Methods Of Continuum Mechanics Research Articles

Symmetric form of the magnetohydrodynamics equations

It is well known that many linear hyperbolic systems of mathematical physics are symmetric hyperbolic systems. In the case of nonlinear equations, the question of whether they can be written in symmetric form is far from simple.

State of the Art of Coupled Thermo–hydro-Mechanical–Chemical Modelling for Frozen Soils

AbstractNumerous studies have investigated the coupled multi-field processes in frozen soils, focusing on the variation in frozen soils and addressing the influences of climate change, hydrological processes, and ecosystems in cold regions. The investigation of coupled multi-physics field processes in frozen soils has emerged as a prominent research area, leading to significant advancements in coupling models and simulation solvers. However, substantial differences remain among various coupled models due to the insufficient observations and in-depth understanding of multi-field coupling processes. Therefore, this study comprehensively reviews the latest research process on multi-field models and numerical simulation methods, including thermo-hydraulic (TH) coupling, thermo-mechanical (TM) coupling, hydro-mechanical (HM) coupling, thermo–hydro-mechanical (THM) coupling, thermo–hydro-chemical (THC) coupling and thermo–hydro-mechanical–chemical (THMC) coupling. Furthermore, the primary simulation methods are summarised, including the continuum mechanics method, discrete or discontinuous mechanics method, and simulators specifically designed for heat and mass transfer modelling. Finally, this study outlines critical findings and proposes future research directions on multi-physical field modelling of frozen soils. This study provides the theoretical basis for in-depth mechanism analyses and practical engineering applications, contributing to the advancement of understanding and management of frozen soils.

ПЛАСТИЧЕСКАЯ ТВЕРДОСТЬ КОМПОЗИЦИОННЫХ ПОКРЫТИЙ НА ОСНОВЕ ХРОМА

One of the common problems leading to the failure of agricultural machin-ery units is a significant change in their geometric characteristics, which is associated with the wear of individual elements of power hydraulic equipment. To restore these parts, it is advisable to use methods of applying a dispersed-hardened galvanic com-posite coating, accompanied by the introduction of tool material into the coating due to direct contact of the tool with the workpiece. As a result, wear-resistant sediments with specified physical and mechanical properties are obtained, depending on the amount of wear of various sections of the surface being restored. (Research purpose) The research purpose is determining the strength parameters of dispersed-hardened galvanic composite coatings used for the restoration of power hydraulic equipment of agricultural machinery. (Materials and methods) Hydraulic cylinders of the drive of working bodies of agricultural machinery were used as experimental samples. It was noted that the coordinated change in tool pressure depending on the degree of wear of the surface makes it possible to obtain dimensional coatings with specified properties. (Results and discussion) A comparison of the results obtained in solving the contact problem of the contact of two bodies, solved by the methods of continuum mechan-ics, and experimental studies, and determined for this type of composite material the relationship between the magnitude of the force of pressing particles into the coating and the depth of their penetration. The conducted research allowed us to introduce the concept of plastic hardness, which qualitatively and quantitatively characterizes the properties of the resulting galvanic precipitation. (Conclusions) The relations obtained in the work allow us to control the process of forming a composite galvanic deposit during the restoration of power hydraulic equipment of agricultural machinery, preventing overhardening of such a coating, and setting it the required degree of hardening.

ФОРМИРОВАНИЕ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ МАССИВА ШТАБЕЛЯ КУЧНОГО ВЫЩЕЛАЧИВАНИЯ ЗОЛОТА

Engineering and geological conditions of formation and operation of the technogenic massif of sandy-clay clay pelletised ores of gold heap leaching stack were investigated. Key factors determining the formation of stress-strain state of heap leaching stack were identified. The formation of the stress-strain state of the stack massif was evaluated. The main research methods included the use of numerical modelling of the stress-strain state of the stack massif with the application of continuum mechanics methods. It was established that the optimal approach to the assessment of the stress-strain state is a complex analysis based on an algorithm approximated to the conditions of formation and operation of the heap leach stack array. The modelling takes into account the stages of stack construction, compaction from the impact of mining transport equipment, as well as the weight of overlying rocks, taking into account different degrees of water saturation during operation. Filtration modelling made it possible to determine the zone of full saturation at given irrigation parameters. The formation of the stress-strain state of the heap leaching gold stack massif and its stability were analysed by longitudinal and cross-sectional modelling.

