One Hundred Years of Hertz Contact

Recent Advancements in Understanding of Growth and Properties of Antiwear Tribofilms Derived from Zinc Dialkyl Dithiophosphate Additives under Nanoscale Sliding Contacts

Zinc dialkyl dithiophosphate (ZDDP) is a key antiwear additive in lubricants that forms robust phosphate glass-based tribofilms to mitigate wear on rubbing surfaces. The quest to unravel the enigma of these antiwear film formations on sliding surfaces has persisted as an enduring mystery, despite nearly a century of fervent research. This paper presents a comprehensive review of nanotribological investigations, centering on the tribochemical decomposition of ZDDP antiwear additives. The core of the Review explores investigations conducted through the in situ AFM-based technique, which has been used to unveil the underlying stress-assisted thermal activation (SATA) mechanism behind the formation of antiwear tribofilms on diverse surfaces. A thorough analysis is presented, encompassing governing factors, such as compression, shear, and temperature, that wield influence over the intricate process of tribofilm formation. This is substantiated by a spectrum of structural and chemical characterization-based inferences. Furthermore, atomic-scale computer simulation studies are discussed that provide profound insights into tribochemical reaction mechanisms and elucidate the details of chemical processes at atomic level.

Organization of collagen fibers and tissue hardening: Markers of fibrotic scarring after spinal cord injury in mice revealed by multiphoton-atomic force microscopy imaging

Spinal cord injury is a dramatic disease leading to severe motor, sensitive and autonomic impairments. After injury the axonal regeneration is partly inhibited by the glial scar, acting as a physical and chemical barrier. The scarring process involves microglia, astrocytes and extracellular matrix components, such as collagen, constructing the fibrotic component of the scar. To investigate the role of collagen, we used a multimodal label-free imaging approach combining multiphoton and atomic force microscopy. The second harmonic generation signal exhibited by fibrillar collagen enabled to specifically monitor it as a biomarker of the lesion. An increase in collagen density and the formation of more tortuous fibers over time after injury are observed. Nano-mechanical investigations revealed a noticeable hardening of the injured area, correlated with collagen fibers' formation. These observations indicate the concomitance of important structural and mechanical modifications during the fibrotic scar evolution.

Optimizing the accuracy of viscoelastic characterization with AFM force-distance experiments in the time and frequency domains

Atomic Force Microscopy (AFM) force-distance (FD) experiments have emerged as an attractive alternative to traditional micro-rheology measurement techniques owing to their versatility of use in materials of a wide range of mechanical properties. Here, we show that the range of time dependent behaviour which can reliably be resolved from the typical method of FD inversion (fitting constitutive FD relations to FD data) is inherently restricted by the experimental parameters: sampling frequency, experiment length, and strain rate. Specifically, we demonstrate that violating these restrictions can result in errors in the values of the parameters of the complex modulus. In the case of complex materials, such as cells, whose behaviour is not specifically understood a priori, the physical sensibility of these parameters cannot be assessed and may lead to falsely attributing a physical phenomenon to an artifact of the violation of these restrictions. We use arguments from information theory to understand the nature of these inconsistencies as well as devise limits on the range of mechanical parameters which can be reliably obtained from FD experiments. The results further demonstrate that the nature of these restrictions depends on the domain (time or frequency) used in the inversion process, with the time domain being far more restrictive than the frequency domain. Finally, we demonstrate how to use these restrictions to better design FD experiments to target specific timescales of a material's behaviour through our analysis of a polydimethylsiloxane (PDMS) polymer sample.

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.

Definition of Atomic-Scale Contact: What Dominates the Atomic-Scale Friction Behaviors?

