Fluctuations of the core which is burning at one end are investigated in the paper. The research object belongs to a wide range of fluctuating one-dimensional objects with moving boundaries and loadings. The classical mathematical model considering viscoelasticity on the basis of the structural model of Foigt is used for the description of fluctuations. By introducing the dimensionless variables it became possible to reduce the number of parameters (which affect the process of fluctuations) to two. The parameters characterize the speed of the border’s motion and viscoelastic properties of the core. The method of Kantorovich-Galerkin is applied for the solution. Eigen functions of the boundary problem with a motionless border are taken as dynamic modes. The solution when the speed of the border’s motion is equal to zero is precise. The error of the solution increases, when the speed of the border’s motion increases. By neglecting the small values, it became possible to obtain quite a simple expression for the amplitude of resonant fluctuations. The expression obtained for the amplitude of fluctuations contains the integrals having no analytical solution, therefore they were obtained numerically. The solution has a mode structure that allows analyzing the resonant properties of the core. The obtained solution made it possible to analyze the phenomena of the established resonance and the process of passing through the resonance. The analytical expression describing the increase in amplitude of fluctuations is obtained for the established resonance. The passing through the resonance is analyzed quantitatively. The graphs of the amplitude of fluctuations changing in the resonant area for the first dynamic mode at various values of the parameter characterizing the viscoelasticity are presented. Also the graphs of the maximum amplitude of fluctuations are provided when passing through the resonance at the first dynamic mode, depending on the parameters which characterize the viscoelasticity and speed of the border’s motion. The results of numerical calculations are processed by means of the least squares method. The expressions for the maximum deformations of the core when passing through the resonance at the first and second dynamic mode are obtained. The gained expression allows depending on the speed of the border’s motion, the coefficient of viscoelasticity and strength of the core’s material which make it possible to estimate the core durability.

This article is the first part of the review devoted to the description of modern approaches to the construction of interatomic potentials based on the embedded atom method (EAM) for various one-component materials. We consider the general ideology of the molecular (atomic) dynamics method and outline the shortcomings of the approach to modeling atomic systems using the classical pair-interaction potentials. The basic ideas and relations of the embedded atom method are presented, as well as various modifications of the method, including MEAM. The algorithm for numerical implementation of EAM potentials in calculations of molecular dynamic systems is considered, as well as the ways to improve the efficiency of the computational algorithms, including those related to the introduction of the cut-off radius and the justification of its choice for various materials. The review focuses on the methods of construction and types of embedding functions for a variety of materials, as well as the physical and mechanical properties of materials, which are well described in some kind of potential. A brief review of the methods for obtaining potential parameters is given, e.g. by using the quantum mechanical calculations (often referred to as "first principles" or "ab initio") or using experimentally determined properties (diffraction, X-ray methods or electron microscopy), as well as a list of physical and mechanical properties that can be determined for a material using molecular dynamics methods with the application of modern potentials constructed by EAM. The authors have considered in detail the works which offer those potentials that (at present) most accurately describe the properties of such "difficult" (for forward modeling) materials, such as beryllium, iron, tungsten, niobium, titanium, uranium and others. The relevance of studying the structure and properties of these materials is largely due to the prospects of its application in materials for nuclear power engineering, aerospace industry, and biomedicine. Also, this review is devoted to the construction of EAM potentials capable for describing the structure and properties of a number of metals (lithium, nickel, copper, aluminum, etc.), which are considered both in the melt state and after crystallization.

