional shear in the core. Clamping and hinged support of the contour are considered as boundary conditions. The initial motion conditions are assumed homogeneous. The boundedness of the solution at the plate center is used. The solution of the initial-boundary value problem for the sandwich plate is obtained by expanding the desired deflection and relative shear into a series using a system of eigenfunctions, which have the same form for the adopted boundary conditions. Transcendental equations for finding the corresponding eigenvalues are written out, and their values are presented in a table. Graphs of the fundamental natural frequency variation depending on temperature are constructed. Calculation formulas for deflection and relative shear are presented. The numerical analysis results are presented in the form of graphs of the plate deflection dependence on temperature and the coordinate of the inner ring of the force load.

The widespread use of composites in mechanical engineering, aerospace technology, construction, calculations of buildings and structures taking into account their interaction with foundation soils, as well as calculations of underground structures and mine workings together with the surrounding rock mass (soils and rocks are essentially composites of natural formation) poses the task of a reliable, fast, and convenient method for determining the mechanical characteristics of such composite materials. In geomechanics, determining mechanical properties is often time-consuming and very costly, and sometimes these properties cannot be determined experimentally. Thus, it can be stated that currently in engineering and scientific activities, the problem of determining the effective characteristics of composite materials is relevant. This work is a continuation of studies [1,2] on determining the effective stiffness tensor and, accordingly, the effective technical characteristics of composite materials (Young’s moduli, shear moduli, and Poisson’s ratios) using probabilistic methods and the asymptotic averaging method. The proposed approach allows reducing the problem of determining the effective mechanical characteristics with random values of the composite material phase characteristics to solving a set of standard periodic problems on a cell, without resorting to considering a representative volume element. In contrast to previous works [1,2], where the problem with random inclusion arrangement [1] and random values of inclusion sizes (radii) under the condition of periodicity of their centers arrangement [2] was considered, this work solves the problem for composites of periodic structure but with random values of their mechanical characteristics. The paper presents four options for evaluating the effective characteristics of the deformation properties of periodic structure composite materials with random values of the deformation characteristics of their phases. The applicability of the proposed probabilistic approach to determining the effective stiffness tensor on a periodicity cell is shown. This approach allows obtaining not only average values (effective stiffness tensor) but also three main central moments – from the 2nd to the 4th order (variance, skewness, and kurtosis), characterizing the random distribution function of the effective stiffness tensor. The approaches presented in this article for evaluating the effective deformation characteristics of periodic structure composite materials with random values of mechanical characteristics can be applied to determine viscoelastic, thermophysical, and other physical and mechanical properties.

Based on the refined theory, an initial-boundary value problem of non-isothermal viscoelastic-viscoplastic dynamic bending deformation of fibrous plates is formulated. The geometric nonlinearity of the problem is considered in the Karman approximation. The coupling of the simulated thermomechanical problem is taken into account. Across the thickness of composite plates, the displacements of points in tangential directions and temperature are approximated by 7th-order polynomials. An explicit numerical time-stepping scheme is used to solve the formulated non-stationary reduced two-dimensional problem. The non-isothermal viscoelastic-viscoplastic and viscoelastoplastic bending behavior of rectangular elongated fiberglass plates with cross-ply and spatial reinforcement structures is investigated. The structures are transversely loaded with short-term high-intensity excess pressure. It is shown that for correct determination of the magnitude and shape of residual deflections of such structures, they must be calculated taking into account the thermal response arising in them, even in the absence of external heat sources of non-mechanical origin. It is demonstrated that for adequate determination of the residual deformed state of the composite materials of such plates and their residual deflection, it is necessary to use the refined bending theory, rather than its simplest version—the traditional non-classical Ambartsumyan theory. It is shown that neglecting the dependence of the plastic properties of composite components even in fiberglass structures leads to a significant (several times) overestimation of the intensity of residual deformations of the composite phases and to significant distortion of the shape and magnitude of residual deflections. Even in relatively thin fiberglass plates, replacing the planar reinforcement structure with a spatial one while maintaining the total fiber consumption can lead to a reduction in the residual deformed state of the epoxy binder by more than 10%. It is demonstrated that after the cessation of inelastic oscillations, fiberglass plates acquire a corrugated shape with folds oriented in the longitudinal direction.

