The paper presents a finite element analysis of the localization of plastic deformations in the region of fracture of the model disk  during rotation. At a certain angular velocity of rotation of the disk,  an "ejection"is observed experimentally. This effect occurs when the  material stability is lost, is analogous to the known "necking"in the  specimen tension. In view of the finiteness of the observed  experimental displacements and for the detection of the  "tightening"effect in a numerical experiment, the equilibrium  equations are integrated taking into account the finite deformations.  The model calculation was carried out in a quasi-static setting with a  step-by-step increase in the rotational speed. The plastic behavior of  the metal alloy of the disk material is described according to the  Huber-Mises limit surface. The material parameters used in the calculation are determined from the experimental tension curve of the sample. Elasto-plastic governing relations are used in finite  deformations with a multiplicative decomposition of the deformation  gradient into the elastic and plastic components. In fully plastic  deformation of metals, due to the constancy of the first invariant of  plastic deformations, the process of deformation is close to isochoric. In such cases, linear isoparametric finite elements show the effect of “volumetric locking which distorts the numerical result. Therefore, in  calculations we use twenty-node volume finite elements of the second order, which have no specific feature. The calculations were carried out on the IMERS-Fidesis hardware-software complex. The  energy and noise efficiency of a cluster in distributed computations is studied. The article concludes by comparing the numerical results  with the experimental data and the energy efficiency level of the cluster.

The paper considers the numerical method of solving problems of strong interaction between a liquid (gas) and a deformed body:  the fluid exerts a force on the body, the body changes its shape, the altered shape of the body changes the flow. The developed  method is demonstrated on the test problem of air flow around the  valve. The problem is solved in a three-dimensional formulation. The deformable body flows around an unlimited airflow at right angles. The authors consider the body deformation dependence in the  presence of a defect (hole) in it located in different positions. The air flow is calculated in the FlowVision software package. FlowVision  uses the finite volume method for approximation of the fluid motion  equations. It implements an explicit and implicit methods of  integrating these equations. FlowVision can solve interdisciplinary problems: simulate multiphase flows using the VOF method, set the  motion of bodies (movement of impermeable boundaries) along a  fixed computational grid, simulate flows in rotating machines using  the sliding grid method, solve fluid-body interaction problems using two-way coupling between FlowVision and FEM software. The body deformation is calculated in the CAE Fidesys software package. CAE Fidesys allows to conduct various types of full-cycle strength  engineering analysis from the construction of a mesh to the visualization of calculation results. For the numerical solution of solid mechanics problems CAE Fidesys uses the finite element method and the spectral elements method. CAE Fidesys allows to solve both  linear and non-linear, static and dynamic strength problems. For  joint calculation, a two-way coupling technology was developed that performs two-way communication between the CAE Fidesys and  FlowVision systems. With the use of this technology, a numerical investigation of the problem of flow past a valve carried out. The  behavior of the valve is compared with various variations in the  location of the elliptical hole in it. The results lead to the conclusion  that the associated FlowVision- CAE Fidesys software package  calculates valve characteristics on meshes of moderate dimension with reasonable accuracy.

The determination of effective stiffness tensor of microinhomogeneous and, in general, macroscopically homogeneous composite medium is related to so-called problem of many-body interaction. Solution to the problem can be found only as an  approximation. In this paper we consider a solution to such a  problem for porous-cracked medium that is a terrigenous rock  having anisotropic elastic properties. The elastic anisotropy is a  result of many factors including anisotropic properties of clay  minerals and preferential orientation of non-isometric  heterogeneities. Different Effective Medium Theories for calculating  effective stiffness tensor of cracked porous medium use so called  Effective Field Hypothesis (H1, H2 and H3). For example, T-matrix  method, Mori-Tanaka method, General Singular Approximation method, and Effective Field Methods use the Effective Field Hypothesis. Thus, different methods produce similar results.  When constructing models of rock’s effective properties the rock is  treated a composite “made by nature”. In this case of importance is  a proper approximation of the real medium by a parametric model  medium that reflects specific features of rock’s microstructure. The  microstructure is a result of rock evolution. Therefore, the model of  the medium and the model parameters play very important roles in the modelling. To prove this statement, two models of a cracked- porous medium’s properties were created using two different methods: the T-matrix method and General Singular  Approximation Method. The methods were applied for two different  parametric models of one and the same rock. The models were build  based on visual analysis of rock’s thin sections. Each of the  constructed models has different number of parameters. The  parameters are also different. However, a common feature of the two models is that for rocks of this type it is necessary to take into  account a rigidity of contact between mineral grains and organic material. Besides, a connectivity of different heterogeneities should  be also parametrized. For each model a set of parameters was found and a porosity interval where the models produce similar results in terms of elastic wave velocities is determined.

