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The features of the propagation of elastic longitudinal and rod waves in single crystal cylinders under shock loading against a rigid wall are shown. The finite element method in a three-dimensional formulation simulates the shock loading of cylindrical bodies with the same height for cases of different orientations of the single crystal symmetry axes relative to the cylinder symmetry axis. The shock loading of the cylinders against a rigid wall is modeled with the same initial velocity, which ensures elastic deformation of the cylinders. The materials of the cylinders are zinc single crystals characterized by auxeticity. It is shown that the values of the velocities of propagation of elastic waves in cylinders depend on the direction of propagation, the ratio of the height of the cylinder to the diameter, and also on the location of the ultrasonic wave receiver. [ABSTRACT FROM AUTHOR]

The article presents the results of solving the model problem of deformation of a spherical body of a single-crystal with cubic symmetry of properties (titanium nickelide) under the action of a comprehensive compression pulse. The approach applied makes it possible to divide the elastic deformation energy into the energy of volume change and the energy of shape change for materials with cubic symmetry of properties. To solve the problem, various mathematical models were used to take into account the anisotropy of elastic properties in single crystals with cubic symmetry of properties. Their differences are determined by the relationships between uniform volumetric deformation and internal pressure. The choice of the model is determined depending on the orientation of the directions of the axes of the computational coordinate system relative to the directions of the main crystallographic axes of the single-crystal. The effect of the use of various mathematical models on the accuracy of the solutions obtained is shown. [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical calculations of dynamic loading of a target from a single-crystal alloy VZhM8 with a steel isotropic projectile. The loading of the target from VZhM8 was carried out along the direction [001] coinciding with the direction of the crystallographic axis. The initial loading velocity was 600 m/s. Calculations were made using original programs in three-dimensional formulation. The velocity profiles of the rear surfaces of the targets during dynamic loading with and without fracture are presented. [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical modeling of dynamic loading of a target made of 2024 aluminum alloy with a steel projectile of cylindrical shape. A comparative analysis of the application of two different fracture criteria to the numerical simulation of the deformations process of the targets material was conducted. In one case, the process of destruction of the material of the target was simulated using the fracture criterion based on accumulated plastic deformations. In the other case the Hoffman fracture criterion recorded through full stresses was used. The obtained calculation results were compared with experimental data for a loading velocity of 151 m/s. [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical calculations of dynamic loading of thin cylindrical targets with a ratio of cylinder heights to its diameter 1 : 1 and 5 : 1. The propagation of elastic waves in cylinders with different ratios of heights to the radius of the VZhM8 single-crystal nickel alloy with cubic symmetry of properties in order to determine the propagation velocities of rod waves in the [001], [011] and [111] directions was simulated in this paper. The problem of loading of a target from VZhM8 by a steel projectile with a starting velocity was carried out by the finite element method in a three-dimensional formulation. [ABSTRACT FROM AUTHOR]

The paper presents the results of calculations of the elastoplastic deformation of the target using two variants of the decomposition of the total stress tensors into parts, corresponding to the volume strain and shear strain. The processes of elastoplastic deformation of a target made of a single-crystal VZhM8 alloy under shock loading by a steel projectile are simulated. The influence on the results of numerical simulation of the application of two variants of the decomposition of the total stress tensors for the target of a single-crystal alloy VZhM8, possessing auxeticity in the direction of loading, is shown. [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical simulation of the dynamic loading of a target from an anisotropic aluminum alloy AA7010-T6 with an isotropic aluminum projectile with different velocities. The process of destruction of an anisotropic target material was simulated by applying the fracture criterion from accumulated plastic deformations. This criterion makes it possible to take into account the anisotropy of the strength characteristics of the target material and to simulate the process of accumulation of microdamages. To study the effect of anisotropy of the mechanical characteristics of the material on its deformation, two types of calculations were carried out: in the first case, the mechanical properties of the target material along the loading direction were minimal, and in the second case, maximal. This statement of the problem corresponds to the statement of the problem in natural experiments in which the direction of the material rolling is oriented parallel or perpendicular to the direction of the load. [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical simulation of the dynamic loading of an target from an anisotropic aluminum alloy 2024 by an isotropic aluminum projectile. The process of spalling destruction of an anisotropic target material was modeled with the help of two models of elastoplastic deformation of the material, in the first case the fracture criterion from accumulated plastic strains. In the second case, the elastoplastic material deformation model is supplemented by a fracture criterion containing the ultimate porosity. The obtained results of the calculations were compared with the experimental data for the case of the initial shock loading rate of 630 m/s. Numerical modeling of spall destruction of target is performed by the finite element method in a three-dimensional formulation. [ABSTRACT FROM AUTHOR]

The formation of a crack under shock loading in HCP single crystals in the (101̅0) plane is simulated in the work. The simulation was carried out using the finite element method in a three-dimensional statement using the example of a zinc single crystal. The mathematical model allows to take into account the anisotropy of elastoplastic properties, the anisotropy of the propagation velocities of longitudinal and bulk waves, auxeticity, and the anisotropic pressure caused by bulk deformation in HCP single crystals. The formation of a crack is modeled as the fusion of individual elements in which the limiting porosity in a single crystal is exceeded in tension. The results of a comparison of velocity profiles of the rear surfaces of targets from a zinc single crystal obtained in calculations and in natural experiments by other authors are presented. [ABSTRACT FROM AUTHOR]

