Elastic Contact Mechanics Research Articles

Damage mechanism of proppant and conductivity reduction post fracturing in unconventional reservoirs

To investigate the impact of proppant embedding and crushing damage on the conductivity in unconventional oil and gas development, experiments on long-term conductivity under suspension injection of proppant were conducted on shale and tight sandstone samples. Based on elastic contact mechanics theory, finite element software (Abaqus) was secondarily developed to globally embed proppant meshes with cohesive elements, analyzing the dynamic changes involving proppant embedding, deformation, and crushing under different closure pressures. The results indicated that the conductivity of fractures is highly sensitive to closure pressure. When closure pressure increases to 40 MPa, the conductivity of shale damage exceeds 60 % compared to 10 MPa. Larger proppants and shale reservoirs accelerate the decline in conductivity significantly, compared to tight sandstone. Combined with laser scanning and fractal dimension identification, the roughness of shale fracture (JRC48) was found to be much greater than that of tight sandstone (JRC37), leading to significantly higher stress concentration between proppants and shale, resulting in a smaller crushing ratio. Additionally, the deformation of shale and contacting proppant is significantly greater than in sandstone, resulting in a rapid decline in shale oil production. These findings provide theoretical guidance for ensuring effective inflow near oil wells, necessitating optimization of proppant injection sequence and placement concentration.

Elastic and Elastoplastic Contact Mechanics of Concentrated Coated Contacts

Machines operate under increasingly harsher contact conditions, causing significant wear and contact fatigue. Sub-surface stresses are responsible for the premature contact fatigue of rolling element bearings, meshing gears, and cam–follower pairs. Surface protection measures include hard, wear-resistant coatings. Traditionally, contact integrity has been predicted using classical Hertzian contact mechanics. However, the theory is only applicable when the contact between a pair of ellipsoidal solids of revolution may be considered as a rigid indenter penetrating a semi-infinite elastic half-space. Many coatings act as thin bonded elastic layers that undergo considerably higher pressures than those predicted by the classical theory. Furthermore, inelastic deformation of bonded solids can cause plastic flow, work-hardening, and elastoplastic behaviour. This paper presents a comprehensive, integrated contact mechanics analysis that includes induced sub-surface stresses in concentrated counterformal finite line contacts for all the aforementioned cases. Generated pressures and deformation are predicted for hard coated surfaces, for which there is a dearth of relevant analysis. The contact characteristics, which are of particular practical significance, of many hard, wear-resistant advanced coatings are also studied. The paper clearly demonstrates the importance of using efficient semi-analytical, detailed holistic contact mechanics rather than the classical idealised methods or empirical numerical ones such as FEA. The novel approach presented for the finite line contact of thin-layered bonded solids has not hitherto been reported in the open literature.

Role of lung lobar sliding on parenchymal distortion during breathing.

Sliding between lung lobes along lobar fissures is a poorly understood aspect of lung mechanics. The objective of this study was to test the hypothesis that lobar sliding helps reduce distortion in the lung parenchyma during breathing. Finite element models of left lungs with geometries and boundary conditions derived from medical images of human subjects were developed. Effect of lobar sliding was studied by comparing nonlinear finite elastic contact mechanics simulations that allowed and disallowed lobar sliding. Lung parenchymal distortion during simulated breath-holds and tidal breathing was quantified with the model's spatial mean anisotropic deformation index (ADI), a measure of directional preference in volume change that varies spatially in the lung. Models that allowed lobar sliding had significantly lower mean ADI (i.e., lesser parenchymal distortion) than models that disallowed lobar sliding under simulations of both tidal breathing (5.3% median difference, P = 0.008, n = 8) and lung deformation between breath-holds at total lung capacity and functional residual capacity (3.2% median difference, P = 0.03, n = 6). This effect was most pronounced in the lower lobe where lobar sliding reduced parenchymal distortion with statistical significance, but not in the upper lobe. In addition, more lobar sliding was correlated with greater reduction in distortion between sliding and nonsliding models in our study cohorts (Pearson's correlation coefficient of 0.95 for tidal breathing, 0.87 for breath-holds, and 0.91 for the combined dataset). These findings are consistent with the hypothesis that lung lobar sliding reduces parenchymal distortion during breathing.NEW & NOTEWORTHY The role of lobar sliding in lung mechanics is poorly understood. Delineating this role could help explain how breathing is affected by anatomical differences between subjects such as incomplete and missing lobar fissures. We used computational contact mechanics models of lungs from human subjects to delineate the effect of lobar sliding by comparing simulations that allowed and disallowed sliding. We found evidence consistent with the hypothesis that lung lobar sliding reduces parenchymal distortion during breathing.

