Contact Boundary Research Articles

Modeling and simulation for wear prediction in planar mechanical systems with multiple clearance joints

The main goal of this work is to develop a comprehensive methodology for predicting wear in planar mechanical systems with multiple clearance joints and investigating the interaction between the joint clearance, driving condition, and wear. In the process, an effective contact surface discretization method together with the Lagrangian method are used to establish the dynamic equation of the multibody system. Considering the change of the contact surface, an improved nonlinear contact force model suitable for the complicated contact conditions is utilized to evaluate the intrajoint forces, and the friction effects between the interconnecting bodies are discussed using the LuGre model. Next, the contact forces developed are integrated into the Archard model to compute the wear depth caused by the relative sliding and the geometry of the bearing is updated. Then, a crank slider mechanism with multiple clearance joints is employed to perform numerical simulations in order to demonstrate the efficiency of the dynamic procedures adopted throughout this work. The correctness of the proposed method is verified by comparing with other literature and simulation results. The results show that the wear is sensitive to different initial conditions, and the evolving contact boundary makes the dynamics of mechanical system and the joint wear prediction more complex. This study is helpful for predicting joint wear of mechanical systems with clearance and optimizing the mechanism’s design.

A multiscale method for the heterogeneous Signorini problem

In this paper, we develop a multiscale method for solving the Signorini problem with a heterogeneous field. The Signorini problem is encountered in many applications, such as hydrostatics, thermics, and solid mechanics. It is well-known that numerically solving this problem requires a fine computational mesh, which can lead to a large number of degrees of freedom. The aim of this work is to develop a new hybrid multiscale method based on the framework of the generalized multiscale finite element method (GMsFEM). The construction of multiscale basis functions requires local spectral decomposition. Additional multiscale basis functions related to the contact boundary are required so that our method can handle the unilateral condition of the Signorini type naturally. A complete analysis of the proposed method is provided and a result of the spectral convergence is shown. Numerical results are provided to validate our theoretical findings.

Promising La2Mo2O9–La2Mo3O12 Composite Oxygen-Ionic Electrolytes: Interphase Phenomena

The La2Mo2O9-La2Mo3O12 composite materials represent a novel class of highly conductive materials demonstrating increased oxygen-ion conductivity. Extensive research of (100 - x)La2Mo2O9-xLa2Mo3O12 composites over a wide range of concentrations (x = 5, 10, 15, 20, 30, and 100) was carried out for the first time. An increase in conductivity, oxygen surface exchange coefficient, and oxygen diffusivity is observed for composites compared to individual oxides, which is associated with the segregation of different ions on the surface of the grains and the formation of a La5Mo3O16 new phase at the contact boundary of La2Mo2O9 and La2Mo3O12. 3D-modeling of the composite microstructure was performed on the basis of SEM-image analysis data in order to estimate the conductivity of the interphase layer between the La2Mo2O9 and La2Mo3O12 grains containing La5Mo3O16. The electrical conductivity values of the composite materials calculated from a 3D-simulated microstructure and the experimentally measured conductivity correlate and demonstrate a composite effect.

Analisis Data Gravitasi Untuk Identifikasi Struktur Bawah Permukaan Daerah Potensi Panas Bumi Cipari

Geothermal prospect in Cipari has been shown by spring who has a temperature of about 50°C and is categorized as a low temperature. The presence of spring on Cipari earth's surface is an indication of geothermal structures' existence on the surface and a geothermal system below the surface. Geophysical methods can be used for subsurface structures identification, one of them is the density method with gravity data. This study has an objective to identify the subsurface structures in Cipari geothermal potential area using GGMPlus gravity data. Terrain and Bouguer corrections were used to obtain Complete Bouguer Anomaly (CBA). Separation of regional and residual anomalies using Butterwoth and Bandpass filters. The rock contact boundary was obtained by the FHD method and geological structures such as faults were obtained by the SVD method. FHD and SVD results were used as information for 2D forward modeling. The ABL map shows anomalous contrasts in areas that have rock contacts and geological faults. The high anomaly in the center of the study area indicates the Cipari anticline. Data processing and analysis concluded that the area around the Cipari hot spring has anticline, several rock contacts, and normal fault structures. The fault in the study area is part of the geothermal system which is confirmed by GGMPlus data.