Based on the Lagrangian formalism of analytical mechanics extended to continuous systems, equations of dynamics for a system with dissipation are obtained. The system is defined on a certain manifold by a configuration space with a set of first-kind field variables, spatial and boundary densities of the Lagrangian functional depending on field variables, their derivatives with respect to the time variable, as well as some linear transformations of field variables, and a dissipative function bilinear with respect to the first time derivatives of field variables similar to the Rayleigh function in discrete mechanics. Equations of motion having the meaning of Lagrange equations of the second kind for a continuous system with dissipation, and their natural boundary conditions are constructed. The application of the obtained variational formalism of analytical mechanics of continuous dissipative systems to the construction of a linear quasi-three-dimensional theory of generalized thermoelastic shells is considered. The shell model is formulated on a bundle of a two-dimensional smooth manifold corresponding to the reference surface of the shell. The first-kind field variables are defined by the expansion coefficients of the displacement vector and the Biot thermal displacement vector in a biorthogonal system of functions of the dimensionless normal coordinate, forming a basis in the space of square-integrable functions. Through spatial reduction of the volume and boundary densities of the Lagrangian and Rayleigh functionals corresponding to the Lord-Shulman generalized thermoelasticity model, the surface and contour densities of the functionals are obtained in general form, and the Lagrange equations of the second kind for Nth-order shell theory are constructed. The constitutive equations are obtained, and the formulation of the initial-boundary value problem of dynamics for an anisotropic generalized thermoelastic shell is presented.

Polymer composite materials (PCMs) are characterized by high specific strength and stiffness, as well as resistance to cyclic loads. However, sensitivity to out-of-plane impact loads, as well as a large number of failure modes, are among the most significant drawbacks hindering their widespread use in primary load-bearing structures of modern aircraft. Work to confirm the compliance of materials of this type with certification requirements cannot be limited only to full-scale tests due to the infinite number of combinations of material structures. The development of a finite element modeling methodology for PCMs to calculate impact damage from various impact loads is highly relevant. This paper considers the influence of the number of spherical ice hailstones affecting a cylindrical hinged-supported PCM panel on the damage to the panel’s plies. Hail is modeled using the Smoothed Particle Hydrodynamics (SPH) method. Finite element modeling of the panel is carried out layer-by-layer using solid elements in the LS-Dyna software package (Ansys Inc.). A feature of the material model for the panel plies is the linear dependence of element stiffness on its deformation. The interlaminar bonding material model has a bilinear dependence of bonding force on delamination. The dependences of kinetic energy and contact force of hail with the panel on time for cases of one, two, and three hailstones affecting the panel are obtained, as well as the dependences of contact point displacements on time. Damage to the panel was evaluated by degradation coefficients of the ply material. For all considered impact cases, the process of interaction between the PCM panel and hail is shown in graphical form.

A numerical study of compact particle fragmentation during high-velocity perforation of a mesh barrier located at an angle to the initial particle motion line is conducted. Calculations were performed in a three-dimensional formulation based on the complete system of equations of solid mechanics using the smoothed particle hydrodynamics method with the Johnson-Cook viscoplastic model using the LS-Dyna software package. For comparative analysis, calculations for a continuous barrier with similar weight characteristics at the same inclination angles are performed. The work is carried out to confirm the assumption that the dependence of particle fragmentation during perforation of a mesh barrier at an angle differs from the same dependence during perforation of continuous thin barriers. Comparison of the mass of the largest fragment formed during particle fragmentation when perforating mesh and continuous barriers allows concluding that with a change in impact angle, the fragmentation efficiency on a mesh barrier decreases less than on a continuous one. Analysis of changes in the fragment cloud structure indicates that with a change in impact angle, the higher fragmentation intensity on the mesh barrier is due to the action of those mesh wires that, regardless of its inclination, remain in a normal position relative to the initial particle motion line. This is also associated with the absence of a sharp maximum in the dependence of the second moment of particle fragment mass distribution on impact angle during mesh barrier perforation. A comparison of the perforation resistance at different inclination angles of two-component protection schemes using mesh and continuous blast shields is conducted.

Over the past decades, interest in the use of composite materials in aircraft structures has increased significantly. Modern aviation-grade carbon fiber reinforced plastics, in terms of their specific strength properties, can compete with aluminum and titanium alloys. However, the use of polymer composite materials (PCMs) for aircraft parts is a complex technical problem directly related to the features of PCMs. Composite materials (CMs) are multicomponent materials that represent a plastic base (matrix) reinforced with fillers having high strength and stiffness. The combination of different substances leads to the creation of a completely new material whose properties quantitatively and qualitatively differ from the properties of each of its components. The paper considers the results of experimental determination of mechanical characteristics (flexural strength and interlaminar shear strength after exposure to external factors) and comparison of the obtained results with the initial state (before exposure to external factors) of aviation-grade carbon fiber reinforced plastics. During engine operation, due to elevated temperatures, complete or partial evaporation of all liquids that have entered the structure occurs. Therefore, long-term influence of aggressive operational fluids on the product is possible only during prolonged aircraft parking on the ground. Since test results show a fairly large scatter of values, based on the values of the coefficient of variation, a variance analysis of the data was performed. Variance analysis methods allow assessing the magnitude of the influence of specific factors on the studied strength value. The main idea of one-factor variance analysis is to compare the variance of the studied strength value caused by the action of an external factor with the variance of measurement errors of this strength value. If the difference between them is significant, then the factor has a significant influence on the studied material strength. A study and analysis of the average strength value and one-factor variance analysis of the scatter of test results for interlaminar shear and flexure were conducted.