Contact Mechanics Research Articles

Theoretical and Experimental Investigation of Material Removal Rate in Magnetorheological Shear Thickening Polishing of Ti–6Al–4V Alloy

Abstract Magnetorheological shear thickening polishing (MRSTP) is a novel hybrid polishing method that combines the magnetorheological effect and the shear thickening effect. It has great potential for ultra-precision machining of complex surfaces. However, the absence of a correlation between material removal and the rheological properties of the polishing media has posed difficulties for further improvements in polishing efficiency and quality in MRSTP. In this work, a material removal model for MRSTP was established based on the principles of magneto-hydrodynamics, non-Newtonian fluid kinematics, and microscopic contact mechanics. This model combines the material removal model for a single abrasive particle with a statistical model of active grits. When comparing the experimental and theoretical results, it became evident that the developed material removal model can accurately predict the material removal depth of the workpiece under different processing parameters such as rotational speed of the rotary table and magnetic field strength. The average prediction error was found to be less than 5.0%. Furthermore, the analysis of the rheological behavior and fluid dynamic pressure of the polishing media reveals the coupling effects between the magnetic, stress, and flow fields. This provides theoretical guidance for the actual processing of MRSTP. Finally, the maximum material removal rate of 3.3 μm/h was achieved on the cylindrical surface of the Ti–6Al–4V workpiece using the MRSTP method. These results demonstrate that the MRSTP method holds great potential in the field of ultra-precision machining of difficult-to-machine materials.

Normal contact mechanism of flexible film/substrate bilayer structure: Experimental and numerical insight

The film/substrate bilayer structure design plays a crucial role in enhancing the adaptability of flexible tactile sensors in complex environments. Nonetheless, as the cornerstone for machine tactility, the normal contact mechanism of the film/substrate bilayer structure remains elusive. Herein, the normal contact characteristics of polydimethylsiloxane film/sponge bilayer structure (PF/SBS) with different structural parameters, including substrate porosity, film mass ratio, and relative thickness between film and substrate, are investigated by experimental and numerical methods. The roles of the film and substrate structure parameters of PF/SBS in the normal contact process are analyzed by a cohesive contact model from the energy perspective. The results demonstrate that PF/SBS not only modulates the maximum normal force by substrate porosity but also exerts a substantial impact on the critical contact state by the film mass ratios. The contribution of film thickness to the critical separation state can be enhanced up to 90% with increasing relative thickness.

Study on microstructure of 42CrMo steel by ultrasonic surface rolling process

To explore the microstructure formation mechanism of 42CrMo steel under the strengthening of ultrasonic surface rolling process (USRP), the combination of theoretical analysis and experiment was used to conduct in-depth research on USRP. Firstly, according to contact mechanics and Hertz contact theory, the calculation model of contact stress distribution and elastoplastic strain between the rolling ball and the part during USRP is obtained. Secondly, the USRP processing test was carried out by single-factor experimental design method, and the microstructure of 42CrMo steel after USRP was analyzed by LEXT OLS5100 3D laser surface topography instrument and VEGA3 tungsten filament scanning electron microscopy, which found that with an increase in static pressure, residual stress and plastic strain gradually increase, the hardness firstly increases and then decreases, while surface roughness exhibits an initial decrease followed by an increase. The results show that USRP produces violent plastic deformation inside the material under the superposition of high-frequency impact and static pressure, at the same time, it refines the grains, so as to improve the surface performance of the part and improve its fatigue resistance.

Spectral wear modelling of rubber friction on a hard substrate with large surface roughness

Soft-hard matter friction is a long-standing tribology problem that remains unclarified, requiring engineers to empirically predict the wear life. To clarify this issue, this study examines the transient running-in regime of rubber friction on a hard rough substrate and models the temporal wear progression using the spectrum curves of surface roughness for both materials. Performing a series of friction tests and three-dimensional surface-height measurements, the time-dependent behaviours of the power spectral densities (PSDs) are divided into two phases, namely the initial non-steady and long-term steady phases. The detailed spectral analyses of worn rubber surfaces in the initial phase lead to a blended PSD function between self-affine and K -correlation surface models, consisting of one variable (the Hurst exponent) that is saturated by the substrate self-affinity. Supported by the Greenwood–Williamson theory concerning rough contact mechanics, the volumetric estimate with the blended PSD function is used to assess the volume rate of wear debris in the steady phase, which is validated experimentally. These findings not only improve the wear predictions of soft materials from the initial measurements of worn surfaces but also help clarify the constrained multiscale mechanism of wear.