The present work is devoted to the development of the production of
three-layered hollows structures made of VT6 titanium alloy by means of superplastic forming (SPF) and pressure welding. Finite- element modeling can be successfully applied to optimize the  forming process, if the adequate constitutive relations would be  defined and the friction at the contact surface of the material with  the die would be specified. To find the friction coefficient and the  parameters of the constitutive relations for metal forming process,  test experiments are conducted to the forming of sheet into dies of  various shapes. In such test experiments, a biaxial loading is  realized, as in the actual processes of fabricating complicated  structures from sheet by SPF. To this end, Finite-element modeling of the SPF process of sheet forming into dies of two types is performed: (i) into wedge die having cross section in the form of equilateral triangle, and (ii) cone die. Recommendations are given for the choice of the optimum angle at the vertex, determining the geometry of the dies, which results in the constancy of the stresses during forming at constant pressure. The methodology for estimating the coefficient of  friction on the contact surface between sheet and die is given. Finite- element modeling of the SPF process of three-layer hollow structures is carried out using the parameters of the constitutive relations  obtained by the proposed methods. Technological constraints on the geometric parameters of structures, such as the angle of inclination  of the stiffening ribs and the thickness ratio of outer to inner sheet  thicknesses are established, which provides forming without the  formation of folds on the shell and the minimum variability of ribs thickness.

Plastic deformation of rocks and generation of residual deformation field are related to shear and tensile cracks formation.  For conditions of three-dimensional stress state a strength (yield)  criterion is proposed that takes into consideration combined effect of two kinds of failure (shear and tensile failure) and is based on associated flow rule. The developed criteria relations were verified  during description of results of rocks mechanical tests. Acceptable  concordance between calculated and experimental values of breaking stresses and strains was obtained. Developed algorithm for critical  stresses, elastic and plastic deformations determining is easy enough for numerical realization in three-dimensional problems of  mathematical modelling of deformation and failure processes of  large-scale mine technical objects.

The possibility of constructing a system of specialized solutions for strength analysis based on CAE Fidesys is considered. The results of testing CAE Fidesys are presented. The finite element method and the spectral element method implemented in CAE Fidesys are discussed for the problems of mechanics of a deformable solid. The  opinion is expressed that at this stage of the development of CAE  Fidesys it can be used as an alternative CAE for carrying out control  calculations, especially when solving non-typical tasks, in the  solution of which there is a need to modify and adjust the main  computational algorithms incorporated in the software. As a part of  CAE Fidesys all the necessary elements are provided to ensure the  effectiveness of its application - a preprocessor that provides the generation of finite element models, a modular processor for solving linear and nonlinear static and dynamic problems, buckling  problems, estimation effective properties of composite materials,  contact problems, postprocessor for visualization and processing of  results. The results of testing CAE Fidesys are presented in  comparison with the results obtained in ANSYS. The main purpose of the testing was to evaluate the possibilities of CAE Fidesys in terms of: importing geometry from CAD systems; the effectiveness of finite element mesh generator; determination of the stressstrain state of assemblies with a variable contact zone; solving dynamic problems,  including modal and harmonic analysis. Testing of CAE Fidesys was  performed on test cases representing the problems which are  frequently faced in practical work. It is noted that the distinctive  feature of CAE Fidesуs is the highorder spectral elements allowing  one, in some cases, increase the accuracy of calculation without  rebuilding the finite element mesh. It is noted that a comparative analysis of the calculations done on the models with similar finite  element meshes conducted in CAE Fidesуs and ANSYS shows good  coincidence of the results. The conclusion is that CAE Fidesуs can be  used for solving different problems of structural analysis in addition  to another CAE software available on the enterprise, and also taking  into account the practical needs of active users, it can be considered, when combined with the user’s requirements, as the basis of an  industrial solution for a structural analysis.

A geometrically and thermodynamically consistent mathematical model of large strains of materials with elastic, viscous and plastic  properties is proposed. It is believed that at the stage of a strain,  which precedes the plastic flow and during unloading, the viscous  material properties provide the creep process and thus a slow  growth of irreversible strains. While rapid growth of irreversible  strains under plastic flow conditions, viscous properties act as a  mechanism that retards the flow. The accumulation of irreversible  strains, therefore, occurs successively: initially, in the creep process, then under plastic flow and, finally, again due to creep of the material (during unloading). On the elastoplastic boundaries  advancing along the deformable material, there is a change in the  growth mechanism of irreversible strains from creep to plasticity and vice versa. Such a change is possible only under conditions of  continuity of irreversible strains and their change rates, which  imposes the requirement of consistency in the definitions of  irreversible stress distribution rates, i.e., the laws of creep and  plasticity. Changing the production mechanisms of irreversible  strains means various setting up of the source in the differential  equation of the change (transfer) of these strains, hence irreversible  strains are not divided into plastic strains and creep strains. To maximize the visibility of the model’s correlations, the hypothesis on  the independence of thermodynamic potentials (internal energy, free energy) on irreversible strains is accepted. As a consequence of the hypothesis, an analog of the Murnaghan formula is obtained, the  classical position of the elastoplasticity is that the stresses in the  material are completely determined by the level and distribution of reversible strains. The main provisions of the proposed model are  illustrated by the solution in its framework of the boundary value problem of the elastoviscoplastic material motion in a pipe due to a varying pressure drop.

