Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.
The journal Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. At approximately a thousand pages a year, the journal is a comprehensive record of up-to-the-minute research results. Coverage includes Vibration of discrete and continuous systems; Stability and optimization of mechanical systems; Automatic control theory; Dynamics of multiple body systems; Elasticity, viscoelasticity and plasticity; Mechanics of composite materials; Theory of structures and structural stability; Wave propagation and impact of solids; Fracture mechanics; Micromechanics of solids; Mechanics of granular and geological materials; Structure-fluid interaction; Mechanical behavior of materials; Gyroscopes and navigation systems; and Nanomechanics.
Articles in the journal are primarily theoretical and analytical in nature and present a satisfying blend of basic mechanics theory with analysis of contemporary technological problems.
Mechanics of Solids is abstracted and/or indexed in Journal Citation Reports/Science Edition (Web of Sciences Core Collection), SCOPUS, INSPEC, Expanded Academic, Digital Mathematics Registry, Google Scholar, PASCAL, Academic OneFile, Summon by Serial Solutions, OCLC, INIS Atomindex, VINITI - Russian Academy of Science, Science Citation Index Expanded (SciSearch).
Media registration certificate: ПИ № ФС 77 – 82148 от 02.11.2021
The journal Mechanics of Solids is tranlaslated from Russian journal Izvestiya RAN, Mekhanika Tverdogo Tela.
Current Issue
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No 2 (2025)
Articles
On the sensitivity of equilibria to the method of realization of unilateral constraints with piecewise smooth boundaries
Abstract
Two ways of implementing unilateral holonomic constraints with piecewise smooth boundaries are considered. Examples are given that testify both in favor of the proposed methods and against them. The sensitivity of the equilibria of a system subjected to holonomic constraints with piecewise smooth boundaries to the way these constraints are implemented is also discussed using examples. Two problems from the mechanics of systems constrained by a pair of inextensible weightless tethers are considered. In one of these problems, which is most likely academic in nature, equilibria are found and small oscillations near these equilibria are studied. Another problem relates to tethered systems deployed near a uniformly rotating celestial body. For it, the relative equilibria of a load suspended on a pair of tethers are found, and sufficient conditions for the stability of these relative equilibria are studied.
3-27
Solutions of periodic and doubly periodic bending problems of a thin piezo plate with holes or cracks
Abstract
The solutions of periodic and doubly periodic problems of bending of a piezo plate with elliptical holes or cracks are given with an analysis of the results of numerical studies. In this case, complex potentials of the theory of bending of thin electro-magneto-elastic plates are used, holomorphic functions outside the holes are represented by Laurent series in negative powers of variables from the corresponding conformal mappings and, based on the periodicity or doubly periodicity of the electro-magneto-elastic state of the plate, the coefficients of the series from all the holes are expressed through the coefficients of the series from one, the so-called main hole. The determination of the last coefficients is carried out from the boundary conditions on the contour of the main hole using the generalized least squares method. The results of numerical studies for a plate with circular holes or cracks with full or partial consideration of piezo properties, without taking them into account, are described. The patterns of influence on the values of bending moments and their concentration of the geometric characteristics of the discussed plates and the physico-mechanical properties of their materials are established.
28-45
A new method for determining the buckling resistance in the nonlinear range of strains for a column supported by rotational stiffeners
Abstract
An innovational method for solving the Euler–Bernoulli problem of an overall buckling of the uniform column supported by rotational springs of stiffnesses γ1, γ2, N ∙ m free from traditional simplifications (invariable flexural stiffness and length) is given. It is based on a natural and comprehensive constraint on the restored axis length. A system of algebraic equations relating the critical stress σcr to the nonlinear compression diagram ε(σ) of the material, the slenderness of the column λ and the values γ1, γ2 has been obtained, solved and verified in important special cases. It is shown that columns of the same material with the same so-called the reduced spring stiffnesses have identical dependencies σcr(λ). It is shown that columns with λ ≤ λmin(γ1,γ2) cannot be buckled by any axial load F for various types of ε(σ) (Ramberg–Osgood, rational fraction, polynomial, etc.).