Numerical modeling of spalling brittle fracture along the (0001) plane in a zinc single crystal under shock loading by an aluminum projectile was performed in the work. Numerical modeling was carried out by the finite element method in a three-dimensional statement. The mathematical model allows to take into account the anisotropy of bulk compressibility in a single crystal of zinc, auxeticity, anisotropy of the propagation velocities of elastic longitudinal and volume waves. Stresses are determined on the basis of a comparison of velocity profiles of the rear surfaces of targets from zinc single crystal in mutually perpendicular directions when it is destroyed along the (0001) plane in natural experiments and numerical simulation. [ABSTRACT FROM AUTHOR]

Numerical simulation of shock wave propagation processes in layered composite materials with organic matrices reinforced with glass fiber is carried out. Such materials possess a tetragonal symmetry of properties. The elastic deformations in such materials are determined by means of the generalized Hooke law containing 6 independent elastic constants. Numerical simulation of shock loading of composite materials reinforced with glass fiber was carried out in a three-dimensional statement. Comparisons are made between the results of calculations of the velocity profiles of the rear surfaces of obstructions from composites reinforced with glass fiber with the results of natural experiments obtained by other authors. [ABSTRACT FROM AUTHOR]

Numerical simulation of spall destruction of an aluminum single crystal in a three-dimensional statement is carried out in this work. The velocity profiles of the rear surfaces of targets from aluminum single crystals are obtained. A comparison of these velocity profiles with those obtained by other authors as well as with the results of natural experiments is made. Shock loading of an aluminum single crystal is carried out taking into account the anisotropy of its mechanical properties. Spalling is modeled within the framework of continuum mechanics. [ABSTRACT FROM AUTHOR]

The study represents the analysis of numerical simulation of the failure of aluminum targets made of highly porous or solid 2024 alloy under dynamic loading. The calculations employed the finite elements method in threedimensional formulation with the use of proprietary programs. The article presents the results of the numerical simulation of Taylor's test for the projectile made of highly porous aluminum 2024 alloy at the velocities of 75 to 175 m/s. These results are in a good agreement with the results of the experiments. The peculiarities of the destruction of highly porous aluminum targets are shown. [ABSTRACT FROM AUTHOR]

The paper provides a 3D finite element simulation of shock-loaded anisotropic single crystals on the example of a Zn plate under impact using a mathematical model, which allows for anisotropy in hydrostatic stress and wave velocities in elastic and plastic ranges. The simulation results agree with experimental data, showing the absence of shock wave splitting into an elastic precursor and a plastic wave in Zn single crystals impacted in the [0001] direction. It is assumed that the absence of an elastic precursor under impact loading of a zinc single crystal along the [0001] direction is determined by the anomalously large ratio of the c/a-axes and close values of the propagation velocities of longitudinal and bulk elastic waves. It is shown that an increase in only one elastic constant along the [0001] direction results in shock wave splitting into an elastic precursor and a shock wave of "plastic" compression. [ABSTRACT FROM AUTHOR]

The paper discusses the stress rate tensor measures for isotropic and anisotropic solids subjected to significant deformations under dynamic loading. It is shown that the difference of the corotational derivatives for isotopic and anisotropic (transtropic) media is in the absence of the assumption of volume isotropy of anisotropic media, as for example in the case of the Green-Naghdi corotational derivative. The use of the Green-Naghdi derivative instead of the Jaumann derivative allows one to eliminate the error arising when a deformed state of simple shear appears, although this leads to an increase in the computational time. [ABSTRACT FROM AUTHOR]

This paper studies a mathematical model of anisotropic hydrostatic stress in the region of elastoplastic deformations in a 3-D formulation. The influence of this hypothesis on the results of numerical modeling of propagation velocity of bulk waves in the region of plastic deformations and the velocity of free surfaces of deformable bodies is determined. This can be demonstrated in the problem of loading by a hydrostatic compression of a spherical body made of an anisotropic material. The propagation velocities of bulk waves change under dynamic loading by hydrostatic compression, and under static loading. Therefore, the final shape of the initially spherical body made of an anisotropic material is determined by applying the hypothesis of bulk isotropy or bulk anisotropy of the stressed state. [ABSTRACT FROM AUTHOR]

This paper studies the processes of fracture of barriers using the fracture criterion, allowing for consideration of large anisotropy for ultimate values of total plastic strains in various symmetry axes of an anisotropic material in conditions of sign-variable strain. All calculations were performed using the finite-element method under conditions of dynamic loading in three-dimensional graphics with the use of original software. It was shown that when modeling processes of fracture in barriers made of anisotropic and isotropic materials the differences in size and localization of fracture zones increase with the increase in the initial speed of shock loading of barriers. [ABSTRACT FROM AUTHOR]

The failure criteria of anisotropic materials, the criteria being expressed via deformations, are rarely applied in practice, and are usually used for low-ductility materials. Another situation involves the simulation of failures in materials with the high anisotropy of mechanical properties and that suffer elastic-brittle fracture. For such materials the failure criteria are formulated using ultimate strains and strain tensor invariants. For simulating the fractures of materials that are characterized by the anisotropy of strength properties, the failure criteria are applied with the critical values of stresses and strains, as well as their intensities. Using the value of cumulative plastic strain as a failure criterion does reflect the anisotropy of elastic and plastic properties of a material, but it does not reflect that of the strength properties. The application of this method allows accounting the total plastic strain induced by tension and compression in the conditions of the wave strain of targets during their impact loading. [ABSTRACT FROM AUTHOR]