The definition of atomic-scale contact is a very ambiguous issue owing to the discrete atomic arrangement, which hinders the development of contact theory and nano-tribological techniques. In this work, we studied the atomic-scale contact area and their correlations with friction force based on three distinct contact definitions (interatomic distance, force, and interfacial chemical bonds) by performing large-scale atomistic simulations on a typical ball-on-disk contact model. In the simulations, the measured contact areas defined by interatomic distance, force, and interfacial chemical bonds (referred as to A_dist, A_force, and A_bond, respectively) are not equivalent at all, while we interestingly clarify that only A_dist is consistent with the one calculated by continuum Hertz contact mechanics, and moreover, only A_bond is proportional to the friction force indicating that A_bond is the dominant one for determining materials' frictional behaviors. The above fundamental insights into the atomic-scale contact problems are useful to deeply understand the origins of tribological phenomena and contribute to the further prediction of atomic-scale friction.

Review of Tribological Failure Analysis and Lubrication Technology Research of Wind Power Bearings

Wind power, being a recyclable and renewable resource, makes for a sizable portion of the new energy generation sector. Nonetheless, the wind energy industry is experiencing early failure of important components of wind turbines, with the majority of these issues also involving wind power bearings. Bearing dependability is directly tied to the transmission efficiency and work performance of wind turbines as one of its major components. The majority of wind turbine failures are due to bearings, and the vast majority of bearing failures are due to lubrication. The topic of improving the accuracy and life of wind power bearing motion is becoming increasingly essential as the wind power industry develops rapidly. This study examines the various constructions and types of wind turbines, as well as their bearings. We also examined the most typical causes of friction and lubrication failure. Furthermore, contemporary research on wind turbine bearings has been compiled, which mostly comprises the study and development of lubrication technology and other areas. Finally, a conclusion and outlook on current challenges, as well as future research directions, are offered.

Non-Newtonian Thermo-Elastohydrodynamics and Sub-Surface Stress Field of High-Performance Racing Spur Gears

Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair engagement through to maximum normal loading, followed by contact separation. Sliding motion only ceases instantaneously at the pitch point. The regime of lubrication remains mostly in non-Newtonian thermo-elastohydrodynamic conditions. The results show that a starved inlet boundary is attained throughout most of the meshing cycle which leads to the diminution of the pressure spike at the exit from the contact conjunction. The reversing sub-surface shear stresses are the main source of the onset of any inelastic deformation, which is dominated by the primary pressure peak in compliance with the Hertzian maximum pressure. The shear stress field is supplemented by an induced field due to the presence of the pressure spike. Under starved conditions this secondary stress field is diminished. The combined solution of elastohydrodynamics with a thermal network model, non-Newtonian lubricant traction, and sub-surface stress evaluation provides for a comprehensive solution not hitherto reported in the literature.

Dynamic Model of a Conjugate-Surface Flexure Hinge Considering Impacts between Cylinders

A dynamic model of a Conjugate-Surface Flexure Hinge (CSFH) has been proposed as a component for MEMS/NEMS Technology-based devices with lumped compliance. However, impacts between the conjugate surfaces have not been studied yet and, therefore, this paper attempts to fill this gap by proposing a detailed multibody system (MBS) model that includes not only rigid-body dynamics but also elastic forces, friction, and impacts. Two models based on the Lankarani-Nikravesh constitutive law are first recalled and a new model based on the contact of cylinders is proposed. All three models are complemented by the friction model proposed by Ambrosìo. Then, the non-smooth Moreau time-stepping scheme with Coulomb friction is described. The four models are compared in different scenarios and the results confirm that the proposed model outcomes comply with the most reliable models.

Experimental and Numerical Analysis on the Impact Wear Behavior of TP316H Steel

In this work, the contact force model and experiment methods were used to study the dynamic response and impact wear behavior of TP316H steel. The Flore model and the classic Hertz model were selected for comparison with the experimental results, and the model was revised according to the section parameters of the TP316H tube. The results show that there is a large difference between the models without considering the effect of structural stiffness on the impact system and the test results, whereas the revised model has a good agreement. With the rise in impact mass, the coefficient of restitution increases from 0.65 to 0.78, whereas the energy dissipation and wear volume decrease. Spalling, delamination, plastic deformation, and oxidative wear are the main impact wear mechanism of TP316H steel.

