This paper presents a preliminary numerical analysis comparing continuous and discrete protective bumpers for their effect on the initiation of progressive fragmentation of a high-speed 4 particle. The study systematically investigates the effect of the key geometric parameter of a wire bumper – its aperture – on the velocity of fragmentation initiation. Numerical modeling was performed using the Smooth Particle Hydrodynamics (SPH) method in LS-DYNA, incorporating the Johnson-Cook constitutive model and the Mie-Gruneisen equation of state. The simulation results are compared with experimental data from reference [1], which validates the observed fragmentation patterns. The analysis demonstrates that an increase in the bumper aperture (while maintaining constant areal density) significantly alters the fragmentation mode of the projectile. At small apertures, the behavior is similar to that of a continuous bumper, whereas larger apertures promote an earlier onset of fragmentation and alter the process kinetics. The impact point relative to the wire geometry is also a critical factor: aiming between the wires leads to more intensive fragmentation at high velocities, while aiming at the center of a wire causes a stepwise change in the mass of the largest fragment in the low-velocity region. An integral performance metric for fragmentation was introduced to assess the bumper’s overall efficiency across a wide velocity range. It was established that maximum efficiency is achieved with large apertures and by aiming between the wires. The findings confirm that optimizing the geometry of discrete bumpers is a promising approach for designing efficient space debris protection systems.

An engineering model is proposed for analyzing the high-velocity interaction of a rigid projectile with a target of finite thickness under normal impact. A perfectly rigid-plastic model with an incompressible condition is used to describe the mechanical properties of the target material. The mechanical properties of the material are characterized by two parameters: yield strength and density. The proposed model identifies the following interaction modes. The first mode is when the projectile simply penetrates the target to a finite depth, without deforming the back surface of the target. In this case, the model allows one to estimate the volume of the resulting crater and the volume of material ejected from the target in the direction opposite to the impact one. The second mode is when the projectile knocks out a “plug” from the target, moving in the direction of impact. Relationships were obtained for the loss of projectile velocity and the mass of the dislodged plug. The third mode is when, in part of the path, the projectile knocks out the material of the target in the direction opposite to the direction of its movement, and in the final part knocks out the plug in the direction of movement. In this case, simple engineering estimates of the required parameters were also obtained.

New technologies for producing layered composites using self-propagating high-temperature synthesis (SHS) allow for arbitrary combinations of layer thicknesses of intermetallics and ceramics, their elastic and strength characteristics, and parameters determining component durability. This paper develops a model for assessing the durability of a two-layer beam under three-point loading based on the classical scalar damage measure of Rabotnov and the corresponding kinetic equation. Under conditions of piecewise-varying cross-section of a two-layer beam, it was possible to obtain an analytical dependence of the time to failure on the parameters of the kinetic equation of the lower layer material. For this purpose, the solution for a homogeneous isotropic beam in the case of linear distribution of the longitudinal components of the stress tensor across the cross-section was considered. The form of the dependence of the damage measure on the cross-section coordinate and the current position of the neutral axis was found, which identically satisfies the equation of equilibrium of the longitudinal forces of the beam. In the limiting case of representing the stress field in a piecewise-constant form of the plastic hinge type, the solution for a homogeneous beam corresponds to the classical solution of Rabotnov-Mileiko. For the case of a two-layer beam, a solution in the space of two-layer parameters is proposed, as was done earlier for problems of static strength of layered composites. It is shown that for a significant range of two-layer parameters, finding the time to failure of a two-layer beam is similar to the solution for a homogeneous beam based on the proposed measure of damage. As a result, an analytical dependence of the time to failure of a two-layer beam on the parameters of the kinetic equation for the damage measure of the lower layer material has been obtained, and the range of two-layer parameters where this result is correct has been determined.