Middle Ordovician bottom current deposits in the western margin of the North China craton: Evidence from sedimentary and magnetic fabrics

AbstractIn many modern deep‐water slope environments, deposits formed by bottom currents (contourites) are rather common. However, reports on ancient contourites in deep‐water environments are scarce and most of them remain contentious. Based on the study of high‐resolution sedimentological, sedimentary geological and magnetic fabric characteristics, this study presents the key evidence of bottom current activity in the Middle Ordovician Kelimoli Formation from the western margin of the North China craton, and reconstructs the deep‐sea circulation pattern and the direction of deep‐water bottom currents in the middle and low latitudes during the Middle Ordovician. Six typical carbonate microfacies are identified in the Kelimoli Formation, which can be grouped into three sedimentary facies types related to the main interpreted depositional processes (bottom current, undifferentiated bottom current and hemipelagic settling, and hemipelagic settling). The evidence of bottom current deposits are five‐fold. Firstly, it is possible to observe a variety of traction current structures, which mainly represent bed‐load‐dominated transport of sediments. Secondly, there are multi‐scale inverse grading and bi‐grading, as well as inversely‐graded and normally‐graded sedimentary sequences, which reflect the periodic change of bottom current activity. Thirdly, gradual or sharp contact boundaries and small internal erosional surfaces indicate omission surfaces caused by the oscillating variation of bottom current velocity. Fourthly, the continuous rhythmic change of sedimentary fabrics on the microscopic scale reflects sustained, waxing and waning current intensities. Fifthly, the anisotropy of magnetic susceptibility reveals the microscopic fabric characteristics of imbricated magnetic grains, which represent the continuous action of directional current, and the restored palaeocurrent direction indicates that the current is mainly parallel to the slope strike. After the palaeo‐north correction of the North China craton clockwise rotation of 120° to 150° since the Ordovician, anisotropy of magnetic susceptibility shows that the direction of bottom current in the study area is towards the north‐east/east. Therefore, it is speculated that there was a clockwise deep‐water circulation in the middle and low latitudes of the southern hemisphere during the Ordovician. This study not only provides sedimentological evidence for the Ordovician bottom current activity, but also contributes to a better understanding of the Ordovician palaeoceanographical environment, especially the Middle Ordovician deep‐sea circulation pattern.

НЕСТАЦИОНАРНЫЕ ВОЛНЫ В ЛИНЕЙНО-ВЯЗКОУПРУГОМ ЦИЛИНДРЕ С ЖЕСТКИМ ВКЛЮЧЕНИЕМ

We have constructed a solution to a non-stationary dynamic problem for a linear-viscoelastic homogeneous infinitely long cylinder with a rigid axial inclusion exposed to an axisymmetric radial load uniformly distributed along the element of cylinder. On the contact surface with a rigid inclusion, the displacements are equal to zero. The hereditary properties of the material of the cylinder are taken into account using the Boltzmann–Volterra linear integral relation, and the Poisson's ratio of the material is considered time-independent. The integral Laplace transform in time is applied to the initial problem and the analysis of the solution in images is carried out. In the case when the hereditary kernel is exponential two-parameter, originals of the displacement and stresses are constructed in a form of series. Asymptotic formulas for the stresses behind the front that first came from the loaded boundary are obtained. The constructed solution to the non-stationary problem is valid over the entire time range and does not require that the viscosity be small. With the help of constructed solution for the case of an exponential relaxation kernel, investigations of wave process in cylinder cross-section with various initial parameters are carried out. It is established that in the case of a compressive external load, significant tensile stresses occur at certain moments at the contact boundary with a rigid inclusion. They decrease with the growth of the parameter characterizing the viscosity of the material. With a stepwise change in time of the external load, the dependence of the maximum tensile stresses at the boundary with a rigid inclusion on the inclusion relative radius and the viscosity parameter of the material is investigated.

Усиление деревянных конструкций композитами

The technical-and-economic efficiency of wood structures can be implemented by their longitudinal, transverse or combined reinforcement. Both metal and composites made of high-strength fibers (glass, carbon, aramid, basalt, etc) can be used as reinforcing materials. Schemes of reinforcement of wood and wood-glued structures by composite materials are described. The rational geometry of twisted composite reinforcement is proposed, which provides high adhesion to wood material. A method for determining the calculated resistance of a twisted bar to pulling out of wood is given. When calculating the holding force of the calculated pull-out resistance should take into account both the friction force at the contact boundary and the force of crushing the wood under the surfaces of the helical line. It makes possible to increase strength, rigidity, as well as the operational characteristics of wood structures, including load-bearing capacity, durability and reliability in chemically aggressive environments.

