Metamaterials are artificially created materials which unusual properties are due to their geometric structure, not the chemical composition of the base material. The control of physical and mechanical properties through the structure is fundamental for metamate-rials. The tools of the numerical analysis used in this work overweigh experimental tests due to the automation of research, reduced material and financial costs. Here, a tetrachi-ral metamaterial is investigated under uniaxial compression conditions. The base materi-al is described as an elastic medium. An analysis of the influence of the metamaterial's structural organization on its mechanical response is carried out. To do this, two meth-ods of connecting unit cells are considered: "joining" and "overlapping". The following are selected for the analysis: (1) the tension – torsion coupling effect; (2) effective elastic properties (Poisson's ratio and Young's modulus); (3) porosity; and (4) the state of stress and strain. The porosity of the samples obtained by the "joining" method was 80 % and the "overlapping" method resulted in 84 %, the volume of the base material in the second case was 1.6 times larger. It was found that the tension – torsion coupling effect is affect-ed not only by the volume of the base material but also by the internal organization of the structure, namely, the versatile chirality of the touching faces of the unit cells. Analysis of the numerical experiment results showed that the three – dimensional samples have a zero value for the effective Poisson's ratio. The Young's modulus of the sample in which the cells were connected by the "joining" method turns out to be almost 2.7 times higher. Both samples can be described as an anisotropic medium with a lattice in the cubic sys-tem medium, which is shown by studying the properties of metamaterial samples when loaded along three orthogonal axes. The construction created by the "joining" method is characterized by a more heterogeneous pattern of stress distribution and presence of stronger stress concentrators.

This work proposes the elaboration of the variational principle of L.I. Sedov for modeling dissipative processes. The formulated variational principle makes it possible to propose the dissipative models using the known model of a reversible process (the known Lagrangian), adding the required number of dissipation channels. Dissipation channels are non-integrable variational forms that are linear in the variations of the ar-guments. The arguments of the dissipation channels are the generalized variables of the corresponding bilinear terms of the Lagrangian. Variational models of heat transfer pro-cesses are considered as examples. The paper introduces the thermal potential, which is taken as the main kinematic variable. The temperature and heat flux are determined from the expression of the possible work done on variations of the first derivatives of the thermal potential, by analogy with continuum mechanics, where internal forces do the possible work on the strain variations. The equations of heat conduction laws of the considered heat transfer models are obtained as compatibility equations by eliminating the thermal potential from the equations of constitutive relations for temperature and heat flow. It is shown that the proposed procedure for elaboration of the dissipative models makes it possible to obtain the laws of thermal conductivity of Fourier, Maxwell – Catta-neo, Gaer – Krumhaksl, Jeffrey and more general laws of thermal conductivity. For the simplest heat transfer model, a single dissipation channel was introduced, which made it possible to obtain a heat transfer equation containing the second and first time deriva-tives. This model takes into account the wave properties and dissipation by the diffusion mechanism. In a particular case, it is reduced to the classical model of heat conduction. For more general gradient models of heat transfer, additional dissipation channels are sequentially introduced. In accordance with the differential order of the heat balance equation, the variational method makes it possible to formulate a consistent spectrum of boundary conditions at each non-singular point of the surface. In addition, for a bounda-ry value problem in time, the variational principle determines pairs of alternative condi-tions at the initial and final times of the process under consideration.

Crystal plasticity models combined with an explicit consideration of a polycrystalline structure are an effective tool for studying the deformation phenomena throughout length scales. A numerical solution to the boundary-value problems with an explicit account for misrostructural features requires extensive computational resources. The use of explicit time integration schemes effectively reduces computational costs yet providing a qua-sistatic solution with a high degree of accuracy. In this paper, we discuss the numerical aspects of crystal plasticity finite element simulations of quasistatic deformation phe-nomena in terms of explicit dynamics. The equations for plastic strain rate are formulated in a way to minimize strain rate sensitivity, which is the necessary condition for simulat-ing quasistatic deformation at artificially high strain rates. The problems of model verifi-cation and testing at the micro, meso, and macroscales are discussed using the example of aluminum single- and polycrystals.

Single-crystal superalloys, used in production of gas turbine blades, have a pro-nounced anisotropy of mechanical properties and high short-term, long-term and ther-mal fatigue strength. Based on a microstructural model of elastoplastic deformation, which takes into account the presence of octahedral and cubic slip systems, a study was carried out of the influence of the crystallographic orientation of single-crystal samples on the level of plastic strain under uniaxial tension and on the range of plastic strain under intense thermal cycling. Anisotropy of the plastic properties of single crystals manifests itself in the dependence of the level of plastic strain on the direction of load-ing. The contribution of octahedral and cubic slip systems under uniaxial loading in dif-ferent directions with respect to the crystal lattice has been evaluated. The evolution of the spatial orientation of plastic strain with a monotonic increasing of loading has been studied; the initiation and competing growth of local maxima have been analyzed. The angular coordinates of all possible 7 local maxima within the stereographic triangle are found and the load ranges of their dominance are indicated. The results of studying the influence of temperature and hardening on the orientation distribution of plastic strain are presented. The influence of the sample crystallographic orientation on the plastic strain level under symmetric and nonsymmetric cyclic loading has been studied. The results of modeling the cycle-by-cycle kinetics of plastic strains and their orientation distribution are presented. The results of the computational experiments for corset sam-ples for thermal fatigue tests showed a significant sensitivity of the plastic strain range to the deviation of the sample axis from the [001] orientation even by a few degrees, which indicates the need to revise the accepted tolerance of 10 degrees.

The effects of intermittent plasticity, despite almost 200 years of history since its dis-covery, are still intensively studied by mechanics, materials scientists, and technologists processing metals and alloys by plastic deformation. With the development of experi-mental methods and instrumentation, more and more new mechanisms are being discov-ered that are responsible for the violation of the monotonicity of the response (stresses) under monotonic effects (growth of strains). To describe these effects, constitutive mod-els (constitutive relations) based on various (macrophenomenological, thermodynamic, structural-mechanical, physical) approaches have been proposed and continue to be developed. Despite the variety of reasons for the emergence of discontinuous plasticity, it is generally recognized that in order to build correct constitutive models, it is necessary to analyze the processes that occur during inelastic deformation at the meso- and microlev-els, and to describe the evolving structure of materials at various scale levels. Thus the use of physically oriented models is the most promising area of studies for the formula-tion of constitutive relations. The proposed article provides a brief overview of works constructing physically-oriented constitutive models suitable for studying the effects of discontinuous plasticity. The first part of the review presents models based mainly on the phenomenological ap-proach to the formulation of a set of equations for studying the evolution of the defect structure of single- and polycrystalline alloys, most of which use the continuum descrip-tion. When creating physically-oriented models, special attention is paid to the consid-eration of the mutual influence of defects of various natures, including the interaction of impurity atoms with dislocations. The second part of the review considers works based on the introduction of internal variables, a multilevel physically-oriented approach. Un-fortunately, second-class models are currently very limited; nevertheless, the authors consider them the most promising for constructing constitutive models that adequately describe the effects of discontinuous plasticity.