For a practically important truss structure of an aircraft, it is proposed to replace the tubular metal rods with composite ones, why provide metallic fittings on the ends of the composite rods to ensure that loads are transferred to the fastening units. As a connection of the composite tubular rod with a metal rivet, a reverse cone design is taken, which has a jamming effect, which increases the shear strength of multilayered composites. Such a connection functions until the axial force N rips out the rivet from the rod, i.e., until there is a “leap” (jump). The magnitude of the force N is determined from the conditions of equilibrium, stability of equilibrium and coupling depth limits of transverse deformations of the composite tubular rod. The position of the balance of the rod-rivet system is determined from the condition of the extreme of potential energy; the stability of the equilibrium is determined according to the Sylvester criterion; the opening of the junction is estimated by the magnitude of the radial displacement of the internal angular point of the cone of the rod. The thin-walled tubular rod is considered to be in a state of axisymmetric bending, and the wedge part of the rod behaves as an alternating cross-sectional ring. It is assumed that the rivet is absolutely rigid due to its three-dimensionality. Film glue is laid between the composite rod and the rivet. Based on the developed mathematical model and obtained resolving equations, two problems are investigated. In the first task, the calculation of the cone coupling of a carbon-plastic thin-walled rod with aluminium riveting was carried out. The found axial critical force is compared with the experimental one. In the second task, the rod-rivet connection area is reinforced by a circular winding of unidirectional carbon-fiber and the increase of the axial critical force is shown. The comparison of the calculated data with the results of the experiment showed that the discrepancy does not exceed 18%.

This paper investigates the interaction between a spherical ice impactor and monolithic (D16) and reinforced aluminum plates in the velocity range from 460 to 1300 m/s. Monolithic plates with twice the yield strength, spall, and shear strength are proposed as reinforced specimens. The behavior of the materials is described by a compressible, porous, elastic-plastic model that takes into account strength properties, shock-wave phenomena, and the combined formation of spall and shear failures. Ice is modeled as a single-phase medium without phase transitions with averaged physical and mechanical properties. Calculations were performed in a two-dimensional axisymmetric case using the non-commercial software package “Impact. Os.2”. Before conducting parametric studies, test calculations and a sensitivity analysis of the computational mesh for three and five nodal elements were performed. The behavior of homogeneous and reinforced specimens under high-speed impact is predicted. Signs of increased impact resistance were identified via increased prolongation time, axial deflection, and the ballistic limit. The initiation time and evolution of fracture foci in ice and aluminum, the shape of the dent on the surface, and the process of plugging were predicted. The shapes of ballistic curves, free surface velocity profiles, and ice damage curves were determined. It was found that monolithic and reinforced aluminum plates were penetrated by a single “plug” shearing mechanism. Ice always failed via a dominant brittle mechanism. Specimens with increased spall and shear strength exhibited the greatest impact resistance. However, samples with increased spall strength exhibited the greatest resistance.

The material functions in the constitutive relations of grained soils generally contain three invariants of the strain (strain rate) or stress tensor, depending on the type of constitutive relations. Therefore, experimental determination of these functions requires true triaxial loading or deformation testing machines. Commonly used compression machines (without lateral expansion) and stabilometers do not allow for independent three-component loading. The results of multiplane shear tests cannot be represented in terms of invariant variables (stress and strain intensities) without knowledge of the transverse strain coefficient. This paper presents the results of transverse strain coefficient measurements using a true triaxial testing machine for coarse-grained sand. The deformation consisted of two stages. The first stage was uniform compression to create a denser soil. The second stage was soil compression under uniaxial increment of compressive stress. If the sand after the first stage (bulk compression) is considered as a new material that is loaded under uniaxial compressive stress, then the stress and strain increments are to be related to the beginning of the second stage. The study shows that in such a case, the transverse strain coefficient exceeds 0.5 during the volumetric strain increase. Determining this coefficient for total strains reveals that it approaches the value obtained by the authors using a kinematic-type test if the strain deviator module increases and before dilation occurs. However, the final value of the transverse strain coefficient measured on a force-type testing machine decreases significantly after dilation occurs. Dilation is defined as the increase in volume of the material under shear.

