Computational Continuum Mechanics最新文献

{"title":"Deformation state of a graphene sheet within the framework of the continuum moment-membrane theory of elasticity","authors":"Самвел Оганесович Саркисян, Кнарик Араратовна Жамакочян, Лусине Самвеловна Саркисян","doi":"10.7242/1999-6691/2024.17.1.4","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.4","url":null,"abstract":"The paper proposes an approach to finding the stress-strain state (SSS) of structures containing graphene, a novel nanomaterial that has currently found а wide range of practical applications in nanoelectromechanical systems. Graphene is a 2D basic building block for other carbon structures such as membranes, sheets, nanotubes, etc. To describe the SSS of a graphene sheet, the phenomenological continuum moment-membrane theory of plates is used, from which, due to the fact that graphene is an ultrathin material, the concept of thickness is excluded. The physical elasticity relationships of a graphene sheet are expressed through its rigidity characteristics, determined using the harmonic potential of interatomic interactions in carbon. A differential formulation and the corresponding variational formulation are given for the problem of static deformation and determination of the natural frequencies and modes of vibration of a graphene sheet. The variational formulation is based on the Lagrange principle and is implemented numerically using the finite element method. Finite element relations are constructed taking into account moment effects of the behavior of a graphene sheet. For approximation, a 4-node rectangular finite element is used. Numerical solutions to several problems of static deformation of a graphene sheet under conditions of a plane stress state and transverse bending are presented, and the analysis of its natural vibrations is also performed. Good convergence of numerical simulation results in all considered problems is demonstrated. The obtained numerical solutions are essential in designing and calculating resonators in which ultrathin nanostructures are used. The establishment of the fact that a graphene sheet has a high intrinsic frequency falling in the GHz region (for example, quartz resonators are characterized by megahertz frequencies) opens up new prospects for using graphene itself as an ultrasensitive nanomechanical resonator for detecting small masses and ultrasmall displacements.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"112 47","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Модель накопления повреждений в ортотропном композиционном материале","authors":"Юрий Витальевич Баяндин, М. С. Головин, Михаил Владимирович Банников, Сергей Витальевич Уваров","doi":"10.7242/1999-6691/2024.17.1.5","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.5","url":null,"abstract":"The paper presents a theoretical and experimental study of the influence of damage accumulation in composite material on the elastic fourth-rank tensor and on the strength under quasi-static, cyclic and dynamic loads. Layered polymer composites (glass or carbon fiber-reinforced plastic) are considered. This work aims to develop a mathematical model that accounts for the impact of damage in the composite material on the fourth-rank tensor of elastic properties. The constitutive relations for an orthotropic composite material are proposed, taking into account the accumulation of damage during tensile or shear loading. A numerical simulation using the finite element method is done for a periodicity cell for composite variants (unidirectional, layered, etc.) to determine the effective elastic properties. Quasi-static loading experiments were conducted on composite samples (carbon plastic) to validate the model and the degradation of elastic properties was determined by measuring the longitudinal sound speed. The full-scale experiments confirmed that damage accumulation in carbon fiber-reinforced plastic leads to the degradation of its effective elastic properties. In this connection, a technique was developed to take into account irreversible damage in an orthotropic composite material through the components of the ductility tensor, which may be helpful for the design and analysis of composite structures. The findings of the study could help with the creation of new materials with enhanced mechanical characteristics, as well as with raising the quality of already-existing materials. The developed mathematical model of orthotropic composite material can be used to enhance the structural strength properties and boost the application safety in a variety of industry.