Use of the Green Function in the Study of Morpho-structural Changes

Currently, automation and robotization of research is being introduced into all areas of medicine and veterinary medicine, including histological analysis. At the same time, it is necessary to provide an automated decision-making system for quality control of histological images preparation. The technological process of histologic analysis running in spatial and temporal basis has been studied. The process of histologic analysis is a complex dynamic system including the stages of biomaterial preparation and study of morphostructural changes in tissues. The problem of process flow description is based on the law of mass conservation during biosphere transfer, which takes into account the equation of flow continuity in Euler and Lagrange variables. In controlling the histologic process, the errors associated with process failure were taken into account. The solution was obtained using an impulsive transient Green's function. In the period 2000-2023, according to statistical data, an increase in the number of cancer cases was observed, which makes the development of an automated histological analyzer relevant. The aim of the study was to build a control model for the automated process of histological analysis. Research Methods. The approaches to the device design were based on the theory of histologic analysis, application of continuum mechanics methods, methods of solving differential equations using Green's function. Results. The technique of histologic analysis was studied. The analytical solution describing the control of the automated technological process of histological analysis in conditions of possible disturbances caused by perturbations, such as "marriage" and time delay in the preparation of histological specimens has been obtained. Preparation of high-quality histological images will accelerate the diagnosis in the study of morphostructural changes in tissues, which will help to reduce the risks of developing not only cancer, but also other diseases. Conclusion. Express analyzer of histological analysis will reduce the time of preparation of histological images and the burden on highly qualified medical personnel.

Web Application for Mathematical Modeling of Unsteady Oil Flow in Porous Medium

Introduction. The analysis and interpretation of hydrodynamic research data are based on theoretical models and computational algorithms. Despite the demand for this topic, numerous issues related to unsteady fluid flows in oil reservoirs still require solutions. Therefore, mathematical setting of problems related to the account of unsteady fluid flow, the development of effective numerical methods and algorithms, their solution using modern web technologies are pressing. This study is aimed at developing a web application for mathematical modeling of the process of fluid filtration in single- porosity reservoirs when conducting a hydrodynamic study at a production well.Materials and Methods. To solve the problem, the methods of continuum mechanics and computational mathematics were applied. A model of oil flow in a single-porosity reservoir was presented. Python and JavaScript programming languages were used in the development of the application. The calculation results were stored in a relational database implemented using PostgreSQL tools.Results. A new web application has been developed for modeling the oil filtration process in single- porosity reservoirs. It is applicable for studying fluid dynamic processes and can be used to predict flowrates, production and calculation of optimal well operation modes.Discussion and Conclusion. The developed web application provides for building pressure and temperature fields in the reservoir near a flowing and shut-in production well and at various distances from it. This information makes it possible to urgently assess the duration of hydrodynamic studies, as well as to regulate the operation of wells. The application can be deployed in an existing network infrastructure and use all the functionality by connecting to a remote server. It is optimized for use on various platforms and has broad prospects for further development.

Comprehensive scrutiny of surface mechanical parameters of graphyne-based materials for metal-ions and metal-air batteries applications: A perspective and a hybrid atomistic-continuum model

Graphyne family, as a low-dimensional carbon allotrope, is utilized for metal-ion and –air batteries as the anode and cathode materials due to their unique characteristics. These novel carbon nanomaterials can provide more theoretical storage capacity than graphene, while their specific surface mechanical parameters and vibrational frequencies can influence battery performance. However, there needs to be clear information that can explain the effects of these parameters on battery efficiency. In this respect, the influences of the surface elasticity, residual stress, density, vibrational modes, and frequencies of α, β, and γ-graphyne circular monolayers on anode and cathode materials have been investigated in current research using the hybrid molecular dynamics simulation and modified classical continuum mechanics methods. Concerning metal-ion batteries, the results disclose that the suitability sequence for anode materials can be expressed as γ-graphyne > graphene > β-graphyne > α-graphyne monolayers. In the case of metal-air batteries, the competence sequence for cathode materials is in the order of γ-graphyne > β-graphyne ∼ graphene > α-graphyne monolayers. Therefore, γ-graphyne with suitable storage capacity, low volume expansion, good surface elasticity, low surface residual stress, and appropriate specific surface area is the promising anode and cathode material for metal-ion and -air batteries, respectively.