Layered materials are widely used in mechanical engineering, aerospace engineering, and construction. The soils underlying buildings and structures often have a layered structure, and the masses that contain underground structures and mine workings are composed of layered rocks. To solve the problems of stress-strain state, strength, and stability of products and assemblies made of layered materials, as well as buildings and structures, taking into account their interaction with the soils of the foundations and in the calculations of underground structures and mine workings, reliable, fast, and convenient methods for determining their mechanical characteristics are required. In geomechanics, the determination of mechanical properties is often time-consuming and very expensive. In some cases, these properties cannot be determined experimentally. Therefore, it can be stated that the problem of determining the effective characteristics of composite materials is currently relevant in engineering and scientific activities. This work is a direct continuation of the research [1,2] and develops a method for determining the effective stiffness tensor and, accordingly, the effective deformation characteristics (Young’s modulus, shear modulus, and Poisson’s ratio) of composite materials, an important special case of which are layered media, using probabilistic methods and the method of asymptotic averaging. A method is proposed that uses probabilistic and statistical methods to process the results of laboratory studies of layers in order to determine the effective properties of layered media. The paper considers two approaches to determining the distribution law of the variable characteristics of the layers of layered materials as random variables. A simpler and less time-consuming option has been identified. When comparing the results of laboratory studies of a layered rock massif with the results obtained using the developed methodology, it was found that the experimental values of the deformation characteristics are significantly higher. The approaches presented in this article for assessing the effective deformation characteristics of layered media with a periodic structure and random mechanical characteristics can be used to significantly specification the characteristics of natural composites, such as rock and frozen soils, as well as in the development of new composite materials with specified characteristics.

Shape memory materials (SMMs), in particular, titanium nickelide, are being increasingly used as sensing elements and actuators in thin-walled aerospace, medical, and construction equipment due to their adaptability. The effectiveness of using SMMS in shells and plates depends largely on the ability of mathematical models to accurately describe the complex thermomechanical behavior of the material during finite deformations. The classical momentless theory of shells based on the Kirchhoff-Love hypotheses and the assumption that membrane forces dominate bending forces offers the possibility of developing effective analytical and semi-analytical calculation methods. However, when applied to SMMS, it is necessary to take into account the phase transformations, hysteresis, and anisotropy properties of SMMS thin sheets caused by the characteristics of the manufacturing process. The purpose of this review is to systematize modern approaches to modeling the instantaneous stress-strain state of shape memory polymer (SPF) shells, to identify the limits of applicability of the instantaneous hypothesis for materials with shape memory, and to determine promising areas for the development of computational models that combine the instantaneous theory with phenomenological and micromechanical relationships. The main groups of models used in conjunction with the instantaneous shell theory are analyzed, including phenomenological macroscopic models, micromechanical approaches, and numerical implementations based on the finite element method. Special attention is given to the conditions for the applicability of the instantaneous approximation, such as the ratio of shell thickness to curvature radius, the nature of boundary conditions, and the intensity of phase transformations. It has been shown that the theory of shells without moments can be successfully used to calculate thin-walled elements in cases where deformations caused by phase transformations dominate bending deformations, and boundary conditions do not lead to local edge effects. It has been established that phenomenological models with internal variables, such as the volume fraction of martensite and the tensor of transformational deformation, can be naturally integrated into the theory without moments under the condition that the hypothesis of plane stress is used.

A spatiotemporal variational model of adhesive interactions is proposed, extended to spatial and temporal deformation processes, thus making it possible to account for the influence of surface adhesive properties on dynamic processes. The model is based on a generalization of Sedov’s variational principle, which ensures consistency between the reversible and irreversible parts of the equilibrium equations and the equations of motion in the case of dynamics. For the plane problem in terms of material coordinates, boundary conditions are formulated at the contact interface between media using adhesive moduli that describe the reversible and dissipative processes of adhesive interaction between the two media. It is shown that the dynamic generalization significantly expands the possible number of physical parameters, since the tensors of adhesive elastic moduli can include tensors of odd rank. The possibility of representing the adhesion model not only in terms of displacements but also in terms of velocities allows its use in fluid dynamics problems. In particular, conditions between the fluid and the capillary walls are formulated, as well as boundary conditions at the ends of the capillary where the fluid surface is free from kinematic constraints. Adhesive interactions with the external environment are defined in a plane formulation by adhesive moduli that describe the reversible and dissipative processes of adhesive interaction. As an example, the Brinkman flow of a viscous fluid in a capillary is considered, taking into account independent adhesive dissipation channels at the fluid-capillary wall interface. A solution is obtained for a particular problem of steady flow in a plane channel using a version of the adhesive interaction model – the “spring” model of adhesion. It is shown that accounting for adhesive properties allows modeling of flow deceleration effects near the wall, describing the transition from slip to no-slip regimes, which can be used for more adequate modeling of microcapillary flows.