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"105 38","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140987117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling of nanochannels in synthetic membranes","authors":"Максим Сергеевич Алексеев, Роман Ростиславович Пономарёв, Владимир Сергеевич Шелистов, Владислав Анатольевич Попов, Ирина Викторовна Моршнева, Евгений Афанасьевич Демёхин","doi":"10.7242/1999-6691/2024.17.1.1","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.1","url":null,"abstract":"The behavior of a diluted electrolyte in a system of joint microchannel and nanochannel with charged dielectric walls under the action of external potential difference and external pressure is investigated numerically. The surface charge on the nanochannel walls prevents the ions of corresponding polarity from passing through it. Consequently, the system in question acquires ion-selective properties and can, under certain assumptions, be viewed as a fragment of an ion-selective membrane, including one synthesized by creating nanopores in a dielectric material. Such systems are used in experiments to control the movement of charged particles through concentration polarization. The objective of the work is to investigate the influence of a single pore on electrolyte flow and the possibilities to control that flow by changing the geometric and physical properties of the pore. The investigation relies on the specially developed simplified models based on cross-section-averaged Nernst-Planck, Poisson and Stokes equations that are subsequently reduced to a single nonlinear differential equation. The simplified models allow identifying the impact of different physical mechanisms of electrolyte movement: pressure-based (generated by the external mechanical action) and electroosmotic (generated by the electric field). A finite-difference method with semi-implicit time integration is used for the numerical solution of equations. It has been found that the behavior of the system qualitatively matches the behavior of a cell based on a non-ideally-selective ion-exchange membrane. In particular, the model correctly predicts the underlimiting and limiting electric current regimes, as well as vortex formation near the nanochannel inlet due to concurrency between electrolyte movement mechanisms. The proposed models can be extended to describe a channel with arbitrary geometry and an electrolyte with arbitrary number of charged species.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"119 50","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Расчеты сжатия сферической слоистой системы ударными волнами с учетом переноса тепла излучением в различных приближениях","authors":"Светлана Александровна Грабовенская, Вячеслав Викторович Завьялов, Александр Александрович Шестаков","doi":"10.7242/1999-6691/2024.17.1.11","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.11","url":null,"abstract":"Numerical modeling is one of the basic tools to investigate physical phenomena that occur in materials compressed by shock waves. A study of the behavior of shock waves using simplified models is helpful in the analysis of more complex systems, for instance, in the problems of inertial thermonuclear fusion on laser facilities. Mathematical simulation of the nonstationary radiative heat transfer in a spectral kinetic statement is rather complicated because the system of equations is nonlinear and large in size. Generally, the kinetic transport equation is solved in 7D phase space, which requires huge computational resources. The initial system is often approximated under certain assumptions but this immediately causes questions as to whether the simplified model is applicable to particular calculations. In this study, several economic radiative heat transfer models were implemented in a 2D hydrodynamic code. Based on these models, test calculations were performed to simulate the compression of a layered spherical system by shock waves, taking into account radiative heat transfer. When the shock wave reaches the center of the sphere, it is focused and reflected. In the neighborhood of the focal point of a converging wave, temperature gradients increase; therefore, thermal conduction and radiation become the main mechanisms of energy dissipation to be considered when taking into account heat transfer. Maximum densities and temperatures at the center of the sphere and their average values in its regions were calculated. In addition, the time when shock and heat waves cross the sphere center was determined, and their behavior before and after focusing at the sphere center was estimated. It is shown that solutions to such problems can be found much faster and with adequate accuracy when applying simplified models.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"115 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of the discrete vortex method in combination with the fast multipole method in hydrodynamic problems","authors":"Межлум Альбертович Сумбатян, Андрей Сергеевич Пискунов","doi":"10.7242/1999-6691/2024.17.1.7","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.7","url":null,"abstract":"In this paper, the flow of a non-viscous incompressible fluid is discussed in terms of vorticity. In the framework of the discrete vortex method, each material particle of the fluid is considered in Lagrange variables; in this case, the velocities are determined by the Biot-Savard law. Thus, the influence of vortices on each other is taken into account. The aim of the work is to construct a numerical method of different orders of accuracy in the problems of vortex dynamics. The fast multipole method used in combination with the standard midpoint and fourth order Runge-Kutta methods significantly reduces the algorithmic complexity. In the fast multipole method, any vortex system is represented by discrete vortices. The fluid domain, determined by the motion of vortices, is divided into several ring-type