PNRPU Mechanics Bulletin
Frequency: Bimonthly
Publisher: Perm National Research Polytechnic University, Perm, Russian Federation
DOI: 10.15593/perm.mech
Languages: Russian, English
Editorial Contact:
Address: Editorial Board "PNRPU Mechanics Bulletin", Russian Federation, Perm, 614990, Komsomolsky ave., 29
Phone: +7 (342) 2-198-444
E-mail: pnrpu.mechanics@gmail.com
PNRPU Mechanics Bulletin is an open-access periodical published scientific peer-reviewed journal.
PNRPU Mechanics Bulletin has no article processing and/or article submission charges.
All Journal's Content, including articles, is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). Editorial of the Journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles and allows readers to use them for any other lawful purpose in accordance with Budapest Open Access Initiative's definition of Open Access.
Journal intended for researchers specializing in the field of continuum mechanics, mathematical modeling of physical and mechanical processes, micro and mesomechanics, senior students of natural areas.
Editor-in-Chief: Peter V. Trusov – prof., DrSc (Perm, Russian Federation)
Deputy Editors:
Pavel S. Volegov – C.Sci. (Perm, Russian Federation)
Valery E. Wildemann – prof., DrSc (Perm, Russian Federation)
Editorial Board
Holm Altenbach – prof., DrSc (Magdeburg, Germany)
Boris D. Annin – academician RAS, DrSc (Novosibirsk, Russian Federation)
Alexander C. Belyaev – corr. member RAS, prof., DrSc (Saint Petersburg, Russian Federation)
Evgeny N. Barkanov - prof., DrSc (Riga, Latvia)
Antonio M. Cazzani - prof., DrSc (Cagliari, Italy)
Victor A. Eremeev – prof., DrSc (Cagliari, Italy)
Samuel Forest – prof., DrSc (Evry, France)
Francesco dell’ Isola – prof., DrSc (Rome, Italy)
Anna G. Knyazeva – prof., DrSc (Tomsk, Russian Federation)
Rimma E. Lapovok – prof., DrSc (Clayton, Australia)
Aleksey M. Lipanov – academician RAS, DrSc (Izhevsk, Russian Federation)
Dmitriy S. Lisovenko – corr. member RAS, prof., DrSc (Moscow, Russian Federation)
Evgeny V. Lomakin – corr. member RAS, DrSc (Moscow, Russian Federation)
Stepan V. Lomov – prof., DrSc (Leuven, Belgium)
Sergey A. Lurie – corr. member RAS, prof., DrSc (Moscow, Russian Federation)
Valery P. Matveenko – academician RAS, DrSc (Perm, Russian Federation)
Evgeny A. Mityushov – prof., DrSc (Yekaterinburg, Russian Federation)
Radik R. Mulyukov – academician RAS, prof., DrSc (Ufa, Russian Federation)
Sergey V. Panin – corr. member RAS, DrSc (Tomsk, Russian Federation)
Vladimir P. Radchenko – prof., DrSc (Samara, Russian Federation)
Yuriy L. Raikher – prof., DrSc (Perm, Russian Federation)
Varvara A. Romanova – DrSc (Tomsk, Russian Federation)
Sergey B. Sapozhnikov – prof., DrSc (Chelyabinsk, Russian Federation)
Anatoly A. Tashkinov – prof., DrSc (Perm, Russian Federation)
Emilio Turco – prof., DrSc (Alghero, Italy)
Executive Secretary – CSc. Dmitriy S. Gribov
Editors – Matvey N. Baldin, Natalya V. Kotelnickova
Until 2012, Journal was named «Bulletin of Perm State Technical University. Mechanics» (ISSN 2078-6603).
Current Issue
No 3 (2025)
- Year: 2025
- Articles: 10
- URL: https://ered.pstu.ru/index.php/mechanics/issue/view/461
- DOI: https://doi.org/10.15593/perm.mech/2025.3
Abstract
A new principle of functioning of a bending-type piezoelectric actuator using the effect of interaction of its initial curvature and controlled piezoelectric transformation of the shape of its cross-section is proposed. As a result, the bending of the longitudinal axis of the curvilinear actuator does not arise from its direct bending (as is realized according to the traditional bimorph type scheme), but indirectly from a controlled change in the shape - a bending of its cross-section in the transverse plane. Piezoelectric transformations of cross-section are carried out through a "bimorph" bend of its initial rectangular shape with transition of single-layer cross-section to convex "arched" and two-layer to biconvex tubular - "lentil" forms. Such transformations of the cross section increase the axial moment of inertia and, as a result, cause the appearance in the cross sections of the considered curvilinear rod PlatCB (Plate Curvilinear Bimorphic) or TubCB (Tubular Curvilinear Bimorphic) actuators of unbalanced bending moments, the action of which is partially straightening, i.e. reduces the value of initial curvature of the longitudinal axis of the rod actuator in the working longitudinal plane. Mathematical models of deformations of PlatCB, TubCB actuators have been developed as the interaction of two related processes: "active" is a controlled piezoelectric transformation of the cross-section shape, and "reactive" is a transition of the actuator to a new equilibrium curvilinear shape in order to increase its bending characteristics - maximum displacements and blocking forces produced by the actuators in the working longitudinal plane. Numerical results are presented and regularities of influence on the resulting bending characteristics of various structural parameters are revealed: initial curvature, width and thickness of initial rectangular sections of PlatCB, TubCB actuators. It was found that the resulting bending characteristics for the TubCB actuator are most significantly improved with the transformation of its thin two-layer rectangular section to a biconvex "lentil" - tubular shape.