Comparison of direct and inverse methods for 2.5D traction force microscopy

Essential cellular processes such as cell adhesion, migration and division strongly depend on mechanical forces. The standard method to measure cell forces is traction force microscopy (TFM) on soft elastic substrates with embedded marker beads. While in 2D TFM one only reconstructs tangential forces, in 2.5D TFM one also considers normal forces. Here we present a systematic comparison between two fundamentally different approaches to 2.5D TFM, which in particular require different methods to deal with noise in the displacement data. In the direct method, one calculates strain and stress tensors directly from the displacement data, which in principle requires a divergence correction. In the inverse method, one minimizes the difference between estimated and measured displacements, which requires some kind of regularization. By calculating the required Green's functions in Fourier space from Boussinesq-Cerruti potential functions, we first derive a new variant of 2.5D Fourier Transform Traction Cytometry (FTTC). To simulate realistic traction patterns, we make use of an analytical solution for Hertz-like adhesion patches. We find that FTTC works best if only tangential forces are reconstructed, that 2.5D FTTC is more precise for small noise, but that the performance of the direct method approaches the one of 2.5D FTTC for larger noise, before both fail for very large noise. Moreover we find that a divergence correction is not really needed for the direct method and that it profits more from increased resolution than the inverse method.

Effect of the density of pillar-patterned substrates on contact mechanics: Transition from top to mixed contact with a detailed pressure-field description

Different contact regimes between a spherical lens and a periodically patterned substrate are observed, when they are pressed against each other. Top contact occurs when only the highest substrate sections touch the lens, whereas mixed contact implies that both the highest and the lowest substrate sections come into contact with the lens. In this paper, we study how the pattern density of the substrate, along with its physical properties and those of the lens, determine the transition from top contact to mixed contact. Experiments and numerical simulations had been performed, as complementary approaches to obtain data, and a theoretical analysis has been developed to gain insight on the effect of the physical parameters on the contact transition. As a result, a phase diagram is presented, in terms of the load and the contact radius, that combines the observations of the three approaches (experimental, numerical, and theoretical), unveiling the boundaries of three contact regimes: (1) deterministic-driven contact, (2) top contact, and (3) mixed contact.

Fundamentals and Advances in Elastohydrodynamics: The Role of Ramsey Gohar

This paper commemorates Ramsey Gohar by acknowledging his contributions to the fields of contact mechanics and elastohydrodynamic lubrication (EHL) within the context of the developments of these subjects. A historical discourse is provided on elastohydrodynamics, from its inception in the 1940s to present. We demonstrate that Ramsey Gohar was not only a pioneer in the discoveries and fundamentals of the subject, but also led or contributed significantly to continual advances in the understanding of EHL and its diverse applications.

Non-Empirical Law for Nanoscale Atom-by-Atom Wear

Wear of contact materials results in energy loss and device failure. Conventionally, wear is described by empirical laws such as the Archard's law; however, the fundamental physical and chemical origins of the empirical law have long been elusive, and moreover empirical wear laws do not always hold for nanoscale contact, collaboratively hindering the development of high-durable tribosystems. Here, a non-empirical and robustly applicable wear law for nanoscale contact situations is proposed. The proposed wear law successfully unveils why the nanoscale wear behaviors do not obey the description by Archard's law in all cases although still obey it in certain experiments. The robustness and applicability of the proposed wear law is validated by atomistic simulations. This work affords a way to calculate wear at nanoscale contact robustly and theoretically, and will contribute to developing design principles for wear reduction.

Cartilage-like tribological performance of charged double network hydrogels

A synthetic hydrogel material may offer utility as a cartilage replacement if it is able to maintain low friction in different sliding environments and achieve bulk mechanical properties to withstand the severe environment of the joint. In this work, we compared the tribological behavior of four double network (DN) hydrogels to that of fresh porcine cartilage in both water and fetal bovine serum (FBS). The DN hydrogels were comprised of a negatively charged 1st network and a 2nd network wherein comonomers of varying charge (i.e. neutral, positive, negative, and zwitterionic) were introduced at 10 wt% to an otherwise neutral network. A steel ball probe was used to perform microindentation tests to determine the surface elastic modulus of the samples and estimate their contact areas during sliding. Friction tests using a stationary probe with a stage that reciprocated at a range of speeds were performed to develop lubrication curves in both water and FBS. We found that the DN hydrogels with a neutral or zwitterionic 2nd network had the lowest friction and shear stresses, notably below that of cartilage. The differences in charge and structure of the samples were more evident in water than in FBS, as the lubrication responses for all the hydrogels spanned a wider range of values. In FBS, the lubrication responses were pushed towards elasto-hydrodynamics with nearly all friction coefficient values falling below 0.3. This indicates that the FBS interacts with the hydrogels and cartilage samples in a similar manner as that of cartilage by maintaining a robust layer of solution at the interface during sliding. These DN hydrogels prove to fulfill, and in some cases surpass, the lubrication demands for cartilage replacement in load bearing joints.