46-67
Multifunctional shuttle for processing small diameter and ultra-thin semicon-ductor wafers
Abstract
In a first for Russia, a 100 mm diameter wafer was processed to create holes for TSV structures using automated equipment designed for 150mm diameter wafers without needing to reconfigure the installations. A shuttle wafer was developed for this purpose. The reliability of the silicon shuttle was determined through experimental studies of the mechanical strength of silicon. The thickness of the ultra-thin Si wafer that can be processed without damage in the shuttle wafer on installations with a vacuum table was calculated based on the data obtained.
68-82
On various functions called entropy when using classical mechanics
Abstract
Thermodynamic entropy and four different functions used to describe it within mechanical models are considered. It is shown that all four variants have properties that differ significantly from the properties of entropy introduced in thermodynamics based on experimental data. It is established that, in order to comply with the approaches used in thermodynamics, the widely used mechanical model of a rarefied gas should consider almost exclusively processes that assume the presence of external forces acting on the system. It is noted that such a requirement allows a new approach to the use of mechanical models for studying irreversible physical phenomena.
83-95
Mechanics of blood flow and wall deformation in the abdominal aorta
Abstract
The medical problems of vascular mechanics are discussed in relation to the issues of blood flow and deformation of the walls in the abdominal part of the human aorta, including the formation of an aneurysm. The articles analyzed that present modern medical concepts about the hydromechanics of blood flow and deformations of arterial walls, as well as which provide the physical parameters necessary for mathematical modeling. The results of coupled mathematical modeling of blood flow and deformations of the walls in the abdominal part of the aorta in various pathological processes in it, considered in modeling as mechanical damage, including in the presence of an aneurysm, are presented. The effect of an aneurysm on the deposition of red blood cells from the blood flow is also analyzed.
96-118
Evolution of the single-wall carbon nanotubes bundle structure under compressive deformation
Abstract
The change in the structure and properties of a carbon nanotube (CNT) bundle under the action of uniaxial compression deformation in the framework of a quasi-three-dimensional computer experiment is investigated. The equilibrium configurations of the CNT bundle cross section are considered and their energetic properties are analyzed. It is found that up to a compression strain of 12% the bundle deformation develops almost homogeneously, while at higher strains a number of structural rearrangements begin in the bundle and regions with different degrees of ellipticity of CNT cross sections are formed. When the compression strain reaches 24%, even more significant structural changes are observed, including the formation of collapsed CNTs. The presented results reveal the mechanisms of absorption of external impact energy by the CNT bundle, which is important for the development of materials damping shock and vibration loads.
119-136
Generalized cesaro formulas in 3D and 4D elasticity theories
Abstract
Generalized Cesaro formulas are found, allowing to determine the displacement field with an accuracy of up to quadratic polynomials through integro-differential operators from the strain tensor-deviator in 3D elasticity theory and 4D elasticity theory. It is shown that quadratures for the pseudovector (pseudotensor in 4D elasticity) of local rotations and deformation of volume change are determined by the strain deviator field with an accuracy of up to linear polynomials in coordinates. Conditions for the existence of the listed quadratures are presented in the form of five (nine for 4D) third-differential order compatibility equations with respect to the strain tensor-deviator components.
137-148
Modeling of hydraulic autofrettage of thick-walled cylindrical shells taking into account elastoplastic anisotropy caused by the Baushinger effect
Abstract
The present work is aimed at developing a method for calculating residual stresses during autofrettage of cylindrical shells, allowing for elastic-plastic anisotropy caused by the Bauschinger effect. The proposed calculation method is based on the joint solution by the method of variable elasticity parameters of integral equations of equilibrium and compatibility of deformations, written in Euler coordinates for nonlinear deformation measures. The results of the work are in good agreement with the results of other authors obtained with similar initial data.