Analysis, Modeling and Experimental Study of the Normal Contact Stiffness of Rough Surfaces in Grinding

Grinding is the most important method in machining, which belongs to the category of precision machining processes. Many mechanical bonding surfaces are grinding surfaces. Therefore, the contact mechanism of grinding a joint surface is of great significance for predicting the loading process and dynamic characteristics of precision mechanical products. In this paper, based on the collected grinding surface roughness data, the profile parameters and topography characteristics of the asperity were analyzed, the rough surface data were fitted, the asperity profile was reconstructed, and the parabola y = nx2 + mx + l of the cylindrical asperity model was established. After analyzing the rough surface data of the grinding process, the asperity distribution height was fitted with a Gaussian distribution function, which proved that asperity follows the Gaussian distribution law. The validity of this model was confirmed by the non-dimensional processing of the assumed model and the fitting of six plasticity indices. When the pressure is the same, the normal stiffness increases with the decrease in the roughness value of the joint surface. The experimental stiffness values are basically consistent with the fitting stiffness values of the newly established model, which verifies the reliability and effectiveness of the new model established for the grinding surface. In this paper, a new model for grinding joint surface is established, and an experimental platform is set up to verify the validity of the model.

CD56 brightCD16 -Perforin - regulatory Natural Killer Cells Associated with the Suppression of Chronic Graft-Versus-Host Disease Prevent CD4 + T Cell Proliferation through PD-1 and LAG-3 Dependent Pathways

Background: Chronic graft-versus-host disease (cGvHD) is a major cause of morbidity and mortality after Hematopoietic Stem Cell Transplantation (HSCT). Previously, in large cohorts of HSCT patients we identified increased numbers of CD56 bright, granzyme B -, perforin - NK cells (NK reg) to be associated with a lack of cGvHD development. Transcriptome analysis of HSCT patient samples identified a unique transcriptome among the CD56 bright NK reg cells which associated with patients who failed to develop cGvHD, including overexpression of genes IL7R, GPR183, and Granzyme K, and low expression of genes such as perforin, granzyme B, and CD16. We then utilized the transcriptome information and further cell phenotyping to determine the optimal sorting approach for viable NK reg cells to allow for functional analysis by the sorting of CD56 brightCD3 -CD16 - cells. Functional analysis suggested that the NK reg population suppresses CD4 + T cells through a non-cytolytic, and direct cell-cell contact-dependent mechanism, though the exact receptor and ligand interaction of which CD4 + T cell populations are impacted is unknown. We hypothesized that the NK reg cell suppressive mechanism may be more specific than the more widely studied regulatory cell population, T reg cells, by suppressing CD4 + T cell subpopulations involved in inflammatory responses. Methodology: To investigate the suppressive capacity of NK reg cells, the cells were isolated from healthy donor peripheral blood and co-cultured with allogeneic CD4 + T cells, CD8 + T cells, T reg cells, T reg cells and dendritic cells, B cells, or NK cells for 96hrs. After 96hrs, the proliferation and viability of the responder cells were evaluated via proliferation dye dilution, and 7-AAD dye, respectively. To determine if the CD4 + T cell suppression is specific to a T helper (T h) cell subset we stained the co-cultured cells with a T h1/T h2/T h17 Phenotyping Kit. Further, PD-1 and LAG-3 neutralizing antibodies were added to the NK reg/CD4 + T cell co-culture to determine the receptor dependence. All samples were acquired with the BD FACSymphony Flow Cytometer and the data was analyzed via Kaluza software. Results: CD56 brightCD16 -perforin - NK regcellsstrongly suppress CD4 + T cell proliferation (approximately 96% suppression of CD4 + T cell proliferation at the 1:1 ratio of NK reg cells to CD4 + T cells). The contact-dependent mechanism of NK reg suppression of CD4 + T cell proliferation was significantly decreased when blocking either the PD-1 (15% decrease in suppression, p=0.03), or LAG-3 (29% decrease in suppression, p=0.04) receptors, at the 1:2 ratio of NK reg cells to CD4 + T cells. When both receptors are blocked the inhibition of suppressive effect is comparable to that of the LAG-3 blocking antibody being added individually (30% decrease in suppression, p=0.03). The suppressive mechanism of NK reg cells was observed to be selective in that they strongly suppress CD4 + T cell proliferation, but do not result in statistically significant suppression of CD8 + T cell, T reg cell, B cell, NK cell, or a specific T h cell subset proliferation (p>0.05). Further, though the average proliferation of the T reg cells co-cultured with NK reg cells and dendritic cells compared to just NK reg cells was greater (127% proliferation compared to 100% proliferation, respectively), we did not observe NK reg cells to induce a statistically significant proliferative effect towards the T reg cells in the presence of dendritic cells. Conclusion: As a result of our studies, we have confirmed the NK reg cell immune suppressive function towards CD4 + T cell proliferation, a main contributor to cGvHD development. Further, we demonstrated a PD-1/LAG-3-dependent direct contact mechanism of NK reg cell suppression, which is selective of total CD4 + T cells, with a lack of suppressive effect towards CD8 + T cells, T reg cells, B cells, and NK cells. The results of these studies contribute to our better understanding of how NK reg cells may induce a cell-specific suppressive function to promote immune tolerance, providing potential cell therapeutic applications for enhancing NK reg cell suppressive function through increasing PD-1/LAG-3 ligand or receptor expression on NK reg cells.