In the article theoretical basis of flexible bodies’ large displacement within a multibody system as well as practical  experience of flexible multibody dynamics simulation with integrated  computer-aided design software systems EULER and Fydesis are  considered. The hypothesis of flexible body undergoing both small  elastic deformations and large motion within a multibody system is  used [2]. The derivation of dynamic equations of motion of flexible  bodies was first published in [3]. The derivation uses classical  (linear) finite element method (FEM) and the Craig–Bampton method [1] of FE model’s matrices reduction. No additional approximations are involved, thus obtaining the most general  equations in given problem definition. In the Craig–Bampton method a finite element model of a flexible body is reduced approximating  small elastic deformation with a set of modes: static modes where  the bound nodes’ displacements equal one unit, and normal modes  where the bound nodes are fixed. The full finite element model and  the reduced model are prepared in Fidesys software [4] and are  transferred to EULER software to be used in a dynamics simulation as a part of a multibody system. For the flexible body’s  spatial motion representation a floating frame of reference is used. A floating frame of reference defines the motion of a rigid body, related to which flexible body’s motion is considered as small deformations.  The dynamic equation for flexible bodies are derived from Lagrange  equations of the second kind. As generalized coordinates the floating frame of reference’s position and the modal coordinates vector are  used. The expressions for the inertial forces vector and the  generalized mass matrix are derived from the expression for the  kinetic energy of the body. The article also contains all the other terms of the dynamic equation and the expressions for  constraint equations’ components calculation. In the article an example of real practical motion simulation for KAMAZ-5308 vehicle  with taking into consideration the flexibility of the vehicle’s frame is  given. A finite element model of the frame with the load platform  was developed to consider it’s flexible deformations. The following assumptions have been adopted for simulating the vehicle:  additional attachments to the frame and platform, load platform’s  wooden flooring are considered significantly less rigid than the basic  structure; brackets for attaching the suspension and the cabin are considered very rigid in comparison with the structure itself;  roundings and technological apertures are not considered. As the  interface for dynamic reduction, there are 26 nodes corresponding to the places of attachment to the frame of the rest of the car -  suspension, load and cabin. After the development of the finite element model in the Fidesys software, four files are created,  containing the stiffness and mass matrices, model geometry, normal  and static modes. The obtained model of the frame is used in the EULER software as part of a multibody system motion simulation.  The model of a car with a flexible frame is used to take into account  the effect of the dynamics of the car as a whole on the stress-strain state of the frame in the lane change maneuver.

We study several algorithms for solving the coupled problem of hydrogeomechanical modeling of fluid filtration in a deformed  fractured rock, allowing to describe the mutual influence of filtration  and rock deformation processes on the dynamic parameters of the  medium: porosity, permeability, rock stiffness and fracture  extensions. These algorithms allow solving the problems of choosing  the location and drilling trajectory of a well either wellbore stability,  ensuring high productivity of the formation due to optimization of  the design of hydraulic fracturing and sand control. Together with seismic and reservoir testing data, coupled hydrogeomechanical  modeling allows optimizing the tactics and strategy of reservoir  development. The disturbance of formation stress-strain state in the  near-well zone leads to the development of deformation processes and fracture zones, as well as changes in pore pressure and filtration properties in the reservoir. At the first stage, we verify external and  internal iterative external coupling procedures. The specially  developed research code was used for internal coupling procedure.  For external coupling, a finite element simulator FIDESYS was used  which solves numerically the problems of geomechanical stresses  and deformation distributions in the rock. We developed the control  module to organize the iterative process of geomechanical and  hydrodynamic simulators, including reading special simulation data formats, unit conversion, as well as the value fields projection on  different model grids. In this paper, we present the modeling for  several problems and discuss the computation results. Effective  elastic-strength properties are determined numerically at every  mesh node as a result of solving the time consuming spatial  elastoplastic problem. Therefore, the reduction in the frequency of  data exchange is important in this approach. One of the goals of this numerical study, related to the above methodology, is to determine the effect of the coupling frequency on the solution. Based on the  computation results for the example of the cyclic CO2 injection  procedure in the Bazhenov Formation formation (Palyanovo section), only the local production characteristics are sensitive to  the coupling frequency. The results obtained in this paper allow us to conclude that the role of geomechanical effects of fractured rock deformations saturated with a fluid is significant for modeling the formation  processes.

In the article, types of parallelism used in architectures of modern computer systems are considered, and the ways of their  manifestation in programs are described. Six paradigms of parallel  programming are analyzed, and the relationship of paradigms to  generations of highperformance computing systems is shown.  Different methods of description and representation of parallelism  based on various kinds of program models are considered. The  reasons that determine challenges of developing efficient software  packages for parallel computing systems are discussed. The connection between the  material under discussion and the actively developed Internet  encyclopedia of properties and features of AlgoWiki parallel algorithms is noted.