The paper is devoted to development and implementation of algorithms for a numerical solution of a coefficient inverse Stefan problem. This problem arises in a modeling for a process of ice wall formation around a projected horizontal section of a mine shaft. The ice wall is formed by an artificial ground freezing to convert soil pore water into ice. The temperature field modeling is based on an enthalpy form of a two-dimensional Stefan problem. The aim of the study is to determine the volumetric heat capacity for the rock layer on the base of additional information about temperature evolution in thermal wells. The problem of coefficients’ identification is stated as a variation form of the coefficient inverse Stefan problem. As a result, two algorithms for a numerical solution of the stated inverse Stefan problem have been developed. The first algorithm is based on the conjugate gradient iterative optimization method. The second algorithm is based on the steepest descent iterative optimization method. Under the first algorithm the calculation of the discrepancy functional gradient and determination of parameters for the optimization method are performed by solving a sensitivity problem and an adjoint problem. Forms of these problems have been obtained for the stated direct Stefan problem. For the second algorithm the discrepancy functional gradient and parameters for the descent step method are determined by calculating sensitivity coefficients. Solutions of the direct problem, the sensitivity problem and the adjoint problem are performed by the finite element method. The special feature of the used optimization methods is that these methods have regularizing properties. In order to verify effectiveness of the proposed algorithms, the computational experiments have been performed. The first and second experiments are related to determining only one unknown volumetric heat capacity for an ice domain or a cooling domain. The third experiment is devoted to determining the volumetric heat capacity for the both domains. The results of the experiments show that both algorithms allow to determine the volumetric heat capacity with a sufficiently good accuracy. However, a convergence rate of the second algorithm is higher than the rate of the first algorithm. The presented approach to modeling the process of ice wall formation as the coefficient inverse Stefan problem and the developed algorithms can be used for designing and improving the initial data for building mine shafts with a technology of artificial ground freezing.

The paper considers the problem of the normal impact and penetration of rigid spatial bodies into the half-space of the elastoplastic medium. For the medium, a model of a linearly compressible elastoplastic medium is adopted with a linear dependence of the yield stress on the pressure (the Mises-Schleicher-Botkin plasticity condition). The solution of the problem is carried out numerically in a three-dimensional formulation using the software package LS-Dyna. The elastic-plastic penetration medium is considered using a fixed Euler grid with the allocation of empty cells into which the material flows during deformation. The strikers are modeled by a rigid undeformed body in the Lagrangian coordinate system. For comparison, the parameters of the penetration process, i.e. the resistance forces to penetration and the penetration depth of the strikers, were also obtained within the framework of the local interaction model on the basis of the analytical solution of the problem of expanding the spherical cavity. Earlier the applicability of the local interaction model to the determination of the force and kinematic characteristics of sharp conical bodies is shown based on the data of the inverted experiments and numerical calculations in an axisymmetric formulation. Verification of the model applicability aimed at describing the motion of three-dimensional bodies in the full three-dimensional formulation has not been carried out before. The investigated bodies, i.e. a circular cone, three- and tetrahedral pyramids, and a body with a star-shaped cross-section, have the same area of the base, the normal to the lateral surface of the bodies makes up a constant angle of 600 with the direction of motion. The peculiarity of constructing the shape of the three-dimensional bodies in question is the fact that within the framework of the local interaction model these bodies should have the same resistance to the introduction, which coincides with the resistance to the introduction of the circular cone. All these bodies have a height less than the height of the cone. The results of the three-dimensional numerical calculations of the bodies’ penetration along the normal into an elastoplastic medium with subsonic and supersonic velocities are presented, which demonstrate an increase in resistance to penetration proportional to a decrease in body height. For the bodies of the same height, the changes in the form of the cross section do not lead to significant differences in the strength of the resistance and penetration depth.

Analytical solutions are obtained to determine the critical plane orientation for multiaxial stress state. This critical plane is the plane of development of fatigue damage under cyclic loading. The cases of in-phase and antiphase cyclic loadings are considered for the classical fatigue range (low-cycle and high-cycle fatigue). Generalizations of the Findley fatigue criterion are proposed taking into account the orientation of the critical plane for modes of very-high-cycle fatigue under in-phase and antiphase cyclic multiaxial loadings. These generalizations are based on the similarity of the left and right branches of the bimodal fatigue curve. The procedure aimed at determining the parameters of the generalized criterion is described according to the data of two uniaxial fatigue tests for tension-compression at various coefficients of the cycle asymmetry. The stressed state of the compressor disk of the gas turbine engine are calculated by the finite element method for a low-cycle fatigue (take off-flight-landing cycles) and for very-high-cycle fatigue (vibrations of blades). For low-cycle fatigue the effect of aerodynamic, centrifugal and contact loads for the contact system of disk, blades, fixing pins and shroud are taken into account. For very-high-cycle fatigue the additional stresses due to high-frequency torsional vibrations of blades and shroud are calculated. In both cases, a stress concentration zone was defined in the vicinity of the contact between the disc and the blades, in which the fatigue damage originates. The distribution of stresses and the proposed generalizations of the fatigue fracture criteria were used to obtain estimates of disk durability for both low-cycle fatigue and very-high-cycle fatigue modes. Numerical analysis showed that real time durability for the considered fatigue modes can be very close taking into account the characteristic cycle period. Therefore, in predictions of a safe operation life both mechanisms of fatigue must be taken