On Surrogate Duality and Competition between Entropy and Potential Energy in the Finite Element Model of Elastic Contact Mechanics

The competition between entropy and energy that usually occurs in thermodynamics — an increase in one usually leads to a decrease in the other — was also shown to hold in static–elastic contact mechanics in our previous work on solving contact problems with an iterative algorithm. In this paper, we first present a theoretical analysis of the surrogate duality of the optimization model of contact problems, propose several propositions characterizing the surrogate duality, and identify the condition under which the fractional objective function of the surrogate dual problem is quasi concave. Second, we further clarify the correspondence between the concepts of statistical physics and the finite element model of contact problems so that the concepts of statistical physics can be more cleanly used to solve contact problems. Third, we provide examples to calculate the contact force with an improved iterative algorithm based on the quasi concavity that more clearly verifies the competition between entropy and potential energy, and the competition shows strong negentropy behavior: potential energy increases while entropy decreases throughout the iterative process.

The Role of Stiffness in Versatile Robotic Grasping

Traditionally, robotic grippers are based on stiff materials, enabling end effectors with high load capacity and precision for industrial applications. Recent advances in soft robotics have led to a proliferation of novel gripper designs with increased conformability to accommodate objects of varying shape, size, material, and surface properties, allowing for grippers that can safely manipulate a wide range of objects. While compliant materials offer noted advantages for robotic grasping, their ability to deform limits their load capacity. Therefore, stiffness selection is critical in gripper design, and the use of materials with tunable stiffness can be exploited for new functionality. Here, we present a mechanics-based investigation of the design of versatile grippers that can accommodate both soft and stiff grasping modalities. We examine the ability to form contact and how different types of gripping forces, including frictional, normal, and adhesive interactions, can be leveraged and controlled. We use analytical models based on elastic beam theory and contact mechanics to quantify the relationship between gripper deflection, contact area, contact pressure, and load capacity. We then use these models to define quantitative conditions for successful grasping as a function of the geometry of the object and the stiffness and geometry of the gripper. Finally, we conclude with an experimental case study and a discussion of how stiffness can be selected and modulated to realize successful grasping for different classes of objects.

Micro-asperity tribocorrosion of CoCrMo, Ti6Al4V, and 316 stainless steel in air and physiological solution: Small scale reciprocal sliding of a single diamond tip

