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The possibility of modeling elastoplastic deformations in materials characterized by anisotropy of elastic and plastic properties without restrictions on the anisotropy magnitude of linear compressibility of the material is shown. The mathematical model of elastoplastic deformation of anisotropic materials is applicable for symmetry cases when it is possible to decompose the elastic deformation energy into the volume change energy and the shape change energy. To simulate the processes of deformation of anisotropic materials by the dynamic finite element method, the anisotropic pressure caused by uniform volumetric deformation is introduced into the difference scheme instead of the isotropic pressure. In this case, the total stress tensor is uniquely decomposed into the anisotropic pressure tensor and the total stress tensor deviator. A criterion is given for the possibility of using the anisotropic pressure when modeling the elastic-plastic deformation in anisotropic materials instead of the spherical part of the stress tensor within the framework of the model of a volume-isotropic material. [ABSTRACT FROM AUTHOR]

Modeling of deformation processes under shock loading of a barrier made of single-crystal of zinc is carried out taking into account the anisotropy of the thermal and cold parts of pressure. The anisotropy of the cold part of pressure is determined by different values of the linear compression moduli depending on the direction. The anisotropy of the thermal part of pressure is determined by the anisotropy of the Grüneisen coefficients. Using the example of a single-crystal zinc barrier, it is shown that the use of anisotropic pressure in the mathematical model makes it possible to explain the effect of the absence of the emergence of an elastic precursor earlier than a plastic compression wave on the rear surface of the barrier in the [0001] direction under the conditions of full-scale experiments. Numerical simulation of shock loading of a barrier, made of a single crystal of zinc, by an aluminum impactor was carried out by the dynamic finite element method in a three-dimensional formulation at the Debye temperature. [ABSTRACT FROM AUTHOR]

The determination of the elastic wave propagation velocity using ultrasonic methods for a calculation of the elastic constants imposes constraints on the geometry of bodies. The paper studies the compressional wave propagation in an aluminum cylinder after a collision with a rigid wall and in cylinders made of anisotropic single-crystal zinc with different crystallographic orientation of a single crystal relative to the cylinder axis of symmetry. The initial energy separation from the repulsion energy of cylinders, secondary repulsion energy of cylinder parts from the rigid wall, and elastic strain energy of repulsed cylinders made of isotropic and anisotropic materials are described for single-crystal zinc. The different geometry boundaries are found for the bodies to study the elastic wave propagation with a view to identify the elastic constants. [ABSTRACT FROM AUTHOR]

Nickel titanium single crystal is used to show the importance of the volume compressibility anisotropy in analyzing the elastoplastic deformation processes in metal single crystals with the cubic symmetry. The process of uniform bulk deformation corresponds to the process of nonuniform stress-strain state of metal single crystals of cubic symmetry for several orientations of the theoretical coordinate system relative to crystallographic directions of the main axes. The indicative surface of the volume compressibility (or its reciprocal variable of bulk modulus) has an aspherical shape and is the function of the Euler angles. This is shown for the first time based on the solution of the model problem, viz. determination of the stress-strain state of a spherical body made of nickel titanium single crystal during the transmission of a compressive pulse through the tested material. In general case of orientation of the theoretical coordinate system relative to main crystallographic axes, a spherical body made of nickel titanium single crystal undergoes deformation due to the compressive load and acquires the shape of a two-axial ellipsoid. [ABSTRACT FROM AUTHOR]

The results of a numerical study in a three-dimensional formulation of the processes of elastoplastic deformation of a cubic single crystal based on the Ni3 Al intermetallic (VZHM8) under impact loading are presented. Impact loading is carried out in the [001] direction. The development of deformation processes is studied in the [100] and [010] or [011] and [011] directions. In the former case, the crystallographic directions of the single crystal coincide with the axes of the computational coordinate system and the elastic constants in these directions are the same. In the latter case, only one axis coincides with the [100] crystallographic direction, the other two are rotated by an angle of 45°. It is shown that a change in the elastic constants of a single crystal in new directions results in a change in the volume compressibility in all three directions. This is a consequence of the generalized Hooke's law. In the mathematical model used in this work to describe elastoplastic deformation, it is assumed that the volume compressibility of the single crystal is constant in the region of elastic and plastic deformations. It is shown for the first time that with the above rotation of the coordinate axes in a cubic single crystal, a change in elastoplastic deformations in the direction of the axis of impact loading is observed. [ABSTRACT FROM AUTHOR]