Two cosine wave elastic-plastic contact model

Based on Hertz elastic contact theory, the contact mechanics model of two cosine wave is established. The mechanical characteristics of the model in the elastic, elastic-plastic, and plastic stages were studied. The influence of load on contact deformation and other characteristics is considered. The finite element method is used to analyze the deformation process of the model, and the results are compared with those of the mechanical model. The effects of amplitude and wavelength of cosine wave on its mechanical characteristics are discussed. The results show that the model reflects the relationship between the load and the mechanical characteristics of the model, and the difference of amplitude and wavelength will affect this characteristic.

Analytical Elastostatic Contact Mechanics of Highly-Loaded Contacts of Varying Conformity

In applications requiring high load carrying capacity, conforming contacting pairs with a relatively large contact footprint are used. These include circular arc, Novikov, and Wildhaber gears found, for example, in helicopter rotors. Closely conforming contacts also occur in many natural endo-articular joints, such as hips, or their replacement arthroplasty. The main determining factors in contact fatigue are the sub-surface shear stresses. For highly loaded contacts, classical Hertzian contact mechanics is used for many gears, bearings, and joints. However, the theory is essentially for concentrated counterforming contacts, where the problem is reduced to a rigid ellipsoidal solid penetrating an equivalent semi-infinite elastic half-space. Applicability is limited though, and the theory is often used inappropriately for contacts of varying degrees of conformity. This paper presents a generic contact mechanics approach for the determination of sub-surface stresses, which is applicable to both highly conforming as well as concentrated counterforming contacts. It is shown that sub-surface shear stresses alter in magnitude and disposition according to contact conformity, and lead to the different modes of fatigue failure noted in practice.

Towards Mimicking the Fetal Liver Niche: The Influence of Elasticity and Oxygen Tension on Hematopoietic Stem/Progenitor Cells Cultured in 3D Fibrin Hydrogels

Hematopoietic stem/progenitor cells (HSPCs) are responsible for the generation of blood cells throughout life. It is believed that, in addition to soluble cytokines and niche cells, biophysical cues like elasticity and oxygen tension are responsible for the orchestration of stem cell fate. Although several studies have examined the effects of bone marrow (BM) niche elasticity on HSPC behavior, no study has yet investigated the effects of the elasticity of other niche sites like the fetal liver (FL), where HSPCs expand more extensively. In this study, we evaluated the effect of matrix stiffness values similar to those of the FL on BM-derived HSPC expansion. We first characterized the elastic modulus of murine FL tissue at embryonic day E14.5. Fibrin hydrogels with similar stiffness values as the FL (soft hydrogels) were compared with stiffer fibrin hydrogels (hard hydrogels) and with suspension culture. We evaluated the expansion of total nucleated cells (TNCs), Lin⁻/cKit⁺ cells, HSPCs (Lin⁻/Sca⁺/cKit⁺ (LSK) cells), and hematopoietic stem cells (HSCs: LSK- Signaling Lymphocyte Activated Molecule (LSK-SLAM) cells) when cultured in 5% O₂ (hypoxia) or in normoxia. After 10 days, there was a significant expansion of TNCs and LSK cells in all culture conditions at both levels of oxygen tension. LSK cells expanded more in suspension culture than in both fibrin hydrogels, whereas TNCs expanded more in suspension culture and in soft hydrogels than in hard hydrogels, particularly in normoxia. The number of LSK-SLAM cells was maintained in suspension culture and in the soft hydrogels but not in the hard hydrogels. Our results indicate that both suspension culture and fibrin hydrogels allow for the expansion of HSPCs and more differentiated progeny whereas stiff environments may compromise LSK-SLAM cell expansion. This suggests that further research using softer hydrogels with stiffness values closer to the FL niche is warranted.