The apparatus of tensor nonlinear functions occupies an important place in the nonlinear mechanics of a continuous medium, both in  hydrodynamic applications and in problems of mechanics of a  deformed solid, strength and fracture [1]. Tensor nonlinear defining  correlations simulate the socalled orthogonal effects of the stress- strain state (see in [2] a review on the issue), characterized by  noncollinearity of voltage deviators and the corresponding kinematic  tensor. Such a noncollinearity can explain the Poynting effect and  ratchet [3–9]. The scientific works pays much attention both to the  definition of the main flow parameters and to the stability of such a  flow with respect to small perturbations belonging to a particular class. The statement of the boundary value problem in  perturbations assumes the linearization of all the system equations  near the main process, including the defining correlations. Along with the general form of the tensor-nonlinear determining relations,  the paper considers tensor-linear isotropic media, tensor linear  potential media, the Bingham body (a twoconstant viscoplastic  model), the Saint-Venant flow (ideally rigid-plastic model), and the Newtonian fluid.

In paper initial-regional problems for linear differential equations are
considered The mathematical physics (elliptic, hyperbolic and parabolic) with variables In the factors depending on coordinates and time. Such equations together with input datas we will be To name  initial. The equations with variable factors describe processes in the  composite Materials at which mechanical performances change or a  saltus or it is continuous in Boundary region between phases. Many  problems from various sections linear and nonlinear Mechanics are  reduced to a solution of simple equations with variable factors. In  case of periodic factors on coordinates one of popular modes of a solution of the equations The method of average of Bahvalova– Pobedri (MBP), based on representation of a solution is initial  Problems in the form of an asimptotical series on degrees of the  small geometrical parametre equal to the ratio Characteristic size of a mesh of periodicity to a characteristic size of a skew field. In this  method the initial The boundary value problem is reduced to two  recurrent sequences of problems. The first recurrent The sequence  consists in determination of periodic solutions of auxiliary problems  in a mesh Periodicity. The second sequence consists in a solution of  initial-regional problems for the equation with In constant effective factors. These factors are after a solution on a mesh Periodicity of  auxiliary problems. As base of a recursion in the second sequence in MBP serves Solution of a initial-regional problem for the equation  with effective factors in definition range, Having the same form and  it is exact with the same input datas, as an initial problem. Input  datas in each of recurrent sequences on what or a pitch are only after that as the previous recurrent problems are solved all. In the  present paper the new integral formulas are received, allowing to  express a solution of the initial Problems for the equation with the variable factors depending on co-ordinates and time, through a  solution The same problem for the equation with constant factors. The equation with constant factors Is called as the accompanying  equations, and the problem according to accompanying a problem.  In the kernel The integral formula the Green function and a  difference of factors initial and accompanying enters The equations.  By means of expansion of an accompanying solution in a many  dimensional Taylor series from the integral Formulas equivalent representation of a solution of an initial problem in the form of a  series on the various is received Derivative of a solution of an accompanying problem. Factors at derivatives are called as structural Functions. They are continuous functions of coordinates and time,  converted in zero at Coincidence of initial and accompanying factors. For definition of structural functions it is constructed System of the recurrent equations. Through structural functions factors of the  accompanying are defined The equations, coinciding in a periodic  case with effective factors in MBP. Unlike Method of Bahvalova–Pobedri in the new approach it is necessary to solve one recurrent  sequence of problems For determination of structural functions and  once to solve a problem for a homogeneous skew field with the  effective In performances.

This article is devoted to the problem of thermal convection in porous media with volumetric heat generation modelling, arising in  practice of radioactive waste (RW) disposal safety assessment. In  the first section a brief overview of widespread hydrogeological  codes (FEFLOW, SUTRA, SEAWAT, TOUGH2) featuring the ability to  solve thermal problems is done. We point out the lack of heat  generation caused by radioactive decay model in these programs.  The GeRa numerical code developed by the authors is presented. In  the second section we consider the mathematical model of coupled groundwater flow, solute and heat transport, which is  implemented in GeRa. The model describes these processes in  saturated porous media and takes into account radioactive decay,  sorption on the rock, the dependences of density and viscosity on  temperature. The heat transport equation is written assuming thermal equilibrium between the fluid and the rock. The model  includes heat transport by convection and conduction-thermal dispersion. The heat source terms can be wells and volumetric heat generation due to radioactive decay. The numerical scheme  implemented in GeRa to solve the aforementioned coupled problem  is introduced in the third section. The space discretization is done  using finite volume methods (FVM). Sequential iterative coupling implicit scheme is used for temporal discretization. On each iteration  of the scheme the flow, heat transport and solute transport problems are solved sequentially. The fourth section is devoted to the test  problem of heat generating fluid convection in a closed two- dimensional cavern filled by porous material with isothermal walls.  The results obtained using GeRa code are compared to the  asymptotical solution deduced by Haajizadeh. In the fifth section we  present the results of modelling with GeRa the experiments of  Buretta and Berman in which they investigated the regimes of free thermal convection of fluid with volumetric heat generation in porous media. The dependences of Nusselt number on the Raley number  measured in the experiments and calculated numerically are  compared. In the sixth section we consider the test problem of  continuous injection of high-level RW into an aquifer. Here the ability to model coupled flow, heat and solute transport processes is shown. The numerical solution obtained using GeRa is compared to a known analytical one.