Molecular dynamics simulation of free transverse vibration behavior of single-walled coiled carbon nanotubes

Coiled carbon nanotubes (CCNTs) belong to one of the prominent classes of carbon nanostructures with unique mechanical properties and vibrational behavior due to their helical geometries. In this paper, the free transverse vibration behavior of single-walled CCNTs is investigated by molecular dynamics (MD) simulations and the adaptive intermolecular reactive empirical bond-order (AIREBO) potential under different boundary conditions (B.Cs.). The beating phenomenon is observed in CCNTs due to the presence of longitudinal, transverse, and torsional coupled vibrations and the proximity of their corresponding frequency. Generally, the frequency of the CCNTs decreases by increasing the length () or the number of pitches ( Moreover, the pitch angle plays a more decisive role compared to other geometric parameters. At constant length () of CCNTs, the frequency increases by enhancing the pitch angle Furthermore, the fundamental frequency range of the studied CCNTs is obtained less than 331.9 GHz for lengths greater than 2 nm under different boundary conditions. This indicates that CCNTs have a higher vibration sensitivity than straight CNTs. Therefore, CCNTs can be a proper alternative to straight CNTs in sensors. The results of this study can be used in the design and analysis of nanoelectromechanical systems (NEMs) with CCNTs elements as well as to calibrate continuum mechanics methods.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ЗА МГЕ ПРОЦЕСУ ПІДСИЛЕННЯ ФУНДАМЕНТІВ

Taking into account the presence of weak soils on the territory of Ukraine, additional vertical deformations occur in soil foundations, associated with a violation of their structure. Water saturation of such soilsleads to a change in VAT and affects the conditions for the reliable operation of construction objects. In this regard, it becomes necessary to strengthen the foundations of these building objects, to improve the bearing capacity of these foundations. Therefore, in practice, the search for new ways to strengthen the foundations, improve their bearing capacity is constantly being carried out. In difficult engineering and geological conditions, the deterioration of the physical and mechanical properties leads to a rise in deformations and a decrease in the bearing capacity of the foundations. Reinforcement of foundations is also necessary when constructing superstructures. In the robot, using the numerical method of boundary elements, the behavior under load of a shallow foundation on a natural basis reinforced with cross piles is predicted. Reinforcement of foundation structures requires determination of their bearing capacity and stress-strain state (SSS) after reconstruction. Normative design of foundations, based on subsidence and rolls, which are borderline permissible from the point of view of the operational suitability and reliability of structures, puts forward increased requirements for the accuracy of calculating the displacements of foundations. Thecomplexity of the properties of soils and the many factors that influence their mechanical behavior have long been a barrier before which the mathematical methods of continuum mechanics were de-strengthened. The emergence of modern ECM allowed algebraicizing the mathematical formulation of most problems in soil mechanics, which require taking into account a large number of nonlinear determining factors and the transition to elastic-plastic models. The use of a numerical eexperiment, as never before, closely linked the physical meaning of the problem, its mathematical formulation, numerical methods of calculation and the ECM. In the robot, to obtain a forecast of the bearing capacity of a reinforced foundation, anelastic-plastic model of a discrete soil medium and a numerical MGE are used

Modeling of the electromagnetic field based on rational mechanics approach

AbstractThis article discusses a possibility of deriving the basic equations of electrodynamics by means of the rational continuum mechanics principles and methods. We show that in order to give rise to the challenge, one needs to consider an elastic continuum of two‐spin particles of a special kind. We derive classical Maxwell's equations and discuss reasons limiting their application. After that, we propose more general equations that presumably provide a more correct description of the electromagnetic field.

Three-dimensional FEM–DEM coupling simulation for analysis of asphalt mixture responses under rolling tire loads

As traffic grows by leaps and bounds, deterioration of asphalt surface layers emerges as the primary cause of road network costs. A deep understanding of the tire–pavement interaction is essential for optimizing the surface design of asphalt pavements in the context of aging infrastructure and limited maintenance resources. Most of the current tire–pavement interaction studies have been conducted in the continuum mechanics framework using Finite Element Methods (FEM), which shows limitations in modeling the discontinuity nature of asphalt mixtures. Discrete Element Methods (DEM) offer a promising way to examine the mechanical properties of asphalt mixtures at the particle level, but it is inadequate for modeling deformable tire structure and capturing realistic tire contact forces on the pavement surface. In this study, a FEM–DEM coupling strategy was developed for the modeling of tire–pavement interaction by implementing a DEM model of asphalt mixtures with rolling tire loads from a FEM model. Based on simulations with realistic rolling tire load conditions, this coupling algorithm allows the investigation of particle force chain network evolution, particle displacement and velocity distributions, movements of individual particles, and particle contact force characteristics inside an asphalt mixture. This study offers an enriching expansion of both continuum and discrete mechanics methods for analyzing asphalt mixture responses under rolling tire loads, which can provide insight into pavement surface design.