High-Precision Cutting Edge Radius Measurement of Single Point Diamond Tools Using an Atomic Force Microscope and a Reverse Cutting Edge Artifact

This paper presents a measurement method for high-precision cutting edge radius of single point diamond tools using an atomic force microscope (AFM) and a reverse cutting edge artifact based on the edge reversal method. Reverse cutting edge artifact is fabricated by indenting a diamond tool into a soft metal workpiece with the bisector of the included angle between the tool’s rake face and clearance face perpendicular to the workpiece surface on a newly designed nanoindentation system. An AFM is applied to measure the topographies of the actual and the reverse diamond tool cutting edges. With the proposed edge reversal method, a cutting edge radius can be accurately evaluated based on two AFM topographies, from which the convolution effect of the AFM tip can be reduced. The accuracy of the measurement of cutting edge radius is significantly influenced by the geometric accuracy of reverse cutting edge artifact in the proposed measurement method. In the nanoindentation system, the system operation is optimized for achieving high-precision control of the indentation depth of reverse cutting edFigurege artifact. The influence of elastic recovery and the AFM cantilever tip radius on the accuracy of cutting edge radius measurement are investigated. Diamond tools with different nose radii are also measured. The reliability and capability of the proposed measurement method for cutting edge radius and the designed nanoindentation system are demonstrated through a series of experiments.

Tribology and Dowson

It is with great sadness that we note the passing of Professor Duncan Dowson on 6th January 2020. Duncan was an esteemed member of the Editorial Board of this journal. He will be remembered as one of the founding fathers of tribology and as a true gentleman. He was the last living member of the Jost Committee, set up by the UK Government (1964–1966) to investigate the state of lubrication education and research, and to establish the requirements of industry in this regard [1]. This committee coined the term “tribology”.Duncan contributed to many areas of tribological research and established many of them, including elastohydrodynamic theory and biotribology.[...]

Low Temperature Nanoindentation: Development and Applications

Nanoindentation technique at low temperatures have developed from initial micro-hardness driving method at a single temperature to modern depth-sensing indentation (DSI) method with variable temperatures over the last three decades. The technique and implementation of representative cooling systems adopted on the indentation apparatuses are discussed in detail here, with particular emphasis on pros and cons of combination with indentation technique. To obtain accurate nanoindentation curves and calculated results of material properties, several influence factors have been carefully considered and eliminated, including thermal drift and temperature induced influence on indenter and specimen. Finally, we further show some applications on typical materials and discuss the perspectives related to low temperature nanoindentation technique.

Piezoelectric Actuators for Tactile and Elasticity Sensing

Piezoelectric actuators have achieved remarkable progress in many fields, being able to generate forces or displacements to perform scanning, tuning, manipulating, tactile sensing or delivering functions. In this work, two piezoelectric PZT (lead zirconate titanate) bimorph actuators, with different tip contact materials, were applied as tactile sensors to estimate the modulus of elasticity, or Young’s modulus, of low-stiffness materials. The actuators were chosen to work in resonance, taking advantage of a relatively low resonant frequency of the out-of-plane vibrational modes, associated with a convenient compliance, proven by optical and electrical characterization. Optical measurements performed with a scanning laser vibrometer confirmed that the displacement per applied voltage was around 437 nm/V for the resonator with the lower mass tip. In order to determine the modulus of elasticity of the sensed materials, the stiffness coefficient of the resonator was first calibrated against a force sensor, obtaining a value of 1565 ± 138 N/m. The actuators were mounted in a positioning stage to allow approximation and contact of the sensor tip with a set of target materials. Electrical measurements were performed using the resonator as part of an oscillator circuit, and the modulus of elasticity of the sample was derived from the contact resonant frequency curve of the cantilever–sample system. The resulting sensor is an effective, low-cost and non-destructive solution compared to atomic force microscopy (AFM) techniques. Materials with different modulus of elasticity were tested and the results compared to values reported in the literature.