Fretting and corrosion of metallic medical devices are significant degradation mechanisms that impact performance. Multi-asperity contact surfaces undergo a progressive engagement-damage-redistribution process distributed over the nominal contact surface, implying that relatively short-lived fretting contact engagements of individual asperities are a central element to fretting corrosion processes in modular taper junctions of total hip replacements. In this work, the contact mechanics of single asperity hard-metal surfaces under small scale reciprocal sliding (SSRS) between two contacting surfaces in air and solution (i.e., tribocorrosion), typically less than 100 μm cyclic motion are presented and discussed for Ti–6Al–4V, CoCrMo, and 316L SS alloys. Characteristic scaling factors, based on asperity radius, hardness, and modulus, for characteristic stress and a dimensionless asperity radius are presented based on the interaction between elastic and plastic contact mechanics. The contact and tribological interactions of a 17 μm radius spherical diamond asperity was used to explore damage effects on these alloys in both air and phosphate buffered saline. The volume abraded, depth of penetration, extent of plastic deformation and oxide debris formation were captured as functions of cycles, load, and solution presence/absence. Damage was analyzed and quantified using digital optical microscopy, atomic force microscopy and scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS). The results were analyzed with ANOVA statistics (α < 0.05). The extent of damage follows CoCrMo < Ti–6Al–4V < 316L SS. The wear characteristics varied significantly between alloys with more plastic deformation associated with CoCr and more shearing particle and ribbon formation present for Ti–6Al–4V and 316L SS. Solution immersion did not significantly increase volume loss for any alloy but did increase the amount of released and embedded oxide debris for 316L SS. Titanium also exhibited oxide debris generation and embedding. Importantly, significant (<5 μm) penetration depths were obtained after 100 cycles, indicating that single asperities, continuously engaged with metal under very low loads, rapidly generate extensive debris and plastic deformation.

Direct Measurement of the Transverse Modulus of Carbon Fibres

BackgroundThe transverse compressive properties are integral to fully utilizing the high performing mechanical properties of carbon fibres (CF). Direct measurements of transverse properties of CFs are difficult.ObjectiveA system that directly measures transverse compressive modulus (ET) by utilizing interference speckle patterns to measure sub-pixel resolutions is presented.MethodsThe compression data from an isotropic glass fibre was fitted using an elastic contact mechanics model. An initial section was observed, which was not readily fitted using the model and was systematically removed, resulting in an ET of 82 GPa, comparable to the reported longitudinal tensile modulus (EL) of 86 GPa.ResultsThe response of Ag wire to cyclic compression was measured, with the behaviour consistent with a material undergoing typical cyclic stress–strain into a stable hysteretic loop. Several CFs were compressed and an inversely proportional relationship between ET and EL was observed. Transverse compressive moduli of 8.2 (0.8), 6.5 (0.7), 4.3 (0.3), and 2.1 (0.4) were obtained for Toray T300 and Mitsubishi Pyrofil HS40, Pyrofil TR50S, and Dialead K13312, respectively (numbers in parenthesis are standard deviations).ConclusionHysteresis was observed for some of the polyacrylonitrile (PAN)-based CFs and a method for ensuring an accurate fitting of CFs, including hysteretic load/unload curves, was proposed.

Recognition of Contact Force and Position of a Flexible Array-Less Capacitive Tactile Sensor

As an important medium of human-computer interaction, flexible tactile sensors have a vital influence on the intelligence and safety of a system by accurately identifying the contact position and force. For now, most of the existing flexible capacitive pressure sensors adopt an array structure, which still cannot meet the requirements including simple manufacturing, simple wiring, and low cost. This paper innovatively proposes a flexible array-less capacitive tactile sensor, a 30 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times30$ </tex-math></inline-formula> mm sensor prototype, consisting of flexible electrodes and a dielectric layer of a polydimethylsiloxane (PDMS) and multiwalled carbon nanotube (MWCNT) composite. Under the action of a contact force, the contact area is deformed, resulting in a capacitance change in the flexible sensor. First, Poisson’s equation is used to determine the relationship between the electric potential and position. Then, elastic contact mechanics is adopted to describe the relationship between the electric charges and force. Finally, the contact position and force are recognized by measuring the change in capacitance in real time, based on the classical principle of capacitance. Simulation and experimental results verified the effectiveness of the proposed recognition method, showing that the recognition resolution of contact position can reach <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$500\,\,\mu \text{m}\,\,\times 100\,\,\mu \text{m}$ </tex-math></inline-formula> , and the accuracy of contact force is 95.85%. Theoretically, the proposed flexible array-less sensor in this paper has infinite spatial resolution, and most importantly, it does not rely on complex manufacturing, redundant circuits, or sensor cell arrays. Therefore, it has broad application prospects in related fields such as electronic skin and wearable electronic devices.