Large strains of composite solids made of incompressible isotropic nonlinear-elastic materials are analyzed for the case in  which the parts of these solids are preliminarily strained. The  approaches to exact analytical solutions of these problems are given  and developed in cooperation with V.An. Levin. He is a professor at  the Lomonosov Moscow University. The solution of these problems is  useful for stress analysis in members containing preliminarily stressed parts. The results can be used for the verification of industrial software for numerical modeling of additive  technologies. The problems are formulated using the theory of  repeated superposition of large strains. Within the framework of this  theory these problems can be formulated as follows. Parts of a  member, which are initially separated from one another, are subjected to initial strain and passes to the intermediate state. Then  these parts are joined with one another. The joint is performed by  some surfaces that are common for each pair of connected parts.  Then  the body, which is composed of some parts, is strained as a  whole due to additional loading. The body passes to the final state.  It is assumed that the ideal contact conditions are satisfied over the  joint surfaces. In other words, the displacement vector in the joined  parts is continuous over these surfaces. The exact solutions for  isotropic incompressible materials are obtained using known  universal solutions and can be considered as generalizations of these solutions for superimposed large strains. The following problems are considered in detail:

— the problem of stress and strain state in two hollow circular elastic cylinders (tubes) one of which is preliminarily strained and inserted into another cylinder (the Lam´e-Gadolin problem);

— the problem of torsion of a composite cylinder;

— the problem of large bending strains of a composite beam consisting of some preliminarily strained parts (layers). The  mathematical statements of these problems are given, the methods  of solution are presented, and some results of solution are shown.  The impact of preliminary strains on the state of stresses and strains is investigated, and nonlinear effects are analyzed.

There are variety of factors affecting degradation of composite materials due to environmental effects. In the present manuscript, two  sources of degradation are studied. We first consider an accumulation of damage in carbon-fiber/epoxy-resin material system subjected to cyclic  load. A  multiscale-multiphysics approach is developed for degradation  of glassfiber/ Nylon material system due to moisture accumulation. A  multiphysicsmultiscale approach couples diffusion-reaction-mechanical  process at multiple spatial scales.

Within the framework of the continuum mechanics, the authors develop a two-component impurity-containing model and investigate the mutual influence of impurity diffusion and the basic structure strains. They derive the equation of impurity motion — the  generalized diffusion equation, which allows them to take into  account not only impurity transport due to the basic structure  motion, but also the effect of strain on the diffusion coefficient. The  paper considers modeling problems that qualitatively describe two  most important phenomena that are observed experimentally under  vibration on materials with an admixture, localization of the impurity concentration, and the drop in the generalized rigidity of the sample. In both problems, approximate analytical solutions are  obtained that are in good agreement with earlier numerical studies and experimental data.

An implicit finite difference scheme approximated barotropic gas equations is proposed. This scheme ensures positivity of density  compared to previous methods. Existence of a solution to this scheme is proved for any time and space mesh-steps, an iterative method for  solving the system of nonlinear equations on each time step is proposed.

Estimation of effective properties of composite materials is one of the main problems for the composite mechanics. In this article, a method is developed by which the effective nonlinear elastic  properties of elastomer composites (filled rubbers) are estimated  under finite strains. The method is based on numerical solution of  nonlinear elastic boundaryvalue problems for a representative  volume element (RVE) of elastomer composite. Different boundary  conditions are consequently applied to the RVE: nonperiodic  (displacements of the RVE boundary) or periodic (restraints on  displacements of corresponding points of opposite faces of RVE). An obtained stress field is averaged by volume after the solution of an  elastic boundary-value problem. Effective properties are estimated  as a quadratic dependence of the second Piola-Kirchhoff stress  tensor upon the Green strain tensor. This article presents the results of numerical estimation of effective elastic properties of filled  rubbers under finite strains. Numerical calculations were performed  with the help of Fidesys Composite program module, which is a part  of the domestic Fidesys CAE-system, using the finite element method and the spectral element method. Spectral element method  is one of the most effective and modern finite element method  version. High order piecewice-polynomial functions are reference functions in SEM. There is no need to rebuild or refine mesh to check solution mesh convergence, as mesh is kept in initial state and only  element orders are changed. The subject of investigation was the  filled elastomer effective properties dependence upon the filler  particles special orientation and the filling degree. Graphs of these dependencies are given in the article. The obtained results show that the spectral element method is suitable for numerical solution of the effective properties estimation problem for composite materials. In  addition, the results allow to estimate the influence of non-linear  effects upon the mechanical properties of the composite. The correction for stress from taking the non-linearity into account is  about 25% under the strain 15% in the case of uniaxial tension.