Transitions between nanomechanical and continuum mechanical contacts: new insights from liquid structure

The use of continuum mechanics to describe contacts involving nanoscale and atomic interactions has been one of the key controversies in nanoscience, tribology, and petrophysical and geological studies. By applying a novel nonequilibrium molecular dynamics scheme to wet quartz contacts, this study revealed the key transitions between continuum electrostatic, nanomechanical and Hertzian contact behaviors at around one nm of surface separation, which results in critical contact pressure fluctuations between -30 and 100 MPa. Using a novel liquid-structure analysis scheme based on the spatial distribution of water molecules, the nanomechanical behavior was found to originate from the collapse and localization of layers of water molecules. Moreover, the role of surface curvature on this effect was also quantified and explained based on a new topological descriptor. The findings of this study enrich our understanding of wet contacts and have a wide range of applications from the nanoscale to macroscale.

The soft mechanical signature of glial scars in the central nervous system

Injury to the central nervous system (CNS) alters the molecular and cellular composition of neural tissue and leads to glial scarring, which inhibits the regrowth of damaged axons. Mammalian glial scars supposedly form a chemical and mechanical barrier to neuronal regeneration. While tremendous effort has been devoted to identifying molecular characteristics of the scar, very little is known about its mechanical properties. Here we characterize spatiotemporal changes of the elastic stiffness of the injured rat neocortex and spinal cord at 1.5 and three weeks post-injury using atomic force microscopy. In contrast to scars in other mammalian tissues, CNS tissue significantly softens after injury. Expression levels of glial intermediate filaments (GFAP, vimentin) and extracellular matrix components (laminin, collagen IV) correlate with tissue softening. As tissue stiffness is a regulator of neuronal growth, our results may help to understand why mammalian neurons do not regenerate after injury.

Determination of the mechanical properties of solid and cellular polymeric dosage forms by diametral compression

At present, the immediate-release solid dosage forms, such as the oral tablets and capsules, are granular solids. They release drug rapidly and have adequate mechanical properties, but their manufacture is fraught with difficulties inherent in processing particulate matter. Such difficulties, however, could be overcome by liquid-based processing. Therefore, we have recently introduced polymeric cellular (i.e., highly porous) dosage forms prepared from a melt process. Experiments have shown that upon immersion in a dissolution medium, the cellular dosage forms with polyethylene glycol (PEG) as excipient and with predominantly open-cell topology disintegrate by exfoliation, thus enabling rapid drug release. If the volume fraction of voids of the open-cell structures is too large, however, their mechanical strength is adversely affected. At present, the common method for determining the tensile strength of brittle, solid dosage forms (such as select granular forms) is the diametral compression test. In this study, the theory of diametral compression is first refined to demonstrate that the relevant mechanical properties of ductile and cellular solids (i.e., the elastic modulus and the yield strength) can also be extracted from this test. Diametral compression experiments are then conducted on PEG-based solid and cellular dosage forms. It is found that the elastic modulus and yield strength of the open-cell structures are about an order of magnitude smaller than those of the non-porous solids, but still are substantially greater than the stiffness and strength requirements for handling the dosage forms manually. This work thus demonstrates that melt-processed polymeric cellular dosage forms that release drug rapidly can be designed and manufactured to have adequate mechanical properties.

Dynamic Characteristics of Constrained Manipulators for Contact Force Control Design

The authors present the results of eigenstructure analyses of the dy namics of several manipulator and environment configurations and discuss the implications for successful force controller design. The manipulator configurations considered include single rigid link, sin gle flexible link, two rigid links, and two flexible links. In all cases, the tip of the manipulator is in contact with a deformable environ ment. Particular emphasis is placed on the interaction between the structural stiffness of the manipulator link and the stiffnesses of the contacting regions of the manipulator tip and the environ ment. It is shown that, for given link parameters, this interaction results in distinct changes in the modal structure of the manipula tor/environment system as the effective contact stiffness increases. In particular, the contact force response is dominated by a single mode for a given effective contact stiffness, whereas the control inputs excite all modes except those associated with the contact region vibration. The changes in the modal structure of the manip ulator/environment system predicted by the eigenstructure analysis are verified by experiment for the single flexible link configuration.