Influence of material properties and geometric parameters of an impact pair on contact acceleration during a low-velocity impact

Experimental equipment that can provide suitable acceleration peaks (APs) and acceleration pulse widths (AWs) is required for impact studies. It is necessary to design suitable structures and select appropriate materials of the impact pair for experimental equipment. To propose the control strategies of the AP and AW, the effects of the material properties and geometric parameters of the impact pair on the contact acceleration during low-velocity impacts were investigated. The density ρ1 and velocity v of the projectile, and the elastic modulus E2 and yield strength A2 of the target were the dominant factors affecting the AP. The ρ1, A2, and E2 were the primary factors influencing the AW. The AP increased with a decrease in the ρ1 and increases in the v and elastic modulus E1 of the projectile and the thickness H, E2, A2, strain-hardening constant B2, and strain-hardening index n2 of the target. The AW increased with the ρ1 and decreased with the H, E2, and A2. Based on the elastic stress wave and contact mechanics, the influences of the primary factors on the AP and AW were explained. The strategies proposed in this work agreed with the simulation results and the literature.

Radial load distribution by balls in a ball bearing with variable clearance

Clearance in ball bearing influences the startup torque and stiffness of bearing and affects the load distribution, load carrying capacity, and life of bearing. The present work is related to deep groove single row ball bearing with their rings groove are in a radial plane and the outer ringway track is made elliptical. During this event clearance along the bearing's circumference, rings are no longer constant and vary along with the major to the minor axis. A detailed mathematical model is developed to analyze the performance characteristics of a deep groove single row 6206 ball bearing with variable clearance. Based on Hertz elastic contact theory and contact mechanics, the radial load distribution by balls is calculated. The obtained results and other excerpts of this proposed work open the ground to study ball bearing behavior with variable clearance and its suitability in the field of bearing. The results are further compared with conventional ball bearings and found that the load shared by most loaded ball with variable clearance reduced significantly under the particular angular movement of the outer elliptical ring. Therefore the radial load carrying capacity of ball bearing can be enhanced with variable clearance.

A Fractal Model of Elastic–Plastic Contact Between Rough Surfaces for a Low-Velocity Impact Process

Under the low-velocity impact conditions, in order to study the contact load variation law of the ellipsoid elastic bodies, an elastic–plastic contact analysis model of rough ellipsoid surfaces is provided based on elastic–plastic fractal theory. A spherical elastic–plastic fractal model considering friction factors is established, and the spherical diameter density distribution function and elastic contact mechanics are used as the solution methods. The two contact surfaces are taken as the research object, and the influence of relevant variables on the contact intensity is analyzed. The analysis results show that the fractal dimension and roughness have a greater effect on contact performance, the contact load is positively related to the surface roughness, and the lower friction coefficient has a weaker effect on the contact load, and the correctness of the present model is verified by comparing finite element simulation results and other studies. The modified spherical contact load function provides a theoretical basis for the friction and wear of the microscopic surface, it can be applied for solving the sliding contact problems with different impact velocities and the surface bearing capacity of the impact parts can be improved.

Effect of workpiece curvature on the tool influence function during hemispherical sub-aperture tool glass polishing.

The influence of workpiece curvature on the tool influence function spot during polishing of fused silica glass with cerium oxide slurry, while using a rotating hemispherical pad-foam tool for a wide variety of process conditions (tool displacement, inclination angle, and rotation rate), has been investigated. (Workpiece curvature ranged from 500 mm radius concave to 43 mm radius convex.) The TIF spot decreases in diameter and increases in the peak removal rate on more convex workpieces. In contrast, the TIF spot increases both in diameter and peak removal rate on more concave workpieces. For the range of workpiece curvatures investigated, both the spot size and the peak removal rate changed significantly, as much as 2 times. An elastic sphere-sphere contact mechanics model, which utilizes both a modified displacement (that leads to a change in the applied load) as well as a mismatch factor (that influences the pressure distribution shape), has been developed. The model was validated using both offline load-displacement measurements and finite-element analysis simulations. The model quantitatively describes the measured change in the relative contact diameter and relative pressure distribution, as well as semiquantitively describes the change in the relative volumetric removal rate on a large variety of TIF spots. The change in the volumetric removal rate for convex workpieces is a result of the balance between a decreasing spot size (reducing removal) and an increasing peak pressure (increasing removal), which usually results in relatively small changes in volumetric removal. In the case of concave workpieces, the volumetric removal rate change is also governed by a similar balance, but the spot size increase contribution dominates, resulting in a significant increase in volumetric removal rate. Understanding these trends can enable methods to add greater determinism during the fabrication of freeform optics by adjusting polishing parameters (such as dwell time) while the tool translates along a workpiece surface with different local curvatures.