Investigation of the interface layer phase composition obtained by hot pressing of Cr and Si

The possibility of synthesizing layers of the medium-temperature thermoelectric CrSi2 by hot pressing of the initial components (Cr and Si) has been investigated. The phase composition of samples obtained by hot pressing of Cr and Si before and after annealing in the region of their contact boundary has been investigated by X-ray analysis. It is shown that, under certain conditions, low-temperature synthesis of a CrSi2 layer with a thickness of 50 to 300 μm is possible at the interface between Cr and Si. The synthesis occurs at a temperature significantly lower than that given in the phase diagram, which opens up new technological possibilities for obtaining the CrSi2 compound. Keywords: thermoelectrics, chromium disilicide, phase interface, X-ray phase analysis.

Evaluating the performance of enriched finite elements for Hertzian contact problem

Solution of contact problems in the field of mechanics is often very challenging, as it is hard to predict the contact forces and stresses due to non-constant boundary conditions. It is observed that when standard finite elements of linear order are used to represent the contact boundary, it is difficult to capture the contact forces within the contact region accurately. To improve this situation, different techniques usually are adopted. One such technique is using highly refined mesh at the contact zone. But it increases the computational time. Thus, it is more efficient to adopt the enrichment strategies for the contact elements lying within the contact region. Such elements are also referred to as the enriched contact finite elements. To the best of the authors' knowledge, the effects of contact enrichment with various interpolation orders on the solution accuracy of contact problems have not been exploited completely and hence is the scope for the present work. The current contribution evaluates the performance of enriched finite elements in solving the Hertz contact problem. The enrichment strategy is based on the introduction of extra degrees of freedom for the contact elements in the slave surface. The contact surface is locally enriched to represent the surface more accurately than the bulk. Thus, the improved computational contact formulation helps to correctly approximate the contact forces while keeping the total degrees of freedom low. In this work, the penalty method enforces contact constraints, and material behaviour follows the Neo-Hookean hyperelastic material model. A benchmark problem on the Hertzian contact is considered to demonstrate the FE enrichment technique. The numerical results exhibit the better performance of the FE enrichment over the mesh refinement for the solution accuracy. This work also shows that the higher-order finite elements after enrichment outperform the linear order finite elements in the contact region.

A Finite Element Approach for Nonlinear, Transient Heat Conduction Problems with Convection, Radiation or Contact Boundary Conditions

A Finite Element Approach for Nonlinear, Transient Heat Conduction Problems with Convection, Radiation or Contact Boundary Conditions

Численное решение прямой задачи электроимпедансной томографии в полной электродной постановке

This work is related to one of the methods of medical imaging - electrical impedance tomography (EIT). A feature of the considered two-dimensional mathematical formulation for the direct EIT problem is the use of an elliptic type equation with piecewise constant coefficients and a special integro-differential boundary condition at the contact boundary of the electrodes. For an approximate solution of the problem under consideration, a numerical method was developed using unstructured grids, the finite volume method for barycentric cells, and the Gaussian elimination method with the choice of the main element. The validation of the method was performed on a known analytical solution.

Сравнение эффективности методов решения систем линейных уравнений в задаче моделирования контактного взаимодействия элементов твэла в термоупругой постановке

Various algorithms for solving systems of linear algebraic equations that arise when modeling problems of contact interaction of thermoelastic bodies with a changing configuration of the contact surface are considered. The implementations of modified iterative methods, the Uzawa method, as well as algorithms based on the use of the Gauss method and the generalized method of minimal residuals (GMRES) with two iterative refinement options allowing for the exit from contact of individual sections of the contact boundary are presented. The efficiency of the presented algorithms is compared in relation to a problem simulating thermomechanical processes in a section of a fuel element that includes up to 100 fuel pellets.

Contacts with limited interpenetration

The aim of this paper is to acquaint a wider public of applied mathematicians, numerical analysts and engineers with the model of contact with limited interpenetration as a suitable framework for computation of practical problems. It is mostly based on the newly published Ref. [5]. The model is physically well based on the microscopic structure of a standard material of a body being in an actual or potential contact with a rigid foundation. Such microscopic phenomena are macroscopically interpreted as a certain but strictly limited surface interpenetration of both objects. The essence of this interpenetration is depicted in the graphical abstract. After a brief description of its motivation and the method itself, a comparison with the other contact models available together with the detailed description of the graphical abstract is presented. Furthermore, the application of the method to a quasistatic frictional boundary contact is described. Moreover, a brief description of the methods used in the proof of the existence of solutions of such contact problems is provided. If the depth of the interpenetration tends to zero, then there is some sequence of solutions of such problems and some solution to the corresponding Signorini contact problem such that it is the limit of the sequence. Requirements for the use of the presented model in solving practical problems as well as its other aspects are briefly discussed. Summing up:•the presented and other results published (Refs. [1–4]) create a reliable basis of the numerical analysis of the problems;•the method is ready to be used in solving a wide class of contact problems arising in technical practice.