The paper considers two approaches to assessing the strength of constructions’ elements made of brittle material with sharp stress concentrators under the three-point bending: using a non-local theory of strength (in the top of the sharp notch the stresses are averaged on some basis) and a linear fracture mechanics (the stress intensity factors and the degree of singularity are determined). The finite element method was widely used (ANSYS Workbench, 2D model). These two approaches are connected by the analysis of the stress state at the sharp v-shaped notches with the corresponding approximations of the stress field, which allowed to find the correct values of the stress intensity factors and degrees of singularity on the basis of the optimization procedures. There were conducted the experimental studies of the strength of prismatic samples made of polymethylmethacrylate (PMMA) with a v-shaped notch (the two-edge angles of 25, 90 and 120°) in static three-point bending. In the finite element calculations using a nonlocal strength criterion it is obtained, that a sharp notch with the two-edge angle up to 90° leads to an increase in load of destruction for 15-20 % only compared with the crack-like cut (the angle of 25°) and agrees well with the experimental data. The increase of the two-edge angle of a sharp notch from 25 to 120° leads to increased loads of destruction in 1,5...2 times. There was studied the morphology of fractured surfaces, it is shown that the shallow cuts (up to 1.5 mm) when bending have a grooved fracture surface (a high velocity, periodic picture of cracks’ moving), while the deeper cuts (2.5...5 mm) are characterized by a slow crack propagation and a smooth fracture surface. Information about step of grooves was necessary to establish the size of averaging zone in nonlocal failure criterion.

Fiber optic sensors (FOS) is a rapidly developing part of measuring equipment. They are regularly expanding their application field in various engineering branches due to high operational properties. A large number of research works are carried out in this field all over the world. Most of the published articles are devoted to the application of FOS and their operating principles in terms of optics and electronics. In the present paper a fiber optic sensor is considered as a mechanical system. A sensor forms its readings while interacting with environment, which is the carrier of the measured parameter. In this process it is possible to distinguish three different aspects that determine the measurement result: the physical (optical) laws underlying the sensor transfer function, the nature of the sensor and environment interaction, and the interaction of sensor structural elements (even in the simplest FOS structure it is possible to distinguish several components with different physical and mechanical properties). All these aspects play a decisive role in the readings formation and must be taken into account by sensor designers. The present study describes the methodology aimed at adjusting FOS transfer function by taking into account all the indicated aspects of the readings formation. A fiber optic strain sensor based on the Bragg grating has been considered as an example. The influence of its structure on the readings has been determined by means of mathematical modeling. The contribution of single structural elements (such as glue, optical fiber, substrate with a technological hole, etc.) to this value has been evaluated. General algorithm for determining the effect of the sensor structural elements in its readings has been formulated as the results’ generalization. The algorithm has been tested using the existing model of the fiber optic strain sensor. The efficiency of the method has been proved by a series of laboratory experiments.

This study is devoted to the estimation of the crack propagation direction angle in the plate with the central crack under mixed-mode loading (Mode I and Mode II) in an iso-tropic linear elastic medium using two approaches: the generalized criteria of continuum mechanics (the generalized maximum tangential stress criterion and the generalized strain energy density criterion) and atomistic modeling of the Cu single crystal with the central crack. Molecular dynamics simulations of the central crack’s growth in a plane medium using Large-scale Molecular Massively Parallel Simulator (LAMMPS) are performed. The inter-atomic potential used in this investigation is the Embedded Atom Method (EAM) poten-tial. The specimens with the initial central crack were subjected to Mixed-Mode loadings. The crack propagation direction angles under different values of the mixed parameter in a wide range of values from pure tensile loading to pure shear loading in a wide range of temperatures are obtained and analyzed. It is shown that the crack propagation direction angles obtained by the molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.