The technology of creating a layered composite by self-propagating high-temperature synthesis consists of three stages: preparation of the powder from which the next layer will be synthesized; carrying out an exothermic combustion reaction, during which the synthesis of the layer material and plastic deformation of the layer takes place in a high temperature zone in a strictly defined period of time during the cooling process [1-3]. The upper layer is synthesized immediately on the surface of the finished material of the lower layer and forms a high-strength diffusion layer interface during the pressing process [4-6]. This technology makes it possible to obtain arbitrary ratios of thicknesses, elastic and strength properties of layers, which leads to all possible combinations of the location of the neutral axis relative to the interface of the layers, as well as the type of stress state in them. The case of the transition of the neutral axis from the lower layer to the upper layer is considered, or the initial location of the neutral axis on the upper layer, which leads to an increase in damage in both layers. Previously, [7-8] the conditions for the onset of fracture of a layered composite under three-point loading from the second inner layer were identified, which affects the determination of the maximum static load. In our case, it is also possible to determine the range of layer material parameters for which the critical value of the damage parameter is reached earlier on the second layer from below. In this case, the time to destruction will already be determined taking into account the parameters of the kinetic equation of damage to the second layer. To solve this problem, the dependence of the damage parameters of the first (lower) and second (upper) layers of the beam is derived, which identically satisfy the equilibrium equation for longitudinal forces. It is important to note that the process of damage development on the inner layer is not accessible to visual control. Therefore, it is important to determine in advance the cases of the potential for the development of such a hidden outer layer of degradation of the material.

In this paper, in an even-symmetric formulation, a simple exact solution is obtained to a boundary value problem of the theory of elasticity concerning the tension of a free strip with a short (less than the strip width) absolutely rigid one-dimensional inclusion located at the center of the strip on its vertical axis of symmetry. The solution is obtained by the superposition method as the sum of an elementary solution to a homogeneous boundary value problem for a free strip subject to constant tensile stresses applied to the right and left at infinity, and a solution to an inhomogeneous boundary value problem for the same strip subject to a certain load acting along the vertical axis on the inclusion. The final formulas for the stresses and displacements are represented as series in Papkovich-Fadle eigenfunctions, the coefficients of which are determined in closed form using the Papkovich orthogonality relation. The unknown shear stresses on the inclusion are found through the linear transverse displacements specified here (equal in magnitude and opposite in sign to the transverse displacements in the elementary solution). To do this, such an analytical function constructed from the Papkovich-Fadle eigenfunctions is introduced that it admits an analytical continuation to the entire strip, except for the segment on which the inclusion is located. To construct the analytical continuation, the Borel transform is used. The solution method is independent of the type of homogeneous boundary conditions on the sides of the strip; in particular, the sides of the strip can be clamped or reinforced by stiffeners. In this case, only the Papkovich-Fadle eigenfunctions and the corresponding eigenvalues change. The obtained solution is compared with the numerical solution obtained using the finite element method.