A Bauer–Furuta-type refinement of Kronheimer and Mrowka’s invariant for 4–manifolds with contact boundary

Kronheimer and Mrowka constructed a variant of Seiberg-Witten invariants for a 4-manifold $X$ with contact boundary in 1997. Using Furuta's finite dimensional approximation, we refine this invariant in the case $H^1(X, \partial X; \mathbb{R})=0$.

A semi-analytical method for frictional contact analysis between rock mass and concrete linings

The rock–lining interface typically exhibits a complex frictional contact behavior. Thus far, there has been no analytic method to analyze the frictional contact problems of arbitrary-shaped tunnels with concrete linings. In this work, we propose a novel analytic method to perform the frictional contact analysis of multiple lined tunnels based on the generalized complex variable method. Using two special composite analytic functions, the mechanical field in a multiply-connected domain can be accurately expressed, and the solution to the contact problem can thus be obtained in a closed mathematical form. In the present theoretical framework, the general contact condition is considered, where the contact mode is described using two complementary functions. The basic linear equations are obtained by satisfying the stress and contact boundary conditions at a finite number of discrete points. Since the contact analysis is a highly nonlinear problem, we propose an iterative scheme to determine the contact states at different positions on the rock–lining interface. Finally, a verification example and parametric investigation are performed to demonstrate the effectiveness and practicability of the proposed method.

Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

Realistic Reference for Evaluation of Vehicle Safety Focusing on Pedestrian Head Protection Observed From Kinematic Reconstruction of Real-World Collisions.

Head-to-vehicle contact boundary condition and criteria and corresponding thresholds of head injuries are crucial in evaluation of vehicle safety performance for pedestrian protection, which need a constantly updated understanding of pedestrian head kinematic response and injury risk in real-world collisions. Thus, the purpose of the current study is to investigate the characteristics of pedestrian head-to-vehicle contact boundary condition and pedestrian AIS3+ (Abbreviated Injury Scale) head injury risk as functions of kinematic-based criteria, including HIC (Head Injury Criterion), HIP (Head Impact Power), GAMBIT (Generalized Acceleration Model for Brain Injury Threshold), RIC (Rotational Injury Criterion), and BrIC (Brain Injury Criteria), in real-world collisions. To achieve this, 57 vehicle-to-pedestrian collision cases were employed, and a multi-body modeling approach was applied to reconstruct pedestrian kinematics in these real-world collisions. The results show that head-to-windscreen contacts are dominant in pedestrian collisions of the analysis sample and that head WAD (Wrap Around Distance) floats from 1.5 to 2.3 m, with a mean value of 1.84 m; 80% of cases have a head linear contact velocity below 45 km/h or an angular contact velocity less than 40 rad/s; pedestrian head linear contact velocity is on average 83 ± 23% of the vehicle impact velocity, while the head angular contact velocity (in rad/s) is on average 75 ± 25% of the vehicle impact velocity in km/h; 77% of cases have a head contact time in the range 50–140 ms, and negative and positive linear correlations are observed for the relationships between pedestrian head contact time and WAD/height ratio and vehicle impact velocity, respectively; 70% of cases have a head contact angle floating from 40° to 70°, with an average value of 53°; the pedestrian head contact angles on windscreens (average = 48°) are significantly lower than those on bonnets (average = 60°); the predicted thresholds of HIC, HIP, GAMBIT, RIC, BrIC2011, and BrIC2013 for a 50% probability of AIS3+ head injury risk are 1,300, 60 kW, 0.74, 1,470 × 104, 0.56, and 0.57, respectively. The findings of the current work could provide realistic reference for evaluation of vehicle safety performance focusing on pedestrian protection.