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Abstract
One of main sustainable development principles is associated with changing the energy balance in favor of renewable energy sources. In the future, this means replacing traditional fossil fuels by new fuels characterized by lower levels of gas pollution. Hydrogen, as an alternative to carbonaceous resources, constitutes an ideal clean fuel. Its storage as metal hydrides is one of the best solutions in terms of safety and disposal. Magnesium hydride is more particularly advantageous for both its volumetric capacity and energy balance. However, the implementation of its use faces some difficulties, including the kinetics of hydride formation. The rate and completeness of magnesium to magnesium hydride conversion depends on several parameters. For example, the formation of hydride corresponds to a marked change of volume, reaching up to 30 % from Mg to MgH2. Consequently, the volume increase initiates the occurrence of stresses in the vicinity of the hydride/matrix interface. The stresses caused by deformations of the initial matrix lead to different effects on penetration of hydrogen: tensile stresses contribute but compressive stresses inhibit this process. Although experimental studies were based on hydride nucleation modeling, the presence of grain boundaries was not taken into account in the theoretical models. In theoretical models, this is a classical interpretation of the development of stresses at the interface between two phases. In the present investigation, the calculations are based on a gradient field theory model. The gradient field theory is particularly suitable to describe the elastic behavior of materials at the microscale, where the dimension parameters are on the same level as the characteristic parameter e.g. of the grain size. In the present study, the major results make it possible to conclude that the distribution of strains (stresses) is not restricted to the near vicinity of the hydride core, but it exhibits a longrange character. Furthermore, it is shown that the rapid formation of isolated MgH2 nuclei is replaced by a slowdown of this process during the nucleus coalescence process. Local and discretized hydride formation is only energetically favorable for a specific value of the nucleus volume. As its volume increases, the energy balance changes and the hydride-matrix system transits to a new state with a new level of energy balance. In practice, this means that the growing kinetics of the hydride phase is not steady as it depends on the volume of the converted phase.
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Abstract
The paper presents a mathematical model for solving the second main problem of the theory of elasticity for limited bodies of revolution made of a transversally isotropic material. Non-axisymmetric kinematic conditions are imposed on the surface of the body, specified according to the cyclic law of sine and cosine. The technique involves the development of the energy method of boundary states, which is based on the concepts of spaces of internal and boundary states, coupled by isomorphism. Isomorphism of state spaces allows us to establish the one-to-one correspondence between the elements of these spaces. The internal state includes the components of the stress tensor, strain tensor and displacement vector. The boundary state includes surface forces and displacements of the body boundary points. Finding an internal state comes down to studying the boundary state isomorphic to it. The basis of the internal states is reduced on the basis of a general solution to the boundary value problem of elastostatics for a transversely isotropic body limited by coaxial surfaces of revolution. Orthogonalization of state spaces is carried out, where the internal energy of elastic deformation is used as scalar products in the space of internal states; in the space of boundary states, the work of surface forces on the displacements of points on the boundary of the body is used. Finally, finding the desired state comes down to solving an infinite system of linear algebraic equations with respect to the Fourier coefficients. A solution to the second main problem is presented with boundary conditions simulating transverse expansion (without longitudinal compression) for a circular cylinder made of transversely isotropic large dark gray siltstone. The solution is analytical; the characteristics of the stress-strain state have a polynomial form. Explicit and indirect signs of convergence of the problem solution and graphical visualization of the results are presented.