Robot-Guided Atomic Force Microscopy for Mechano-Visual Phenotyping of Cancer Specimens

Atomic force microscopy (AFM) and other forms of scanning probe microscopy have been successfully used to assess biomechanical and bioelectrical characteristics of individual cells. When extending such approaches to heterogeneous tissue, there exists the added challenge of traversing the tissue while directing the probe to the exact location of the targeted biological components under study. Such maneuvers are extremely challenging owing to the relatively small field of view, limited availability of reliable visual cues, and lack of context. In this study we designed a system that leverages the visual topology of the serial tissue sections of interest to help guide robotic control of the AFM stage to provide the requisite navigational support. The process begins by mapping the whole-slide image of a stained specimen with a well-matched, consecutive section of unstained section of tissue in a piecewise fashion. The morphological characteristics and localization of any biomarkers in the stained section can be used to position the AFM probe in the unstained tissue at regions of interest where the AFM measurements are acquired. This general approach can be utilized in various forms of microscopy for navigation assistance in tissue specimens.

Determination of mechanical properties of spatially heterogeneous breast tissue specimens using contact mode atomic force microscopy (AFM)

This paper outlines a comprehensive parametric approach for quantifying mechanical properties of spatially heterogeneous thin biological specimens such as human breast tissue using contact-mode Atomic Force Microscopy. Using inverse finite element (FE) analysis of spherical nanoindentation, the force response from hyperelastic material models is compared with the predicted force response from existing analytical contact models, and a sensitivity study is carried out to assess uniqueness of the inverse FE solution. Furthermore, an automation strategy is proposed to analyze AFM force curves with varying levels of material nonlinearity with minimal user intervention. Implementation of our approach on an elastic map acquired from raster AFM indentation of breast tissue specimens indicates that a judicious combination of analytical and numerical techniques allow more accurate interpretation of AFM indentation data compared to relying on purely analytical contact models, while keeping the computational cost associated an inverse FE solution with reasonable limits. The results reported in this study have several implications in performing unsupervised data analysis on AFM indentation measurements on a wide variety of heterogeneous biomaterials.

Probabilistic estimation of mechanical properties of biomaterials using atomic force microscopy

Nanoindentation using contact-mode atomic force microscopy (AFM) has emerged as a powerful tool for effective material characterization of a wide variety of biomaterials across multiple length scales. However, the interpretation of force-indentation experimental data from AFM is subject to some debate. Uncertainties in AFM data analysis stems from two primary sources: The exact point of contact between the AFM probe and the biological specimen and the variability in the spring constant of the AFM probe. While a lot of attention has been directed toward addressing the contact-point uncertainty, the effect of variability in the probe spring constant has not received sufficient attention. In this paper, we report on an error-in-variables-based Bayesian change-point approach to quantify the elastic modulus of human breast tissue samples after accounting for variability in both contact point and the probe spring constant. We also discuss the efficacy of our approach to a wide range of hyperparameter values using a sensitivity analysis.

Experimental study of oblique impact between dry spheres and liquid layers

Liquid addition is common in industrial fluidization-based processes. A detailed understanding of collision mechanics of particles with liquid layers is helpful to optimize these processes. The normal impact with liquid has been studied extensively; however, the studies on oblique impact with liquid are scarce. In this work, experiments are conducted to trace Al_{2}O_{3} spheres obliquely impacting on a surface covered by liquid layers, in which the free-fall spheres are disturbed initially by a horizontal gas flow. The oblique impact exhibits different rebound behaviors from normal collision due to the occurrence of strong rotation. The normal and tangential restitution coefficients (e_{n} and e_{t}) and liquid bridge rupture time (t_{rup}) are analyzed. With increase in liquid layer thickness and viscosity, e_{n} and e_{t} decline, and t_{rup} increases. With increase in tangential velocity, e_{t} decreases first and then increases, whereas e_{n} remains nearly unchanged, and t_{rup} decreases constantly. A modified Stokes number is proposed to further explore the relation between restitution coefficients and the impact parameters. Finally, an analysis of energy dissipation shows that the contact deformation and liquid phase are the two main sources of total energy dissipation. Unexpectedly, the dissipative energy caused by the liquid phase is independent of tangential velocity.