Contact Mechanics between Torus and Pit Border for Developing Air-Seeding Seal in Aspirated Bordered Pits

Bordered pits in conifers have been recognized as a significant evolutionary characteristic that served to impede the spread of embolisms between tracheids. Nevertheless, there was a lack of comprehensive understanding regarding the mechanical properties of the torus and the pit border in relation to the formation of contact seals in aspirated pits. A solid mechanics model was developed to study aspirated bordered pits, incorporating the elastic deformation of the torus–margo structure and the contact behavior between the torus and the pit border. Ten pit samples were reconstructed using transmission electron microscopy (TEM) and scanning electron microscopy (SEM) pictures in order to develop mechanical models for pits in the stems of Platycladus orientalis. Due to the limited contact area on the torus surface, the contact pressure between the torus and the pit border exceeded the air pressure in aspirated bordered pits. The external force and the duration required to seal pits decreased when the pit diameter increased and the pit depth decreased. The augmentation of the torus and margo mass necessitated a lengthier duration for the closure of cavities. The findings presented in this study offered theoretical support for the capillary-seeding hypothesis. The aspiration in bordered pits mechanically depended on the structural and material characteristics of the torus and margo.

Injury incidence among adolescent and senior basketball players: a prospective study in 19 teams across an entire season

ABSTRACT Objective To quantify and compare injury incidence between national-level, adolescent and regional-level, senior, male basketball players competing in Serbia overall and according to injury mechanism (contact, non-contact, or overuse), exposure setting (training or games), and history (new or recurrent). Methods A total of 218 male basketball players from 19 teams (106 senior and 112 adolescent players) volunteered to participate in the study. Descriptive data regarding game and training injury incidence were gathered across all players and reported per 10,000 athlete-exposures (AE) with 95% confidence intervals. Results Overall, 26 injuries were reported across 52,509 AE. Ankle (n = 10, incidence rate [IR] = 1.90 [0.97, 3.40]) and knee injuries (n = 8, IR = 1.52 [0.71, 2.89]) accounted for 69% of all reported injuries, with only 1–2 injuries documented for other body regions. Ankle injuries were attributed to contact (60%, IR = 1.14 [0.46, 2.38]) or non-contact mechanisms (40%, IR = 0.76 [0.24, 1.84]). Most knee injuries occurred due to overuse (50%, IR = 0.76 [0.24, 1.84]) or non-contact mechanisms (38%, IR = 0.57 [0.15, 1.56]). Comparisons according to exposure setting revealed significantly higher knee (incidence rate ratio [IRR] = 9.95 [1.85, 53.41], p = 0.004) and ankle (IRR = 39.79 [7.94, 384.67], p < 0.001) injuries per 10,000 AE during games compared to training. Recurrent injuries were most prominent in the ankle (30% of all ankle injuries, p = 0.11). Total contact (p = 0.04), non-contact (p = 0.04), and recurrent IR (p = 0.005) were significantly higher in senior than adolescent players. Conclusion The players examined were most susceptible to ankle and knee injuries, particularly during games compared to training. Ankle injuries were mostly attributed to player contact, while knee injuries were mostly attributed to overuse and non-contact mechanisms. Senior players were at a greater risk of sustaining contact, non-contact and recurrent injuries than adolescent players.