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Abstract
The results of studies of the possibilities of the resonant method of ice destruction implemented by amphibious hovercraft when they move across the ice at the speed of resonant bending and gravitational waves are presented. At this speed, the minimum frequency of bending vibrations propagating in a free floating plate coincides with the minimum phase velocity of gravitational waves. In this case, the Archimedean forces of support (buoyancy forces) are completely balanced by hydrodynamic forces, and the water ceases to support the ice sheet, i.e. its equilibrium is achieved only due to internal elastic forces arising in the plate itself. This leads to a sharp increase in the amplitude of the excited gravitational waves. The possibility of increasing the efficiency of the method of ice destruction due to the interference of resonant gravitational waves excited simultaneously by several amphibious hovercraft is considered. The results were obtained on the basis of experiments performed: in an ice basin; with large-scale models of amphibious hovercraft in the field; with full-scale amphibious hovercraft in various ice conditions, as well as using theoretical dependencies obtained for calculating the stress-strain state of the ice cover from the action of a moving load. When determining the ice-breaking capacity of vessels, changes in the depth of the reservoir and the presence of snow cover on the ice under conditions of bending-gravitational resonance were taken into account. A generalized Maxwell-Kelvin-Voigt model of deformation of a viscoelastic medium was used to describe the viscoelastic nature of the relationship between stresses and deformations in ice. The snow cover was modeled by a viscous layer. Dependences are given that make it possible to determine the increase in the thickness of the destroyed ice by the resonant method due to the simultaneous use of several vessels moving in front, i.e. when ships are located on a line perpendicular to their course. The dependences were obtained taking into account the effect of snow cover, reservoir depth and distance between vessels on the efficiency of the method of ice destruction.
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Abstract
The paper analyzes a series of computer experiments aimed at identifying the self-similar behavior of stresses and continuity (damage) near the crack tip in a steady-state creep mode in a damaged medium. Finite element computations of crack-tip fields under creep regime were carried out using the interdisciplinary, universal finite element platform SIMULIA Abaqus FEA using the UMAT utility, which integrates the process of damage augmentation into the FEM computational scenario. The paper implements computational simulations of uniaxial stretching of a plate weakened by a central horizontal crack in the steady-state creep mode, which includes damage growth that evolves over time according to the mathematical model of damage growth by Kachanov – Rabotnov (KR) according to a power law for various values of exponents of the kinetic equation and the power constitutive equations. The study and analysis of the FE for the crack-tip stress and continuity (integrity) fields for a number of material constants clearly reveal a self-similar behavior of stress and damage fields near the front tip. The structure of the solution is revealed and the values of the exponents in the self-similar variable and the self-similar representation of the solution are found, which can be interpreted as an intermediate self-similar solution of the second type according to the classification of G.I. Barenblatt. It is elucidated that the revealed property of self-similarity of the solution can be interpreted as the intermediate asymptotes of the far field of damage and stress. The obtained figures also clearly show the asymptotes of the near-field stress, characterized by the absence of a singularity in the immediate vicinity of the crack.
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Abstract
The paper proposes two new applications of artificial neural networks for decoding and analyzing results of the surface of elastomer nanocomposite scanning by means of atomic force microscopy (contact and semi-contact modes). The main advantage of this approach is that it enables studying local mechanical properties of the material not only on the sample surface but also in the near-surface layer. In case of the contact operation mode of the atomic force microscope, the artificial neural network was created and "trained" using the database with the pressing models of the probe of the atomic force microscope into a nonlinear hyperelastic medium with rigid spherical inclusions ("contact neural network"). This database contained the results of calculations of indentation curves for various values of the filler particle sizes and their localization in the near-surface layer of the material (depth and horizontal distance from the tip of the probe). The use of such a neural network allows speeding up the construction of indentation curves by several orders of magnitude compared to conventional methods based on the numerical solution of the corresponding boundary value problems for each specific case. As a result, computing time is also significantly reduced, therefore, with an already constructed and "trained" neural network, powerful and high-speed computers are not needed. In the semi-contact mode, the neural network was built using real scans of the relief and phase shift of the probe cantilever oscillations obtained on samples made of a dispersed filled elastomer ("semi-contact neural network"). It was shown that with its help it is possible to quite accurately predict what the results of the semi-contact scanning will look like with an increase in the maximum value of probe indentation (i.e. with a deeper study of the near-surface layer). Further, these modified scans are supposed to be used as a basis for analyzing near-surface layers using a contact neural network.
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Abstract
The paper presents a non-isothermal boundary value problem of material deformation in a rigid round pipe in the presence of a lubricant layer within the large strain model. Deformation and movement of the material and lubricant occur under a pressure difference increasing with time. Initially, the adhesion conditions are satisfied at the boundary of the pipe with the lubricant, then, as the load increases, the lubricant begins to slip, and friction against the pipe causes its heating. Heating of the materials also takes place in the process of accumulation of plastic strains. The base material and the lubricant have elastic, viscous and plastic properties, and also have different values of elastic moduli, yield strength and viscosity coefficient. The dependence of yield strengths and viscosity coefficients on temperature is also taken into account. Reversible deformation, occurrence and development of viscoplastic flow in the lubricant layer and flow propagation into the base material are considered.