subdomains, in each of which the velocities are calculated sequentially. To verify the combinability of the numerical methods, three test cases are considered: the dynamics of the symmetric and asymmetric Lamb-Chaplygin dipoles, as well as the rotation of the fluid occupying a cylindrical region of finite radius. It is known that the latter example is rather complex for direct numerical calculations in contrast to the elementary representation of its analytical solution. In fact, the performed calculations confirm that, without the Fast Multipole Method, the numerical treatment for this test case is hardly possible at a sufficiently large number of discrete vortices within a reasonable amount of time. The results of the test calculations are presented in the form of graphs and tables. The application of the standard discrete vortex methods combined with the fast multipole method shows that, due to the optimal number of subdomains and discrete vortices, the time of calculations can be significantly reduced.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"103 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140987298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Численно-аналитическая модель для интерпретации результатов индикаторных исследований нефтяных пластов: решение прямой задачи при наличии каналов низкого фильтрационного сопротивления","authors":"Константин Михайлович Федоров, Александр Янович Гильманов, Александр Павлович Шевелёв, Алексей Александрович Изотов, Александр Вячеславович Кобяшев","doi":"10.7242/1999-6691/2024.17.1.2","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.2","url":null,"abstract":"The article considers the problem of interpretation of tracer tests in oil reservoirs, into which a specific chemical substance - tracer - is injected via an injection well for flow monitoring and tracer concentration measurements in surrounding production wells. The testing data provide evidence of the existence of low resistance channels in the reservoirs, along which the tracer moves at velocities several orders of magnitude higher than in the reservoir. The nature and properties of these channels are unknown, and a semi-analytical model involving two small parameters is proposed to solve this problem. This makes it possible to construct two non-conjugate solutions: universal numerical and analytical. Such an approach allows us to solve both direct and inverse problems. The present article is devoted to solving the direct problem. The problem of pressure distribution in a rectangular reservoir pattern is solved in dimensionless coordinates and is universal, i.e., it does not depend on the size of the area and the pressure drop. This solution is approximated by power functions and is further used to determine the mass transfer between channel and reservoir. The problem of tracer slug propagation through the channel obeys the law of conservation of tracer mass and Darcy's law. Its solution is found by the methods of characteristics under the condition of smallness of the parameter reflecting the ratio of reservoir permeability to channel permeability. The results of the semi-analytical solution are compared with the numerical solutions previously obtained by other authors. The fundamental difference between these solutions is the presence of numerical diffusion when using the finite-difference method of solution, which leads to the «dissipation» of the trace slug edges.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"116 30","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging","authors":"Екатерина Андреевна Колчанова, Николай Викторович Колчанов","doi":"10.7242/1999-6691/2024.17.1.9","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.9","url":null,"abstract":"The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"116 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Концентрационная конвекция в замкнутой области пористой среды при заданном вертикальном перепаде концентрации и учете иммобилизации примеси","authors":"Борис Сергеевич Марышев","doi":"10.7242/1999-6691/2024.17.1.6","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.6","url":null,"abstract":"This work is devoted to the study of stability of horizontal filtration flow of a mixture through a closed porous domain taking into account impurity immobilization. The instability arises due to the vertical concentration difference of heavy impurities, which creates unstable density stratification. A general mathematical model describing the transport of an impurity through a porous medium is presented. The equations are simplified for the case of low impurity concentration. Simplification made it possible to analytically obtain the solution corresponding to homogeneous horizontal filtration and to study its stability. It is known that, in the narrow regions of porous medium and at weak intensities of the external flow, convection is excited in a monotonous manner. On the contrary, in the case of an infinite horizontal layer, oscillatory instability is observed. A study of the transition between the instability modes is presented. It is shown that the oscillatory regime is observed in long regions or at significant intensity of the external horizontal flow. At low flow intensities, convective cells do not move relative to the region and, hence, there is no reason for oscillations. It has been established that the range of flow intensity values, in which oscillations are observed, grows with increasing length of the domain. Impurity immobilization leads to the stabilization of horizontal filtration with respect to convective perturbations. Critical curves and stability maps are obtained in a wide range of problem parameters and then analyzed. For limiting cases, a comparison is made with the known results obtained for an infinite layer.