Studies of changes in strength and stiffness during three-point bending and stretching, as well as the perception of shock loads of a monolayer obtained by 3D printing with filaments based on PA-6 thermoplastic reinforced with carbon fiber prepregs impregnated with ED-20 epoxy resin with PEA hardener in a ratio of 10:1 after contact exposure to ultrasound with frequencies of 22 and 44 kHz, have been performed. It is shown that under the influence of ultrasound, due to plastic deformation, the thickness of the samples decreases, averaging 5 microns at a frequency of 21.7 kHz, and 10 microns at a frequency of 43.8 kHz, or 2 times more. It was found that the final ultrasonic treatments contribute to an increase in the stress limits in the average cross-section of the sample during three-point bending by 18.7% and 8.6%, respectively. At the same time, the modulus of elasticity increases by 3.1 and 1.97 times, respectively. It was found that, in comparison with the control samples, the stress limits in the middle section during stretching of the prototypes increase on average by 12% and 11%. The extent of the damage area of the prototypes is 1.5-2 times less than that of the control sample. It was found that, compared with the control samples, the impact force transmitted through the monolayer decreases by 23% and 10.8%, respectively. At the same time, the duration of vibrations caused by impact decreases by 26% and 72%, respectively. In general, finishing ultrasonic treatment can be a reserve for increasing the physical and mechanical properties of products made of composite filaments formed using FDM technology.

Approximate analytical solutions are constructed for linearized problems of transverse-shear buckling modes of fiber reinforced composite test specimens under the three-point bending tests. The corresponding problems are formulated based on three versions of a refined geometrically nonlinear theory of plane bending of composite rods, previously constructed by taking into account transverse shear and compression at different orders of displacement approximations through the rod thickness. The first two versions of the theory are based on approximations of axial displacements by third-degree polynomials through the thickness, with the number of unknown functions reduced by one order in the first one by introducing transverse shear functions according to the Reddy-Nemirovsky model. The third version is based on a linear approximation of axial displacement. In all three versions of the theory, a linear approximation through the thickness is adopted for deflection, with the third version of the theory fully consistent with the well-known shear S.P.Timoshenko’s model, constructed taking into account transverse compression. In all of the above equations, geometrically nonlinear terms are introduced that allow the theoretical identification of the investigated buckling modes of composite test specimens of the considered class under the bending loading. It is shown that their failure is entirely due to the implementation of such a shear buckling mode, which is accompanied by delamination in the longitudinal direction of elongated specimens and shear failure in the central section of short specimens. For their theoretical identification, deformation models must be constructed with mandatory consideration of transverse compression, preserving the first-order internal moments of transverse shear stresses in the equations, as well as taking into account the geometrically nonlinear deformation process based on the use of elasticity theory relations in a non-classical (non-standard) geometrically nonlinear approximation. An analysis of the degree of accuracy and meaningfulness of the employed equations is performed. Comparison of the obtained theoretical results in the form of simple analytical formulas with the data of previously conducted experiments on three-point bending of short and elongated test specimens is given.

A special analytical and numerical method of block approximations is being developed for numerical simulation of viscous incompressible fluid flows in porous media. It makes it possible to simulate the physical process with a high degree of accuracy using auxiliary potentials satisfying the Helmholtz and Poisson equations. This method is based on dividing the initial domain into simple subdomains, i.e., blocks of arbitrary shape, and decomposing auxiliary potentials into systems of generalized functions of polynomial type, which are fundamental solutions of the Helmholtz equations. These systems have the properties of completeness and orthogonality for approximating arbitrary flows of a viscous incompressible fluid within the framework of the chosen model. As a model describing flow, the Brinkman equation is used. It implements the generalized law of filtration of a viscous incompressible fluid through a porous media with the given permeability. As a special case it transforms into the Stokes equation for the free flow of the incompressible fluid (it is the porous medium with infinite permeability) and at zero viscosity it transforms into the Darcy filtration equation. The approximation of the solution is performed in discontinuous energy space in norm that ensures convergence of the approximate solution to the exact one on independent block solutions using the Bubnov-Galerkin projection scheme. Based on this method, a highly accurate analytical and numerical algorithm for calculating the effective permeability of porous media with a given geometric structure has been developed. It is an urgent task for accurately modeling the impregnation process of prepregs of composite materials. This method can also be used for analytical and numerical modeling of the various flows in porous media with a complex geometric structure. It plays an important role in the development of oil fields, and also has numerous applications in the creation of various filtration devices.

