Mechanics of Solids最新文献

The constitutive relations are constructed for the model of a thermoviscoplastic body with the normal and tangential stress intensities determined by different methods. The parameters of materials are determined on the basis of experimental diagrams for material hardening at different temperatures under tension-compression and torsion, respectively. The model problem of subsidence with shear between two parallel plates of a parallelepiped made of the St3 steel is solved within the framework of proposed model. A comparison with the solution based on the single curve model showed that the quantitative difference between the solutions does not exceed 7%.

The graphical diagram A – ν₀ proposed earlier by the authors was used to analyze the elastic properties of cubic crystals of simple substances. The elastic properties of crystals both at room temperature and their temperature dependences are considered. As the temperature increases, a general trend is observed for most crystals of simple substances: the points (A, ν₀) characterizing the elastic properties of crystals shift in the direction towards the limiting angle of the diagram (A = 1.5, ({{nu }_{0}} = 0.5)), i.e., in the towards of the region of special extrema being typical for metastable crystals, for example, such as crystals with shape-memory effect. The use of the A – ν₀ diagram made it possible to graphically represent and explain the relationships between the basic values of the elastic moduli of cubic crystals: Young’s modulus ({{E}_{0}}), shear modulus ({{G}_{0}}), and volumetric modulus of elasticity (B).

A problem on a conditional extremum that allows one to determine, based on the second limiting state, the upper limit of the maximum angular velocity of rotation of an axisymmetrically curved, fiber-reinforced disk is formulated. The structure is rigidly fixed to the vase or hub; blades can be attached to the outer edge of the disc blade. The materials of the components of the composition are assumed to be rigid-plastic, having asymmetry under tension and compression; the material of the binding matrix may have cylindrical anisotropy. Plastic deformation of the components of the composition is associated with piecewise linear yield criteria. The reinforcement structures of the disc web have meridional symmetry. A two-layer model of a curved disk with a plane-stress state in each of the fictitious composite layers is used. The discretized problem is solved using the simplex method of linear programming theory. The developed numerical algorithm has been verified. Examples of numerical calculation of the maximum angular velocity of rotation of flat, conical and spherical homogeneous and composite disks with different degrees of their curvature are analyzed. The cases of reinforcement of the disk web along geodetic directions and logarithmic spirals, as well as along meridional and circular trajectories, have been investigated. The comparison for disks of the same mass with the same consumption of reinforcement has been carried out. It has been shown that composite disks with a meridional-circumferential reinforcement structure have the highest load-bearing capacity. It has been demonstrated that even a slight axisymmetric curvature of the disk web leads to a sharp decrease in its load-bearing capacity compared to a similar flat structure.

The resistance of auxetic metamaterials based on a cell in the form of a concave hexagon (with a negative Poisson’s ratio) to penetration by a rigid spherical striker along the normal was experimentally studied. Samples of metamaterials with a chiral and non-chiral internal structure were made on a 3D printer from flexible thermoplastic polyurethane (TPU 95A plastic) and rigid e-PLA plastic. For all four types of metamaterials, samples were prepared whose internal structure differed in the rotation angle (0, 30, 60, or 90°) relative to the vertical axis. The samples were compared by their ability to reduce the kinetic energy of strikers at a speed of about 190 m/s at a temperature of 16°C. It was found that auxetics made of thermoplastic polyurethane with a non-chiral structure rotated by 90° are the most effective in terms of resistance to striker penetration. The dependence of the striker deviation on exit from the samples (up or down) on the direction of rotation of the internal structure of the sample at an angle from 0 to 90° clockwise or counterclockwise, respectively, was revealed.

It is known that an incident bulk P-wave propagating in a homogeneous isotropic halfspace, being reflected from the plane boundary, may exhibit a mode conversion into shear S-wave without the formation of reflected P-waves. The mode conversion takes place, when the incident wave hits the boundary at some critical angles, which depend upon Poisson’s ratio. Herein, it is revealed that the Jeffreys solution for the mode conversion angles needs in in corrections, mainly because of spurious roots, appeared at solving a specially constructed eighth-order polynomial for the P-wave reflection coefficient. The developed approach allowed us to construct a bi-cubic polynomial and obtain analytical expressions for its roots, and to find correct values for angles of incidence, at which the mode conversion occurs.

In the work with the purpose of determining the prospects of using the kinetic physical and mathematical theory of creep of metals for performing design calculations when creating new technology products, the results obtained in describing the theory of uniaxial creep processes of 1570P alloy under conditions of steady-state and abrupt changes in thermomechanical loading parameters are presented. It is established that the new physical and mathematical theory of creep of metals being developed, which, unlike the classical phenomenological theory, takes into account the structure of the metal and its change in the creep process, equally well describes the process under steady-state and non-stationary conditions of thermomechanical loading. The important role of the structural state of the metal on the creep process is shown. The main structural parameter determining the characteristics of the process is the scalar density of immobile dislocations.

Using a mathematical model of large deformations of materials with elastic, plastic and viscous properties, an analytical solution is obtained for the problem of deformation under creep conditions of a viscoelastic material placed in a gap between two rigid cylindrical surfaces, when the outer rigid cylinder rotates due to a twisting moment applied to it, while the inner cylinder is stationary. The displacements, reversible and irreversible deformations, stresses at all stages of deformation, including residual deformations and stresses under full unloading, are calculated.

A refined mathematical model of a cylindrical hydrodynamic suspension is proposed with full consideration of the dependence of the velocity distribution profile of the liquid on the radial coordinate in the supporting layer, which more fully takes into account the influence of viscous friction forces. On the basis of the proposed model, the stability of the suspension is investigated using the frequency criterion of stability of hybrid dynamic systems. A suspension with a light inner body, the reduced density of which is less than the density of the supporting layer, is asymptotically stable near the central position, and remains stable over a large range of changes in relative eccentricity. The use of a refined mathematical model leads to a greater margin of stability and a shorter transition time for suspension with a light inner body. An increase in the angular velocity of rotation of the outer cylinder leads to a significant decrease in the characteristic values of the displacements of the inner cylinder. In this case, a suspension with a light inner body has a large margin of stability and remains operational under significant external overloads. A suspension with a heavy inner body, the reduced density of which is greater than the density of the supporting layer, is unstable near the central position. When it is displaced from the central position along the curve of mobile equilibrium, a stability region may occur, but the stability margin of the suspension with a heavy internal body is insignificant.

The paper is concerned with derivation and application of basic equations of solid mechanics in the special coordinate frame in which the space and the time coordinate axes are not orthogonal. In this frame, the object velocity, in principle, cannot reach the velocity of light. The equations which generalize the classical Lorentz transformations in special relativity are obtained. They demonstrate that, in contrast to the classical theory, the length of the line element cannot become zero and the body mass cannot become infinitely high. As application, the general relativity spherically symmetric problem of gravitational collapse and expansion is considered. The external solution for an empty space and the internal solution for a pressure-free sphere are obtained in the proposed non-orthogonal coordinate frame.

An overview of research methods for improving the physico-mechanical properties of conductive materials grown using additive manufacturing techniques is presented. The review is conducted in order to develop a method for improving the properties of additive steel AISI 316L made by selective laser melting (SLM). This steel is widely used in various industries due to its versatile properties. The main methods of thermal and thermomechanical processing are briefly analyzed. Methods of improving plastic properties by impacting the material to pulses of a strong electromagnetic field, which causes high-density currents in the material considered as well. Based on the review, it is suggested that it is advisable to study the effect of a high-energy electromagnetic field on improving the plastic properties of materials built with selective laser melting.