Calibration of nonlocal generalized helical beam model for free vibration analysis of coiled carbon nanotubes via molecular dynamics simulations

This paper studied the free vibration behavior of coiled carbon nanotubes (CCNTs) using continuum mechanics methods and molecular dynamics (MD) simulations. Based on the continuum mechanics method, a new elasticity model called the nonlocal generalized Washizu beam (NGWB) was innovated by considering the effects of the curvature and cross-section thickness of nanotubes, as well as size-dependent effect. Then, the governing equations for the vibrational behavior of CCNTs were derived and solved using the numerical generalized differential quadrature method (GDQM). The free vibration behavior of CCNTs was also examined by performing the MD simulations to determine the calibrated values of the nonlocal parameter () that are applied in the NGWB elasticity model and to validate and evaluate the obtained results. Since the NGWB elasticity model considers the size-dependent effect on the vibrational behavior, obtained results from it well agrees with the MD simulation results in the present study. For CCNTs, there was a coupling between transverse, longitudinal, and torsional vibrations, which led to the beating phenomenon. The natural frequencies decreases by increasing the number of pitches ( aspect ratio and pitch angle The nonlocal parameter has a more significant effect on the frequencies of CCNTs with smaller geometrical parameters. In addition, the type of boundary conditions affects the calibrated values of the nonlocal parameter, frequency values, and arrangement of vibrating mode shapes of CCNTs. Results of the present study can be applied in the design and analysis of nano-electro-mechanical systems (NEMS), sensors, and nano-composite structures containing CCNTs. Also, the NGWB elasticity model might be useful in the statics and wave propagation studies of CCNTs, and other coiled and curved nano-structures.

Mathematical and Numerical Modelling of Copper Tube Extrusion after Optimizing Geometrical and Operating Parameters

This study aimed to optimize cross-sectional area of the extruder and the flow rate of the material through the extruder. Extrusion process was first modelized using the continuum mechanics method before being simulated with the commercial software LS-DYNA using the Johnson-Cook model based on the finite element method after optimization of the factors with simplex algorithm. The study was carried out on a connecting rod: diameter of 145 mm, cross-section of 1.65 m2, length of 0.25 m, volume of 0.41 m3 and a mass of 37 kg. Optimum parameters obtained were temperature of 850℃, flow rate of 0.237 m/s, die diameter of 19.2 mm, pin diameter of 14 mm, extrusion strength of 565.6 kN and press pressure of 245 GPa. From these factors, a blank was obtained with external and internal diameters of 19.2 and 14 mm respectively over a length of 28 m with a thickness of 2.6 mm. Simulation using LS-DYNA software resulted in a difference in values of 7.4% between optimization and simulation when the difference of 2.4% was found between modelling and simulation. These values make the process optimal for industrial application to improve the extrusion requirements of copper tubes.

Особенности проникания элементов кумулятивной струи в стальную преграду

Based on numerical simulations carried out using numerical methods of continuum mechanics, the influence on the depth of craters, formed in steel barriers of various strengths, geometric and kinematic parameters of elongated cylindrical copper strikers, simulating elements of a cumulative jet, in the range from 0.3 to 8 km/s. For description the behavior of materials of the impactor and barrier, the model of a compressible elastic-plastic medium with a variable value of the yield strength. Determined that the classical hydrodynamic theory of the penetration of a cumulative jet into a barrier is not takes into account the effects of the inertial movement of the barrier after triggering separately taken element (aftereffect). The existence of three regimes is distinguished shock interaction - high-speed, when the elements behave like a liquid body, are worked out, but not inhibited; low speed, when the elements behave like solid body and are decelerated as a whole and intermediate, when the elements are decelerated and are deformed at the same time. It is shown that the braking mode of copper elements at high-speed impact on a steel armored barrier is realized at speeds smaller 800…1000 m/s. It is shown that when interacting with an obstacle, high-speed fragmented cumulative jet, the total depth of armor penetration will be greater, than this is predicted by the classical hydrodynamic theory of penetration, and the more more, the higher the speed of the elements and the greater the distance between them on the one hand and less strength of the barrier on the other side.

