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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 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]

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 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]