Frictionless line-to-line contact: Comparison of mortar and unbiased formulation in combination with Lagrange-multiplier and penalty method

Recent developments in the beam-to-beam contact mechanics have prompted us to investigate further into the relations between different formulations and contact-force models. Specifically we address in this paper the recently developed mortar method for beams and develop its variant based on the penalty method. This allows an in-depth comparison between the two formulations. Furthermore, we design an unbiased approach and introduce a new discretisation technique developed specifically for this method. The unbiased line-to-line method is also combined both with the Lagrange-multiplier and the penalty method. All developed elements have been tested using the same examples to provide an objective comparison between formulations in terms of robustness and computational cost.

Need Fulfillment During Intergroup Contact: Three Experience Sampling Studies.

One challenge of modern intergroup contact research has been the question of when and why an interaction is perceived as positive and improves intergroup relations. We propose to consider the perceived fulfillment of the situationally most relevant need. We conducted three intensive longitudinal studies with recent migrants to capture their interactions with the majority out-group (Nmeasurements = 10,297; Nparticipants = 207). The situational need fulfillment mechanism is consistently a strong predictor of perceived interaction quality and positive out-group attitudes following intergroup interactions. The model is specific to out-group contact, robust to various need types, and works at least as well as Allport's contact conditions. As one of the first studies to test intergroup contact theory using intensive longitudinal data, we offer insight into the mechanisms of positive intergroup contact during real-life interactions and find situational motivations to be a key building block for understanding and addressing positive intergroup interactions.Public significance statement: In this article, we provide evidence that the fulfillment of situational needs during real-life intergroup contacts meaningfully predicts perceived interaction quality and positive outgroup attitudes. Methodologically, this offers a testament to the emerging practice of capturing real-life interactions using intensive longitudinal data. Theoretically, our results give weight to motivational fulfillment as a flexible and effective mechanism for understanding positive intergroup contact.

Simultaneous Evaluation of Tibiofemoral and Patellofemoral Mechanics in Total Knee Arthroplasty: A Combined Experimental and Computational Approach.

Contemporary total knee arthroplasty (TKA) has not fully restored natural patellofemoral (P-F) mechanics across the patient population. Previous experimental simulations have been limited in their ability to create dynamic, unconstrained, muscle-driven P-F articulation while simultaneously controlling tibiofemoral (T-F) contact mechanics. The purpose of this study was to develop a novel experimental simulation and validate a corresponding finite element model to evaluate T-F and P-F mechanics. A commercially available wear simulator was retrofitted with custom fixturing to evaluate whole-knee TKA mechanics with varying patella heights during a simulated deep knee bend. A corresponding dynamic finite element model was developed to validate kinematic and kinetic predictions against experimental measurements. Patella alta reduced P-F reaction forces in early and midflexion, corresponding with an increase in T-F forces that indicated an increase in extensor mechanism efficiency. Due to reduced wrapping of the extensor mechanism in deeper flexion for the alta condition, peak P-F forces in flexion increased from 101% to 135% of the applied quadriceps load for the baja and alta conditions, respectively. Strong agreement was observed between the experiment and model predictions with root-mean-square errors (RMSE) for P-F kinematics ranging from 0.8 deg to 3.3 deg and 0.7 mm to 1.4 mm. RMSE for P-F forces ranged from 7.4 N to 53.6 N. By simultaneously controlling dynamic, physiological loading of the T-F and P-F joint, this novel experimental simulation and validated model will be a valuable tool for investigation of future TKA designs and surgical techniques.