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Abstract
The process of impulse loading of an underwater two-layer pipeline filled with liquid is modeled. To solve the problem, the author's software package developed for the analysis of three-dimensional nonstationary processes of interaction of elastoplastic structures with compressible media is used. The algorithm is based on the improved Godunov scheme, which provides high accuracy of calculations of joint dynamics of liquids, gases and deformable bodies. The method includes an explicit Eulerian – Lagrangian realization with the definition of moving boundaries between the contacted media. Three types of computational meshes are used within one problem: surface meshes of Lagrangian type, consisting of triangular elements that define the initial geometry of objects and track their movement, as well as three-dimensional three-dimensional regular and local meshes automatically generated in the process of calculation and changed at each time step. Initiation of an impulse perturbation having an initial spherical shape is performed at some distance from the pipeline within the calculation domain. Shock waves formed as a result of the pulse perturbation initiation in the surrounding fluid interact with the underwater pipeline fragment and with the rigid bottom. The wave processes in the steel pipe, in the concrete shell weighting it, as well as in the internal fluid of the underwater pipeline are considered. Impulse loads on the underwater pipeline taking into account the influence of rigid bottom are estimated. Shape changes of pipeline shells in the areas of tensile strains formed in the places of maximum bending of the pipeline are shown. It is shown that the proximity of the bottom can significantly increase the impact of impulse loading due to the reflected shock wave from the rigid bottom. Under the action of the same impulse loading, a comparison of the shape changes of the walls of underwater pipelines, hollow inside and filled with liquid, is given. As a result of the initiated pulse loading, the wall deflections of the internally hollow subsea pipeline are observed to be larger than those of the liquid-filled subsea pipeline.
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Abstract
The theory of thermoelastic diffusion describes the interaction between temperature and concentration fields in deformable solids. Most of the known works devoted to the theory of thermoelastic diffusion are constructed by analogy with the theory of elasticity, including generalizations to media with relaxation of heat and mass. In this case, even when taking into account the dependences of properties on temperature and composition, the authors use linear constitutive relations linking the state parameters and physical variables that follow from thermodynamics in the approximation of constant density of the medium. This paper presents a generalization of the basic equations of the theory of thermoelastic diffusion for a medium whose density depends on the main state variables. This is taken into account when deriving the constitutive relations. The result leads to the system of generalized state equations in differential form, the coefficient matrix of which for the variable density loses symmetry. The derivation of relations is based on both the use of the Helmholtz potential and the use of the Gibbs energy as a potential. New mechanisms of heat and mass transfer are discovered. For example, the transfer of a component under the action of a deformation gradient is possible due to two "mechanisms". The first of them is connected with the difference in individual properties of the components (their molar volumes, through which the coefficients of concentration expansion are calculated). The second mechanism of transfer can be called the work of stresses along the deformation gradients. Moreover, in the case of an isotropic body, not only the invariants of the stress and deformation tensors but also their shear components participate in the interaction of fields of different nature. The equations obtained in different ways are outwardly different. However, in any case, they contain all the discovered interaction mechanisms. As in classical theories, the equivalence of the equations can be shown using the standard apparatus of thermodynamics of irreversible processes. In limiting cases, the formulas coincide with those obtained earlier.
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Abstract
Duplex stainless steels are widely used in many branches of modern industry due to the combination of unique mechanical properties and corrosion resistance, but the complex phase composition and microstructure evolving under external thermomechanical effects (including during operation) can lead to significant changes in the properties of steel. A brief overview of studies for duplex steels mechanical behavior under various loading conditions (cyclic loading, fatigue testing, corrosion resistance analysis, hot and cold forming processes) is given. The methods and results of experimental studies, as well as macrophenomenological constitutive relations (constitutive models) proposed in the literature based on these studies, allowing one to describe the behavior of the considered class of materials under thermomechanical effects, are considered. Based on the data presented in the review, one can conclude that the behavior of the materials under consideration is very complex, and there is a variety of physical mechanisms implementing and accompanying deformation processes under various temperature and rate loading conditions. It is also necessary to note the significant influence on the response of the material of the complex phase and component composition, characteristic of the class of steels under consideration. The above circumstances probably determine the absence of universal physical equations, a significant number of various phenomenological constitutive relations and their modifications, oriented on the description of the specific grades of steels behavior. In this regard, the most promising for description the behavior of duplex steels seems to be using the physically oriented multilevel constitutive models. The data presented in this review can be used to determine the most important physical mechanisms of deformation, as well as identifying and verifying the parameters of this class of models.
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