Cu2O nano-flowers/graphene enabled scaffolding structure catalyst layer for enhanced CO2 electrochemical reduction

Nanosized Cu2O catalysts with precisely controlled bud-to-blooming flower shapes are synthesised using modified polyol method. The evolution of the shape when the catalysts are applied to the gas diffusion electrodes improves the key factors influencing the catalyst layer, e.g. volume porosity and triple-phase boundary contact areas. Numerical and experimental studies revealed increased reactant molar concentration and improved CO2 mass transfer due to the structural changes, which influenced the electrochemical CO2 reduction reaction (eCO2RR). The fully bloomed Cu2O nanoflower catalyst, combined with the two-dimensional (2D) structured graphene sheet, formed a catalyst layer with scaffolding structure that exhibited the highest Faradaic efficiency (FE) of 93.20% towards CO at an applied potential of −1.0 V vs. RHE in 1 M KOH. These findings established the relationship between the catalyst layer properties and mass transfer, based on which we could describe the effect of the structural design of the catalyst layer on the eCO2RR performance.

The contact stress distribution in the receding contact of an elastic layer with a rigid base

The receding contact between a semi-infinite elastic strip and a flat rigid base is considered. This problem is analyzed using linear elasticity with a shear force and a bending moment applied to its end and with frictionless contact with the base. The solutions for a separately applied shear force and a bending moment are determined in which adhesion with the rigid base is allowed for each problem. However the receding contact does not allow adhesion and so the superposed problem cancels the stress singularities resulting in a bounded contact pressure distribution. This distribution becomes independent of the out-of-contact length to thickness ratio. The maximum contact pressure is shown to be about one-half of that obtained by using structural mechanics theory with shear deformation included (Timoshenko beam theory). Furthermore the center of pressure of this distribution is at a distance from the contact boundary comparable to the thickness of the layer. Thus the condition of zero bending moment used in classical beam/plate theories should be modified accordingly.

PHYSIC-CHEMICAL PROPERTIES OF TYPICAL CHERNOZEMS OF PRYDNISTERSK PODILLYA

This article analyzes the physic-chemical properties of typical chernozems. According to the methods, a laboratory study was performed. Physic-chemical parameters that are typodiagnostic for subfacial classification division of typical chernozems of the Prydnistersk Podillya are determined. Typical chernozems of the Prydnistersk Podillya are low-humus (2.78–3.98%). With depth, the humus content decreases by an average of 0.2% for every 10 cm, which indicates a uniformly accumulative type of distribution of organic matter in the profile of chernozems. In the same direction, humus reserves are declining. There is a spatial correlation between the humus content and the amount of physical clay in the fine soil.
 Humic acids predominate in the humus to a depth of 90–100 cm (Sgk: Sfk is 1.12–1.78). The general tendency of relative “fulvatization” of the arable layer as a result of its agrotechnical depletion is noticed. In relation to SGC to total organic C, chernozems of the study area are characterized by a high and very high degree of humification of organic matter. It is highest (62–70%) in the soils of the key section “Humentsi”, decreasing to 52–62% and 43–63% in the western direction.
 The humic acids of typical chernozems are dominated by calcium humates (GK-2). The largest number of them (29–35%) is concentrated on the contact boundary of humus and carbonate profiles. The convex nature of the distribution curves of the fraction of 2 humic acids and a sharp decrease in its content deeper than 100 cm, indicates their high migration capacity and the possibility of significant deposition of only a significant excess of calcium carbonates. The intensity of migration processes of the GK-2 fraction decreases in the direction of increasing the stiffness of hydrothermal conditions, due to the pulling of carboxylic acid salts closer to the soil surface, supersaturation of the solution with calcium bicarbonate, and as a consequence, increasing the total alkalinity in the humus horizon.
 The capacity of cation exchange (ECO) of typical chernozems is quite high (29–32 mmol-eq / 100 g of soil) with the dominance of calcium and magnesium cations in the composition of the soil-absorbing complex (GVC). There is a general tendency to increase these indicators in chernozems with low values ​​of SCC of the territory.
 The pH of the aqueous extract of typical chernozems of the Prydnistersk Podillya increases with depth from weakly acidic in the arable horizon to weakly and medium-alkaline within the carbonate profile. The reasons for such changes in the increase with the depth of the concentration of Ca2 + bicarbonates, which in their dissociation leads to an increase in the amount of hydroxyl ion and increase the alkalinity of the soil.
 The carbonate profile of typical chernozems is dominated by migratory forms of carbonate neoplasms - mold, carbonate plaque, veins. The vertical curve of carbonate content has an eluvial-illuvial type of profile structure. The content and reserves of carbonates in the 1.5-meter layer of typical chernozems increase from the west (434–714 t / ha) to the east (979–1847 t / ha).
 Key words: physic-chemical properties, typical chernozems, humic horizon, humic acids, carbonate profile.