Surface generation and material removal mechanism incorporated with the randomness of grain size and distribution in grinding

Grinding process can achieve minimal material removal quantity and multiple material removal mechanisms simultaneously, which makes it extremely popular in industrial applications to meet the requirements of high dimension precision, excellent surface quality and rigorous tolerance. However, due to the randomly-sized and randomly-distributed abrasive grains, an accurate ground surface prediction model remains a significant challenge by considering the actual microstructure of grinding wheel. This research aims to develop a novel surface prediction model to take into account the random nature of the grain size and its distribution in grinding wheel. The generation of ground surface is modeled by calculating the transient trajectory of grain in the whole contact zone. Micro grain-workpiece contact mechanism is revealed in terms of the typical stages of rubbing, plowing and cutting to determine the ground surface morphology. Grinding experiments were performed to compare with the predicted surface morphologies. The proposed model was further validated in the terms of surface topography, roughness and material removal rate. Additionally, material removal mechanism associated with surface generation has been explored by the predicted ground surface and material removal rate under different grain-workpiece interaction states. The provided model is further employed to examine the impact of the randomness of grain size and distribution and grinding parameters on the surface roughness. Thus, the research provides fresh insights into understanding the underlying mechanism in different grain stages as well as revealing the transient contact mechanisms in generating ground surface integrity.

Comprehensive Comparison of MOCVD- and LPCVD-SiNx Surface Passivation for AlGaN/GaN HEMTs for 5G RF Applications.

Passivation is commonly used to suppress current collapse in AlGaN/GaN HEMTs. However, the conventional PECV-fabricated SiNx passivation layer is incompatible with the latest process, like the "passivation-prior-to-ohmic" method. Research attention has therefore turned to high-temperature passivation schemes. In this paper, we systematically investigated the differences between the SiNx/GaN interface of two high-temperature passivation schemes, MOCVD-SiNx and LPCVD-SiNx, and investigated their effects on the ohmic contact mechanism. By characterizing the device interface using TEM, we reveal that during the process of MOCVD-SiNx, etching damage and Si diffuses into the semiconductor to form a leakage path and reduce the breakdown voltage of the AlGaN/GaN HEMTs. Moreover, N enrichment at the edge of the ohmic region of the LPCVD-SiNx device indicates that the device is more favorable for TiN formation, thus reducing the ohmic contact resistance, which is beneficial to improving the PAE of the device. Through the CW load-pull test with drain voltage VDS = 20V, LPCVD-SiNx devices obtain a high PAE of 66.35%, which is about 6% higher than MOCVD-SiNx devices. This excellent result indicates that the prospect of LPCVD-SiNx passivation devices used in 5G small terminals will be attractive.

Finite element analysis of artificial ankle elastic improved inserts

To discuss the influence of artificial ankle elastic improved inserts (hereinafter referred to as "improved inserts") in reducing prosthesis micromotion and improving joint surface contact mechanics by finite element analysis. Based on the original insert of INBONE Ⅱ implant system (model A), four kinds of improved inserts were constructed by adding arc or platform type flexible layer with thickness of 1.3 or 2.6 mm, respectively. They were Flying goose type_1.3 elastic improved insert (model B), Flying goose type_2.6 elastic improved insert (model C), Platform type_1.3 elastic improved insert (model D), Platform type_2.6 elastic improved insert (model E). Then, the CT data of right ankle at neutral position of a healthy adult male volunteer was collected, and finite element models of total ankle replacement (TAR) was constructed based on model A-E prostheses by software of Mimics 19.0, Geomagic wrap 2017, Creo 6.0, Hypermesh 14.0, and Abaqus 6.14. Finally, the differences of bone-metal prosthesis interface micromotion and articular surface contact behavior between different models were investigated under ISO gait load. The tibia/talus-metal prosthesis interfaces micromotion of the five TAR models gradually increased during the support phase, then gradually fell back after entering the swing phase. The improved models (models B-E) showed lower bone-metal prosthesis interface micromotion when compared with the original model (model A), but there was no significant difference among models A-E ( P>0.05). The maximum micromotion of tibia appeared at the dome of the tibial bone groove, and the ​​micromotion area was the largest in model A and the smallest in model E. The maximum micromotion of talus appeared at the posterior surface of the central bone groove, and there was no difference in the micromotion area among models A-E. The contact area of the articular surface of the insert/talus prosthesis in each group increased in the support phase and decreased in the swing phase during the gait cycle. Compared with model A, the articular surface contact area of models B-E increased, but there was no significant difference among models A-E ( P>0.05). The change trend of the maximum stress on the articular surface of the inserts/talus prosthesis was similar to that of the contact area. Only the maximum contact stress of the insert joint surface of models D and E was lower than that of model A, while the maximum contact stress of the talar prosthesis joint surface of models B-E was lower than that of model A, but there was no significant difference among models A-E ( P>0.05). The high stress area of the lateral articular surface of the improved inserts significantly reduced, and the articular surface stress distribution of the talus prosthesis was more uniform. Adding a flexible layer in the insert can improve the elasticity of the overall component, which is beneficial to absorb the impact force of the artificial ankle joint, thereby reducing interface micromotion and improving contact behavior. The mechanical properties of the inserts designed with the platform type and thicker flexible layer are better.