A periodic one-dimensional harmonic crystal subjected to an instantaneous spatially uniform thermal perturbation is considered. Fast  transitional and long evolutionary processes are observed. Time  dependance of thermal and diffusion characteristics is analyzed.  Influence of the crystal finite size on the transitional and evolutionary  processes is considered. The principal difference in long time behavior  for statistical averages for squares of velocities and squares of displacements is demonstrated.

Development of engineering-geological processes, including dangerous, within the boundaries of the area of active influence of  mining operations in the undeground minings (tunnels, preparatory  face or working face) at the massif of mountain rocks, is due to, as  is well known, changing in structure and parameters stress-strain  state (SSTS). Estimation of stresses in the near zone of exposures of the massif (within the first meters) is carried out by a number of instrumental methods, regulated by federal or departmental  documents for those or other engineering and geological conditions  and technologies for mining (pressure installations, disking of core,  extraction of rubbles, etc.). Widely known and experimental  analytical methods based on stress calculations in the neighborhood  of working area from known (measured) initial stresses on the  exposures of the massif. A significant advance in the development of the experimental and analytical approach to the organization of  continuous monitoring and forecasting the development of  hazardous engineering and geological processes in underground  construction is the improvement of seismic methods of remote  evaluation of the structure and parameters of SSTS [1, 6, 12, 13]. It should be noted that at present several regulatory documents on the forecast of dynamic phenomena and monitoring of rock mass during mining of coal deposits, as well as the state of the mine atmosphere  in the excavations and which regulate, among other things, the use of seismic monitoring systems [2, 3, 4]. Similar documents in  departmental formats are also applicable to the conditions of  construction of transport tunnels, hydroconstructions and other  objects of increased responsibility. The article proposes an approach  to the creation of a geoinformation safety panel of underground mining works based on related solutions in prognosis of the  development of stressed state of the massif of mountain rocks and  gas flows within the framework of the Fidesis strength analysis package.

In the paper, our recent phase field approach (PFA) to the interaction between phase transformations (PTs) and dislocations at the  nanoscale is reviewed. It is developed at large strains as a nontrivial  combination of our recent advanced PFAs to martensitic PTs and  dislocation evolution. Finite element method (FEM) simulations are  performed to solve the coupled phase-field and elasticity equations. The evolution of dislocations and high pressure phase in a nanograined material under pressure and shear is studied and utilized for  interpretation of experimental results on plastic strain induce PTs under high pressure in rotational diamond anvil cell.

The analysis of the theory of brittle fracture Frenkel. The analysis is based on the theo-ry of catastrophes. By replacing the variables in the equation of potential energy Fren-kel of the canonical reduced  form of the equation of catastrophe folds. A state variable in the  resulting equation of the fold is the crack length. Equating to zero  first and sec-ond derivatives of the energy on the crack length,  obtained critical force and critical length of crack. Critical crack  length and critical load at Frenkel are independent from each other.  Their values depend only on the internal of the system operating  parame-ters – modulus of elasticity, surface energy and opening of  the crack tip. It is shown that the length of the initial crack grows in  the process of approach to the critical state. The resulting equation  linking the length of a steadily growing crack with the external load  and control parameters of the system. An attempt of modernization theories of brittle fracture Griffith based on the ideas of Frenkel. To  do this in a well-known energy equation in Griffiths introduced the  third member. The energy of this member is inversely proportional to the crack length. Equating to zero first and second derivatives on the crack length, obtained a system of equations. Solving this system of  equations, obtained formulae for critical crack length and critical stress The estimation of permanent member, the third member of the modernized equations Griffiths. The length of the  critical crack for upgrade equation is 20% small-er than the crack  length according to the classical equation of Griffith. The stable crack length in Frenkel and modernized Griffiths equation corre-sponds to the local minimum of potential energy. This fact virtually eliminates  the singularity at zero crack length. The third member in the Frenkel equation can be interpreted as the energy of the crack opening. Thus Frankel joined the force and deformation criteria modern fracture  mechanics. The Frenkel equation, which describes the critical state of a solid body with a crack that precedes the appearance of modern  catastrophe theory in general and in relation to the mechanics of brittle fracture, in particular.