The Friction and Wear Influence of Laser Processing Bionic Brake Drum Unit on the Brake Pad

This article starts with the analysis of the contact between the laser processing bionic brake drum unit body and the brake pad and performs the analysis of the force between the unit body and the brake pad based on elastic mechanics and contact mechanics. By using the Preston equation, the wear of the brake pad caused by the unit body is obtained, as well as the relevant factors and influence rule which affects the wear of the brake pad are found. During laser processing on the bionic brake drum unit body, in order to reduce wear of brake pad, the height of the unit body should be minimized. Besides, the light intensity at the centre of the laser spot should be reduced, and the laser intensity distribution should be more uniform, which can effectively improve the environmental friendliness of the brake drum.

Interfacial fluid flow for systems with anisotropic roughness

.I discuss fluid flow at the interface between solids with anisotropic roughness. I show that the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity. This shows that, in most cases, the surface roughness observed at high magnification is irrelevant for fluid flow problems such as the leakage of static seals, and fluid squeeze-out. The effective medium theory predicts that the fluid flow conductivity vanishes at the relative contact area A/A0 = 0.5 independent of the anisotropy. However, the effective medium theory does not solve the elastic contact mechanics problem but is based on a purely geometric argument. Thus, for anisotropic roughness the contact area may percolate at different values of A/A0 depending on the direction. We discuss how this may be taken into account in the effective medium and critical junction theories.Graphical abstract

Comparison of rolling contact fatigue life between elastohydrodynamic lubricated point contacts pre and post running-in treatment

Abstract Rolling contact micropitting fatigue life is affected by stress fields in shallow subsurface. It is well known that there is a significant dependence, of stress distribution in subsurface, on the surface microstructures. Therefore rolling contact micropitting fatigue lives can be enhanced through modifying surface topography. In this study, running-in method was employed as the method to alter surface microstructures to explore the effect of various morphological characteristics on micropitting fatigue lives. Firstly, various rough surfaces were formed by applying experimental running in processes on a series of ball-on-disc pairs. Meanwhile, the evolutions of topography during the running-in processes were recorded. Secondly, rolling contact fatigue lives of these rough surfaces under elastohydrodynamic lubricated condition were calculated and compared based on Zaretsky's fatigue model combined with elastic contact mechanics. The results have indicated that a running-in process has significantly positive effect on prolonging micropitting fatigue lives. Theoretical analysis of the relationship between topographical parameters and micropitting fatigue lives to ascertain optimum morphological characteristics which are beneficial in reducing micropitting fatigue failures is the key originality of this work. This work provides guidelines on surface morphology for achieving maximum pitting fatigue life for interacting systems. In turn enhanced durability of the systems will lead to significant cost savings.

A 3D analytical model for residual stress in flank milling process

Residual stress in metal cutting is critical due to its significant influence on the work performance of the workpiece. A 3D analytical model of residual stress appropriate for flank milling is established in this paper which takes both mechanical effect and thermal effect into consideration. Firstly, the 3D mechanical stress component is calculated considering its instantaneous and intermitted properties in the milling process. Elastic semi-infinite space contact mechanics and coordinate transformation are employed in the calculation process. Subsequently, the temperature distribution in the workpiece and corresponding thermal stress component are acquired based on the time-varying transient moving heat source model in the milling process. The plastic stress component is calculated based on the radial return method, in which all the stress components are updated during the plastic loading process. Finally, the measurement experiments for milling temperature and residual stress are performed to validate the theoretical models proposed in this work. The fine consistency between the prediction and the experiment demonstrates the accuracy of the prediction model. According to the calculation results of the proposed theoretical model, the plowing effect induced by the squeeze of the cutting edge on the work material is the major source of the residual stress.