Mathematical Modeling of Collisional Heat Generation and Convective Heat Transfer Problem for Single Spherical Body in Oscillating Boundaries

The application of high-energy ball milling in the field of advanced materials processing, such as mechanochemical alloying and ammonia synthesis, has been gaining increasing attention beyond its traditional use in material crushing. It is important to recognize the role of thermodynamics in high-energy processes, including heat generation from collisions, as well as ongoing investigations into grinding ball behavior. This study aims to develop a mathematical model for the numerical analysis of a spherical ball in a shaker mill, taking into account its dynamics, contact mechanics, thermodynamics, and heat transfer. The complexity of the problem for mathematical modeling is reduced by limiting the motion to one-dimensional translation and representing the vibration of the vial wall in a shaker mill as rigid boundaries that move in a linear fashion. A nonlinear viscoelastic contact model is employed to construct a heat generation model. An equation of internal energy evolution is derived that incorporates a velocity-dependent heat convection model. In coupled field modeling, equations of motion for high-energy impact phenomena are derived from energy-based Hamiltonian mechanics rather than vector-based Newtonian mechanics. The numerical integration of the governing equations is performed at the system level to analyze the general heating characteristics during collisions and the effect of various operational parameters, such as the oscillation frequency and amplitude of the vial. The results of the numerical analysis provide essential performance metrics, including steady-state temperature and time constant for the characteristics of temperature evolution for a high-energy shaker milling process with a computation accuracy of 0.1%. The novelty of this modeling study is that it is the first to obtain such a high accuracy numerical solution for the temperature evolution associated with a shaker mill process.

Fewer polymer chains but higher adhesion: How gradient-stiffness hydrogel layers mediate adhesion through network stretch.

The presence of gradient softer outer layers, commonly observed in biological systems (such as cartilage and ocular tissues), as well as synthetic crosslinked hydrogels, profoundly influences their interactions with opposing surfaces. Our prior research demonstrated that gradient-stiffness hydrogel layers, characterized by increasing elasticity with depth, control contact mechanics, particularly in proximity to the layer thickness. We postulate that the distribution of polymers within these gradient layers imparts extraordinary stretch and adhesion characteristics due to network adaptability and stress-induced reorganization. To investigate this phenomenon, we utilized Atomic Force Microscopy nanoindentation to assess the depth-dependent adhesion behavior of polyacrylamide hydrogels with varying gradient layer thicknesses. Two gradient layer thicknesses were achieved by employing different molding materials: glass and polyoxymethylene (POM). Glass-molded hydrogels exhibited a thinner gradient layer alongside a stiffer bulk layer compared to their POM-molded counterparts. In indentation experiments, the POM-molded hydrogel had larger adhesion compared to glass-molded hydrogel. We find that indenting within the gradient layer engenders increased load-unload hysteresis due to heightened fluid transport in the sparse outer polymer network. Consequently, this led to augmented adhesion and work of separation at shallow depths. We suggest that the prominent stretching capability of the sparse outer polymer network during probe retraction contributes to enhanced adhesion. The Maugis-Dugdale adhesive model only fits well to indentations on the thin layer or indentations which engage significantly with the bulk. These results facilitate a comprehensive characterization of adhesion mechanics in gradient-stiffness hydrogels, which could foster their application across emerging contexts in health science and environmental domains.