The basis for the analysis of such characteristics as strength, lifeendurance and safety of machine elements and structures in  standard and emergency situations are the equations and criteria for linear and nonlinear mechanics of deformation and fracture. They are a part of the strength standards and are used both in the design  and in the manufacture and operation of equipment. The article  shows that the results of strength, resource and survivability studies  are the basic component to create the foundations of the  catastrophes and risks mechanics in the technogenic sphere, new  principles, technologies and technical complexes that ensure their safe operation and let in a theoretically grounded manner  prevent the appearance of emergency and catastrophic situations,  and minimize possible damage when they occur. At the same time, the instrument for ensuring safe working conditions is to diagnose  the current parameters of the material state and to determine the  characteristics of stress-strain states in the most stressed zones of  the analyzed technical system. The solution of the problem of  strength and resource evaluation in such conditions includes the  creation of generalized mathematical and physical models of  complex technological, working and emergency processes in  technical systems for analyzing the transition conditions from regular states to the conditions of occurrence and development of accidents and catastrophes. Such models are characterized by a multilevel  structure that affects global, local and object security aspects. The  developments are interdisciplinary in nature and underlie the safety and risks rationing.

Considered small (short) crack in a solid body. In certain cases, there is a difference in the mechanical behavior of solid bodies in the presence of short or long cracks in the same place details. Discusses some of the effects arising from cyclic loading during the initial  growth of short cracks, and transforming it into a long. The urgency  of the problem of small cracks are fairly obvious, but it is not clear  what the crack is considered small. It is possible to give several  definitions of small cracks. For example, it is convenient to refer to  the small cracks are those that meet the lower resolution limit of the flaw detection equipment. However, the resulting absolute sizes are not associated with the process of the mechanical behavior of body  with crack. Better the crack length comparable with the characteristic width of the specimen (parts) or diameter of the  plastic zone at the tip of the crack. Under cyclic loading the behavior of cracks in the area of concentration also has its own  characteristics, which are expressed in the initial acceleration of the  crack, and then, with increasing length, her speed drops. Among the considered types of short cracks can be identified cracks that entirely fit in the areas of high stresses around notches. Such cracks are called mechanically short. The length of such cracks is  comparable with the crack length, determining a threshold stress  intensity factors in the experiments to determine the characteristics  of cyclic crack resistance. As can be seen from the calculations, the mechanically short crack grows rapidly at first, but as the field of  concentration, reaches a minimum and then increases again, leaving a region of concentration. Further, the crack goes into the category of long, following the classic formula of Paris.

In this work questions of numerical modeling of dynamic problems of
the Arctic zone on high-performance computing systems are considered. The physical sizes of field of integration in such tasks  can reach tens and hundreds of kilometers. For correct modeling of  distribution wave indignations on such distances are required high- precision numerical methods taking into account wave properties of  the solvable equations and also a possibility of modeling of difficult  dynamic processes in nonuniform geological environments with a set of contact and free borders. As such numerical method in work the net and characteristic method [1] to the numerical solution of  systems of the equations of mechanics of a deformable solid body is  used. This method allows to use monotonous differential schemes of  the raised order of accuracy [2], to build correct numerical algorithms on borders of fields of integration and on contact borders  [3]. This method was already applied to some problems of seismicity in a two-dimensional case [4], in this work modeling was  carried out in three-dimensional statement. We will mark that the  grid and characteristic method was successfully tested for the  numerical decision of tasks in such fields of applied science as  hydroaerodynamics, dynamics of plasma, the mechanic of a  deformable solid body and corrupting, computing medicine.  Examples of its application are described in different appendices in  operation [1]. 

The paper presents the basics of movable cellular automaton method
aimed for simulating deformation and fracture of materials and media at different scales. Initially, the particle method has been  employed in mechanics of materials only at microscale as molecular  dynamics. Its further development has been led to a group of  methods which are usually called as discrete element method and  used for simulation of loose and granular materials at the  macroscale. The presented method of movable cellular automata  was developed for simulating deformation and fracture of materials  at different scales: at mesoscale with an explicit account for material structure, and at macroscale within the framework of a media with effective properties. The main advantages and differences of  the approach compared with the other methods of discrete  computational mechanics are considered. These advantages, first of all, are determined by the fact that the considered approach is based on two basic methods of discrete simulation: particle method and  cellular automaton method. Employing the formalism of cellular  automata allows explicit description of both processes of damage  generation and evolution as well as of crack healing and  microwelding. More of that, it is possible to describe heat transfer, chemical reactions and phase transitions as well. The second  important advantage of the movable cellular automaton method is the many-body type of interaction among its elements. The use of  many-body interaction allows us to avoid artificial effect of the  particle packing and locality of their interaction on the resulting  behavior of the modeled material that is extremely important for  modeling elastic-plastic matereials. As a further development of the  considered approach, two techniques are discussed which enable to describe contact interaction of solid bodies surfaces at the microand mesoscopic scales within the framework of the particle method.

The transition of water into the ice VII phase was observed in experiments with its step-like shock compression. The transition  occurs from a state “overcooled” by approximately 40 K. In the  experiments, we observed relaxation of pressure as a result of the  transition on a surface of LiF window as well as dispersion of the  compression wave which propagates through the water with the state  parameters needed for beginning of the transformation.