Features of the penetration of elements of the cumulative jet into a steel barrier

Based on numerical simulations carried out using numerical methods of continuum mechanics, the influence on the depth of craters, formed in steel barriers of various strengths, geometric and kinematic parameters of elongated cylindrical copper strikers, simulating elements of a cumulative jet, in the range from 0.3 to 8 km/s. For description the behavior of materials of the impactor and barrier, the model of a compressible elastic-plastic medium with a variable value of the yield strength. Determined that the classical hydrodynamic theory of the penetration of a cumulative jet into a barrier is not takes into account the effects of the inertial movement of the barrier after triggering separately taken element (aftereffect). The existence of three regimes is distinguished shock interaction-high-speed, when the elements behave like a liquid body, are worked out, but not inhibited; low speed, when the elements behave like solid body and are decelerated as a whole and intermediate, when the elements are decelerated and are deformed at the same time. It is shown that the braking mode of copper elements at high-speed impact on a steel armored barrier is realized at speeds smaller 0.8-1 km/s. It is shown that when interacting with an obstacle, high-speed fragmented cumulative jet, the total depth of armor penetration will be greater, than this is predicted by the classical hydrodynamic theory of penetration, and the more more, the higher the speed of the elements and the greater the distance between them on the one hand and less strength of the barrier on the other side. Keywords: High-velocity strike, elongated striker, cumulative jet, steel barrier, crater, inertial movement of the barrier, numerical modeling.

Heat flux during boiling of superfluid helium inside a porous body based on a two-fluid model

The calculation of the recovery heat flux density is considered for superfluid helium boiling on the cylindrical heater inside porous structure. System of equations is based on the methods of continuum mechanics and molecular kinetic theory. The new type of boundary condition on the vapor-liquid interface based on the two-fluid model is formulated. Heat transfer in a free liquid is described by the Gorter-Mellink semi-empirical theory. Inside the porous structure the processes is discussed by the two-fluid model and filtration equation. Experimental data on the boiling of superfluid helium inside the porous structure are interpreted based on the formulated mathematical model. The qualitative and in some cases quantitative agreement between the calculated and experimental values of the recovery heat flux were obtained in the considered range of parameters

A robust numerical method for granular hydrodynamics in three dimensions

Abstract

Development of a generalized physical and mathematical model of working substance processes in an axial turbine stage

Methods of continuum mechanics and equilibrium thermodynamics are used to study a generalized physical and mathematical model of the processes of a working substance (steam, gas) moving in the flow part of an axial turbine stage in the nominal operating mode of the turbine. The mathematical description of the hydrodynamics and thermodynamics of the process is carried out for a one-dimensional model, based on the energy equation in thermomechanical form (the first law of thermodynamics in combination with the Bernoulli equation) for the gas (or steam) flow during its adiabatic (isentropic) expansion in the direction of the axis of the turbine stage. The energy equation is written taking into account both thermodynamic (due to the thermal movement of particles) and hydraulic pressure forces (due to the mechanical action of a continuous medium) of the working substance flow on the walls of the stage flow channel. Numerical calculation of flow rates and enthalpy losses on various elements of the stage (nozzle and working blades) is performed on the example of a model turbine with eight axial-type stages, under specified initial conditions of the process.

Numerical Simulation of Two-Dimensional Gas Flows through Granular Phase Change Materials

A mathematical model and a numerical method for studying two-dimensional plane gas flows through thermal accumulators based on granular or capsular phase change materials (PCMs) are proposed. The considered objects are modeled as porous media with phase transitions occurring in the condensed component. The study is based on methods of heterogeneous continuum mechanics without detailing the processes inside individual particles. The proposed numerical method combines explicit and implicit finite-difference schemes. The method is described in detail, and its convergence is experimentally analyzed. The heating of smoothly narrowing and smoothly expanding thermal accumulators consisting of granular PCM is studied. It is shown that heating in such objects near the inclined walls occurs more slowly than in their central part even in the absence of heat transfer through the sidewalls.

Continuum model of the simple dielectric fluid: consistency between density based and continuum mechanics methods

ABSTRACT The basic continuum model for polar fluids is deceptively simple. The free energy integral consists of four terms: the coupling of polarisation to an external field, the electrostatic energy of the induced electric field interacting with itself and the stored polarisation energy quadratic in the polarisation. A local function of density accounts for the mechanical state of the fluid. Viewed as a non-equilibrium free energy functional of number density and polarisation, minimisation in these two densities under constraints of the Maxwell field equations should lead to the correct equilibrium state. The alternative is a continuum mechanics approach in which the mechanical degree of freedom is extended to full deformation. We show that the continuum electromechanics method leads to a force balance equation which is consistent with the density functional equilibrium equation. The continuum mechanics procedure is significantly more demanding. The gain is a well-defined pressure tensor derived from deformation of total energy. This resolves the issue of the uncertainty in the pressure tensor obtained from integration of the force density, which is the conventional method in density based thermomechanics. Our derivation is based on the variational electrostatics approach developed by Ericksen (Arch. Rational Mech. Anal. 183 299 (2007)).