Deformation of soft substrates during adhesive peel testing

AbstractPeeling of pressure‐sensitive adhesives from low modulus substrates such as human skin induces a significant out‐of‐plane deformation at the crack tip. In the context of medical adhesives, this deformation is related to the pain and injury caused to the skin and underlying tissue during removal. Here, a method is presented to measure the out‐of‐plane deformation of elastic substrates as a medical adhesive tape is removed from the surface, a necessary first step in the eventual quantification of pain. Elastic human skin analogs comprised of a simple bilayer with varied moduli across several orders of magnitude are fabricated. Next, a nonporous medical adhesive tape is peeled from these substrates and the deformation is quantified. A model derived from contact mechanics for a rectangular pressure is fit to the experimental data. By correcting for confinement effects and deformation within the adhesive, good agreement is found between the newly reported model in this study and the experimentally observed deformation.

Correspondence between Electrostatics and Contact Mechanics with Further Results in Equilibrium Charge Distributions

AbstractIt is common in mesoscopic systems to find instances where several charges interact among themselves. These particles are usually confined by an external potential that shapes the symmetry of the equilibrium charge configuration. In the case of classical charges moving on a plane and repelling each other via the Coulomb potential, they possess a ground state à la Thomson or Wigner crystal. As the number of particles N increases, the number of local minima grows exponentially and direct or heuristic optimization methods become prohibitively costly. Therefore the only feasible approximation to the problem is to treat the system in the continuum limit. Since the underlying framework is provided by potential theory, we shall by‐pass the corresponding mathematical formalism and list the most common cases found in the literature. Then we prove a (albeit known) mathematical correspondence that will enable us to re‐discover analytical results in electrostatics. In doing so, we shall provide different methods for finding the equilibrium surface density of charges, analytical and numerical. Additionally, new systems of confined charges in three‐dimensional surfaces will be under scrutiny. Finally, we shall highlight exact results regarding a modified power‐law Coulomb potential in the d‐dimensional ball, thus generalizing the existing literature.

Wave Velocities and Poisson Ratio in a Loose Sandy Martian Regolith Simulant Under Low Stresses: 2. Theoretical Analysis

AbstractThis paper presents a theoretical analysis of the data on wave velocity measurements at small stresses presented in a companion paper describing the experimental results on a Martian regolith loose sandy simulant (Fontainebleau sand) of the soil at the InSight landing site on Mars (Elysium Planitia). Experimental data of wave velocities and Poisson's ratio are interpreted in the light of a granular contact mechanics theory and completed accounting for rugosity effects that are suspected to have stronger effects in sands under low stresses. The asperities of a grain of Fontainebleau sand were investigated through Atomic Force Microscopy, but larger asperities had to be adopted so as to better fit the model prediction with experimental data. A good agreement between the experimental data and the model predictions is obtained for stress above 10 kPa. Below 5 kPa, an area in which asperities are suspected to have a stronger influence, the model is not fully satisfactory, showing that further experimental and theoretical investigation is necessary in a stress zone particularly relevant to surface soils in planets, with probably enhanced effects of asperities on the intergrain contact mechanics.

Wave Velocities and Poisson Ratio in a Loose Sandy Martian Regolith Simulant Under Low Stresses: 1. Laboratory Investigation

AbstractWave velocity measurements were performed on Fontainebleau sand samples used as a Martian regolith simulant to investigate the elastic properties of the surface material at the InSight landing site on Mars (Elysium Planitia). Loose samples (density 1.4 Mg/m3, density index 6%) were prepared by using the pluviation method to mimic the low regolith density at the InSight landing site. A novel device derived from triaxial testing was designed to measure wave velocities at low stresses along a horizontal cylindrical specimen. Four tests were made, in which the confining stress was applied by applying a vacuum between 1 and 80 kPa. Wave velocities were measured by using bender elements under stresses as low as 1.75 kPa, a very low value compared to the standard stress ranges generally considered in terrestrial geotechnics (&gt;10 kPa). The changes in compression and shear wave velocities obey a standard power law, with two slightly different exponents for Vp and Vs, indicating a not perfectly elastic behavior. Data showed greater variability below 5 kPa, indicating some limitations of the bender element technique in this range. A slight decrease in Poisson ratio was detected below 5 kPa, which certainly deserves more investigation. This investigation is useful to better analyze the data of the InSight mission, both in terms of wave propagation at the surface and to interpret some in situ elastic tests carried out with the scoop. These data are interpreted in the light of a granular contact mechanics theory in a companion paper.