The influence of stresses and strains on the chemical reaction rate is studied basing on the concept of the chemical affinity tensor. The  reaction between a deformable solid and diffusive gaseous  constituents is considered. The reaction is localized at the reaction  front and consumes all the matter supplied by the diffusion. Silicon  oxidation and lithiation are examples of such a reaction. Tensorial  nature of the chemical reaction is manifestation of the fact that in  the case of deformable material the reaction is to be considered not  in a point but at an oriented area element. A kinetic equation takes  the form of the dependence of the reaction rate at the oriented area element on the normal component of the chemical affinity  tensor. Stressstrain state affects the reaction rate as it affects the  chemical affinity tensor. If the normal component of the affinity tensor is negative then the reaction at the oriented area element is  impossible. Strains and stresses at which the normal component of  the affinity tensor cannot be positive at any orientation or  concentration of the diffusive constituent form forbidden zones in  strain or stress space. A procedure for forbidden zones construction is developed. The use of the jump relationships for  stresses and strains allows to present the normal component of the  chemical affinity tensor as a dependence on strains/stresses on one  side of the reaction front and the normal to the front. Then it is shown that the boundaries of the zone are determined by maximum  and minimum of a quadratic form that was earlier studied for phase  transitions zones construction. The location and sizes of the zone  depend on the input of the chemical energies of the constituents relatively to strain energies. Besides the deformations  which correspond to forbidden regions, blocking deformations are  also considered which can be unblocked and started-up due to inelastic strains or diffusion.

Development of novel approaches, methods and algorithms for solution of the computational mechanics problems for providing  structural design of aircraft is an actual problem. Its solution allows  to significantly increase bulk and efficiency of numerical  investigations and to guarantee a high confidence of numerical  results for advanced load-bearing structures of different aircraft  made of metallic and composite materials. It is supposed that the  developing methods will be implemented in the specialized replicable industry solutions on the basis of available software alienated from  the developer as import substitution software. It gives feasibility to  take into account important aeroelasticity, strength and fatigue  requirements already in the preliminary design stage. At the final certification stage of the aircraft development the robust  computational methods will reduce the amount of necessary evidentiary tests in accordance with the modern concept of  "certification by calculation". In the paper the requirements are  formulated for development of new technology which is directed on  integrating the available software tools and implementation of new  methods for analysis of strength, fatigue and aeroelastic  characteristics. They include the simulation and analysis methods  that are under development in Russian and foreign research companies and universities. Development of the specialized  replicable industry solution in the framework of “soft import substitution” based on the program tools available in TsAGI and the  CAE-Fidesys software package. New approach to solution of the  coupled problem of interaction of flexible structure with airflow is  demonstrated. Substantial influence of airflow viscosity on aeroelastic characteristics of structure is shown on the example of  numerical analysis of middle-range passenger airplane. The important tendency in development of design methods is application of multidisciplinary approach in investigations on synthesis and  optimization of aircraft structural layouts. It has been illustrated on  the example of wing design of advanced helicopter and on the problem of searching optimal shape of tip part of high-aspect ratio  wing with taking into account strength, buckling and aeroelasticity constraints.

According to the recent development of the Computational Mechanics, the future development and competitive ability of finite  element analysis software seems to be related with the  implementation of complicated physical, mechanical and geometric  models of solids and fluids. These are coupled models, problems that include physical and geometric nonlinearities, the models or  boundary-value problems with small physical or geometric  parameters. Thin-walled solids, deformation with large strains and  shape distortions, problems coupling solids and fluids supply well- known examples. The modeling of composite materials is another  and quite important example nowadays. It begins with solving so- called cell problems and leads to modeling deforming and damaging  of composite structural elements as well as to technological problems simulation. The latter type of problems is the problem of a  resin with short fibers flow into a mold of complex shape. Another  example concerns the process of a resin with long fibers polymerization in a mold followed by the problem of laminate  warping. Porous ground and fractured rock are not composites in the commonly used meaning of the term. However, Compositional  Mechanics methods are used for their analysis. It is reasonable to  mention rather complicated problem of fluid filtration in a porous  media experiencing large strains. It seems that a multi scale approach is the most general technique of composite mechanics. It  results in so-called local problems in the representative volume  element. This paper shows finite-element implementations of local  problems developed by the author. Mechanical models and computational algorithms were implemented as home-made  computer code. The code has been thoroughly tested and can be  used together with FIDESES finite element analysis software as third party package. I may be noted that the developed numerical simulations were elaborated during long term cooperation with the  Technical University of Berlin, Dr. Mirtsch GmbH and famous French  tire maker Michelin. Further development of the package can be  associated with the use of a multi scale approach aiming composite  structural elements deformation and progressive damaging modeling, resin with short fibers flow simulation as well as numerical simulation of laminate production process.