New determination to loaded transmission error of the spiral bevel gear considering multiple elastic deformation evaluations under different bearing supports

In spiral bevel gear transmission system, the target is to get lower noise and higher strength as not only the environmental noise requirements but also customer demands must be met. The load transmission error (LTE) is the primary source of noise, and the elastic deformation is the primary source of strength. This paper proposes a new approach to computing LTE in consideration of effect of the elastic deformation under different bearing supports. Where, elastic deformation evaluation mainly includes the tooth flank contact deformation, shear deformation, especially the shaft deformation. In full consideration of above elastic deformation factors, a spiral bevel gear transmission system having the gear, web, gear shaft and bearing support structures is used as a basic design model by providing the different bearing supports. A numerical formulation of LTE considering multiple elastic deformation evaluations under different bearing supports is proposed by applying the elastic contact mechanics theory. Then, the simulated loaded tooth contact analysis (SLTCA) is used to further verify the numerical results of the formulation analysis. Finally, the given numerical instance can verify the proposed approach.

Elastic Contact Mechanics of Randomly Rough Surfaces: An Assessment of Advanced Asperity Models and Persson’s Theory

In this work, we discuss important improvements of asperity models. Specifically, we assess the predictive capabilities of a recently developed multiasperity model, which differs from the original Greenwood and Williamson model by (i) including the coupling between the elastic fields generated by each contact spot, and (ii) taking into account the coalescence among the contact areas, occurring during the loading process. Interaction of the elastic field is captured by summing the contributions, which are analytically known, of the elastic displacements in a given point of the surface due to each Hertzian-like contact spot. The coalescence is instead considered by defining an equivalent contact spot in such a way to guarantee conservation of contact area during coalescence. To evaluate the accuracy of the model, a comparison with fully numerical ‘exact’ calculations and Persson’s contact mechanics theory of elastic rough surfaces is proposed. Results in terms of contact area versus load and separation versus load show that the three approaches give almost the same predictions, while traditional asperity models neglecting coalescence and elastic coupling between contact regions are unable to correctly capture the contact behavior. Finally, very good results are also obtained when dealing with the probability distribution of interfacial stresses and gaps.

Crystal Indentation Hardness

There is expanded interest in the long-standing subject of the hardness properties of materials. A major part of such interest is due to the advent of nanoindentation hardness testing systems which have made available orders of magnitude increases in load and displacement measuring capabilities achieved in a continuously recorded test procedure. The new results have been smoothly merged with other advances in conventional hardness testing and with parallel developments in improved model descriptions of both elastic contact mechanics and dislocation mechanisms operative in the understanding of crystal plasticity and fracturing behaviors. No crystal is either too soft or too hard to prevent the determination of its elastic, plastic and cracking properties under a suitable probing indenter. A sampling of the wealth of measurements and reported analyses associated with the topic on a wide variety of materials are presented in the current Special Issue.

A review of boundary elements methodologies for elastic and viscoelastic rough contact mechanics

In this paper, we review the main contributions developed by the authors to solve problems involving contact between bodies with a roughness covering several orders of magnitude. A periodic self-equilibrated formulation is introduced to avoid any border problem. Furthermore, when focusing on the steady-state rolling or sliding contact mechanics between viscoelastic materials, we develop a mathematical formulation, parametrically dependent on the rolling/sliding speed, which employs the same computational techniques introduced for elastic rough contacts. In particular, in both cases, we adopt an ad hoc discretization technique enabling us to reach the full convergence.