This paper analyzes the shear load distribution in an eight-bolt single-shear joint of two composite plates, with the bolts installed in two rows. The bolts are made of titanium alloy, and the thickness of the composite plates was varied. The influence of composite plate thickness on the load distribution among the bolts is evaluated. The calculations were performed using two methods: the finite element method (FEM) in a three-dimensional formulation taking into account the contact interaction between the joint components, and an analytical method in a two-dimensional formulation with bolts modeled as springs. The spring compliance was determined using empirical formulas employed by Douglas, Boeing, and Airbus (formulas by Huth). It is established that the most heavily loaded bolt in all joints is the fourth outer bolt, whose load in some cases exceeds the average bolt forces by almost 40%. The results of analytical shear force calculations depend significantly on the compliance value used to determine them. Modeling bolt compliance using the Douglas method can lead to an error in force estimation of nearly 30%. Modeling compliance using the Boeing method reduces this error to about 20%. The best results are achieved using Huth’s formulas, which match the FEM calculations with an accuracy of up to 8%. The use of two-dimensional analytical modeling to determine shear forces in multi-bolt joints reduces computation time by two orders of magnitude compared to three-dimensional FEM, making it an effective tool for the design stage of a rational structure.

This paper addresses the relevant problem of numerical optimization of regular lattice structures subjected to high-intensity dynamic loading. The primary objective of the research is to determine the optimal distribution of beam cross-sectional dimensions within the lattice to ensure the smoothest possible deceleration of an absolutely rigid impactor with a specified initial momentum. The peak acceleration magnitude (peak deceleration) during the interaction is chosen as the key optimality criterion. For a constant impactor mass, this is equivalent to minimizing the generated impact force and ensuring more efficient kinetic energy dissipation. To analyze the dynamic response in detail and account for wave processes within the structure, finite element modeling (FEM) is employed. Particular attention is paid to the effect of gradient geometry variation. The study convincingly demonstrates that varying the cross-sectional areas of the rods across the lattice layers achieves significantly higher energy absorption performance compared to conventional homogeneous structures. To reduce the dimensionality of the optimization problem and increase the computational efficiency of the algorithm, an approach based on the use of a parametric function is proposed. This function describes a continuous field of cross-sections throughout the structure’s volume, thereby reducing the search for an optimal configuration to the determination of a limited set of coefficients. The results of numerical experiments confirm that the proposed design strategy enables the creation of adaptive protective structures with programmable properties. The obtained data can be directly implemented in the design of high-performance energy-absorbing elements, aerospace protective shells, automotive crumple zones, and damping systems operating under extreme impact and vibration loads.

The main provisions of ballistic limit equation (BLE) calculating method representing principal resistance characteristic of orbital space stations modules shells equipped with a shield protection structure, are presented. The (BLE) calculating method is applicable to the high velocity space debris particles impacts, which provides complete projectile dispersion in accordance with the principle of Whipple shield [4]. The BLE calculating stages are described sequentially: projectile and bumper cloud of destructed products formation, the fabric multilayer shield loading formation and its destruction, the protected structure loading formation and its destruction analysis. The projectile and bumper debris cloud formation is described using an analytical method, which is equipped with the dimensionless parameters distributions based on a numerical solution of the high-velocity impact problem using the SPH (Smoothed Particle Hydrodynamics) method. The proposed method makes it possible to obtain the load characteristics on the protected structure or on the fabric multilayer shield. The study of the fabric multilayer shield failure includes an analysis of the energy absorbed by the fabrics composing it, and fabric shield with added mass nonlinear dynamics analysis based on an iterative procedure. A method is described for determining the parameters of the impact of the debris on the protected structure, taking into account the failure of the fabric multilayer shield. The failure of the protected structure is described by a similar iterative procedure, while physical nonlinearity is taken into account by the method of variable elasticity parameters. A qualitative comparison of the protective structure failure analysis results with experimental data and empirical dependencies used in computational practice is presented. №1