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"103 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140987287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Моделирование турбулентной естественной конвекции на основе 2-жидкостного подхода","authors":"Зафар Маматкулович Маликов, Дилшод Примкулович Наврузов","doi":"10.7242/1999-6691/2024.17.1.10","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.10","url":null,"abstract":"The paper provides mathematical modeling of turbulent natural air convection at a heated vertical plate based on a fairly recently developed two-liquid turbulence model. The considered problem, despite its relative simplicity, contains all the main elements characteristic of the currents near the wall due to buoyancy forces. A significant disadvantage of the RANS turbulence models used to solve such problems is that for their numerical implementation it is necessary to set the laminar-to-turbulent transition point, which must be determined experimentally. Thus, all RANS models are unable to describe a laminar-to-turbulent transition zone. Therefore, the main purpose of the work is to test the ability of the two-liquid turbulence model to describe the transition zone. Well-known publications have shown that the two-liquid model has high accuracy and stability, and is also able to adequately describe anisotropic turbulence. The turbulence model used in this work is supplemented with an additional thermal force, which can be ignored in many flows with forced convection. However, in the natural convection currents, it is this force that contributes to the transition of the flow regime. To validate the model, as well as to verify the computational procedure, the numerical results obtained are compared with the results of the well-known RANS turbulence models (the one-parameter Spalart-Allmaras (SA) model and the Reynolds stress transfer (RSM) model), as well as with the available experimental data. It is shown that the two-liquid model adequately reproduces the laminar-to-turbulent transition zone, and the numerical results obtained are in good agreement with experimental data.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"105 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Пульсации течения жидкого металла, генерируемые переменным магнитным полем","authors":"Александр Олегович Полуянов, Илья Владимирович Колесниченко","doi":"10.7242/1999-6691/2024.17.1.3","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.3","url":null,"abstract":"This paper studies numerically a vortex flow of liquid metal driven by an electromagnetic force, which is generated by the interaction of the alternating magnetic field of a short solenoid with the induced electrical current. A short solenoid is placed coaxially to a cylindrical cell at half of its height. The mathematical model used to describe the process is based on the equations of magnetic hydrodynamics in the induction-free approximation. Calculations, which are carried out by the control volume method using the ANSYS Fluent package, show that the average flow has the form of two toroidal vortices. The calculated velocity fields are indicative of the oscillatory behavior of vortices, accompanied by a change in their sizes. In the examined range of the force parameter, the predominant flow pattern is the single-mode oscillatory flow. The dependences of characteristic frequency and Reynolds number on the force parameter, are obtained using spectral analysis. It has been found that the oscillation period is close to the period of rotation of a large-scale vortex. It has been established that the oscillations are of quasi-periodic character, and a distinct oscillation frequency is observed only in the flow region near the solenoid. The effect of velocity fluctuations is strong and can be detected in laboratory conditions when using gallium eutectic. Such experiment is planned for the near future. The flow rate of gallium eutectic will be measured by an ultrasonic Doppler anemometer. The results of numerical modeling and their verifications can be useful in determining the ways of reducing the intensity of vortex flows during the electromagnetic separation of impurities, which is based on the induction mechanism responsible for the generation of electromagnetic force that displaces particles. The data on the oscillation frequency of the unsteady flow can be used in the development of a non-contact technique for estimating the average electrical conductivity of a two-phase medium, such as a liquid metal with undesirable impurities.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"113 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140986674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}