149-178
On the solution of the problem of axial compression of an elastic cylinder with specified ends displacement conditions
Abstract
A new scheme of approximate solution of the problem of axial compression of an elastic cylinder with one movable and the other fixed end with a free lateral surface is presented, refining the known solution obtained using separation of variables when averaging conditions over stresses on the lateral surface of the cylinder. The refinement is made by successive removal of discrepancies: first, in the stress distributions on the lateral surface of the cylinder, then in the radial displacements along the ends and further in the axial displacement of the movable end. Comparison with the results of numerical solution of the problem by the finite element method for different values of the Poisson ratio and different combinations of overall dimensions of the cylinder showed the effectiveness of the proposed approach.
179-195
Dynamics of the energy center of a long-wave low-amplitude disturbance in an anharmonic one-dimensional lattice
Abstract
The dynamics of a disturbance with finite energy in an infinite monatomic nonlinear one-dimensional lattice are analyzed. Based on the energy dynamics approach proposed earlier, we focus on such disturbance spatial characteristic as the position of its energy center. Restricting our analysis to long-wave low-amplitude disturbances, we investigate the dynamics of the α-FPU chain using its continuous version described by the KdV equation. We establish a connection of the Lagrangian and the energy of the original chain with the two conserving quantities of the KdV equation. Using these two quantities and the known properties of the KdV equation, we propose a method for determining the velocity of the energy center of the disturbance at large times based on the initial conditions.
196-209
Nonlinear acoustic waves in hyperelastic rods
Abstract
The excitation of a harmonic wave in a semi-infinite incompressible hyperelastic one-dimensional rod based on the Mooney-Rivlin equation of state shows the formation and propagation of shock wave fronts arising between faster and slower parts of the original harmonic wave. The observed shock wave fronts lead to the absorption of slower moving parts by faster ones, which leads to the damping of kinetic and elastic energy of deformations with the corresponding heat release. It is established that at a sufficient distance from the edge of the rod due to the attenuation of mechanical energy an acoustic black hole appears. The geometrically and physically nonlinear equations of motion are solved by an explicit Lax-Wendroff numerical integration scheme combined with the finite element method for spatial discretization.
210-225
Effects of the energy dissipation pattern on the controlability processes in systems with distributed parameters
Abstract
The paper considers the problem of damping vibrations of a membrane and a plate with the help of forces distributed over their entire area. The proposed method allows us to consider restrictions not only on the absolute value of the control, but also on the absolute value of the derivatives of the functions that specify the control. Sufficient conditions are given for the initial conditions under which the problem of bringing the system to rest in a finite time is solvable, and the time of bringing to rest is estimated.
226-237
On accounting for surface effects in bending of ultrathin plates
Abstract
The equations for axisymmetric bending of a circular plate of the Voepl-von Kármán type are given that account forsurface effects: the presence of a surface layer characterized by its elastic constants and initial stresses, as well as the presence of initial volumetric stresses. An asymptotic solution for large deflections of the problem of a circular uniformly loaded rigidly clamped plate is obtained under the assumption of constant tensile forces. An assessment was made of the plate parameters at which surface effects become significant.
238-266
On the influence of viscous filler on the impact penetration resistance of flexible metamaterials with auxetic properties
Abstract
The properties of flexible metamaterials with negative Poisson’s ratio (with auxetic structure based on a concave hexagonal cell) to resist normal punching by a rigid spherical impactor were experimentally investigated. Samples with a chiral structure fabricated using a 3D printer and made from thermoplastic polyurethane (TPU 95A plastic), with cells filled with air or gelatin were compared for their ability to reduce the kinetic energy of impactors. The experiments were conducted for two velocity regimes. It was found that gelatin filling of auxetic chiral samples made of TPU 95A plastic (in contrast to previously investigated rigid metamaterials based on PLA plastic) does not lead to enhancement of protective properties. According to the results of the experiments conducted for two speed modes, the most effective in terms of resistance to penetration by the impactor were flexible and lightweight samples made of thermoplastic polyurethane filled with air.
267-278