Mechanical phenotyping of mouse embryonic stem cells: increase in stiffness with differentiation

Atomic force microscopy (AFM) has emerged as a promising tool to characterize the mechanical properties of biological materials and cells. In our studies, undifferentiated and early differentiating mouse embryonic stem cells (mESCs) were assessed individually using an AFM system to determine if we could detect changes in their mechanical properties by surface probing. Probes with pyramidal and spherical tips were assessed, as were different analytical models for evaluating the data. The combination of AFM probing with a spherical tip and analysis using the Hertz model provided the best fit to the experimental data obtained and thus provided the best approximation of the elastic modulus. Our results showed that after only 6 days of differentiation, individual cell stiffness increased significantly with early differentiating mESCs having an elastic modulus two- to threefold higher than undifferentiated mESCs, regardless of cell line (R1 or D3 mESCs) or treatment. Single-touch (indentation) probing of individual cells is minimally invasive compared to other techniques. Therefore, this method of mechanical phenotyping should prove to be a valuable tool in the development of improved methods of identification and targeted cellular differentiation of embryonic, adult, and induced-pluripotent stem cells for therapeutic and diagnostic purposes.

Solid Lubricating Films for Extreme Environments

Advances in solid lubricating films for vacuum and high temperature applications are reviewed. Traditional lubricants (e.g. graphite and dichalcogenides) are being improved and new lubricating materials (e.g. amorphous carbons) are being discovered with the aid of recent developments in deposition processes and surface analytical methods. Ion bombardmenttreatments have increased film adhesion, lowered friction coefficients and enhanced the wearlife of MoS2films, as well as created new forms of lubricating carbons (amorphous, polymeric and diamond-like). Composite films and multilayer coating treatments are providing extra protection for surface and films against environmental degradation. Ultralow friction coefficients (<0.01) have been achieved with MoS 2 as well as diamond-like carbon films. Material selection, in some cases (e.g. thin metal films), can nowbe made basedon scientific principles, although many tribomaterials are still being developed by trialand error methods.

Contact Problems at Nano/Microscale and Depth Sensing Indentation Techniques

An overview of development of indentation techniques and connections between contact mechanics and methods of extracting mechanical characteristics from indentation data is given. Observed disagreements between the experimental observations and the models of indentation are discussed. It is shown that this disagreement is often caused by violation of hypotheses that are used in the formulation of the appropriate boundary-value contact problems and strictly speaking one cannot apply directly the solutions of Hertz type contact problems to indentation tests employing the sharp indenters. It is shown that commonly used experimental test involving sharp pyramidal and conical indenters may be applied to study plastic properties of materials while this approach is not very accurate for estimations of elastic modulus of the test solid. The recently proposed by Borodich and Galanov non-direct method that employs data of elastically loading of a spherical indenter is described. It is argued that the non-direct method can be used for determination of both the work of adhesion and elastic modulus of the tested material.

Mechanical characterization of mouse embryonic stem cells

Current cell detection techniques are antibody staining of specific protein markers, morphometric parameters and transgenic markers. These assays are often qualitative and do not quantitatively define the outcome of a cell progression during differentiation. Consequently, we propose to characterize the mechanical behavior of embryonic stem cell, which will predict its stage of differentiation during lineage differentiation. Using the atomic force microscope, we have performed several experiments on mouse embryonic stem cells (mESC) roughly 7-17 microm in diameter and height at the interphase stage of the cell cycle process. Specifically, we conducted single indentation studies on undifferentiated and early differentiating (6 days under differentiation conditions) mESC with a cell indentation range of 2-2.5 microm. The data was used to analyze various contact models that can accurately model the geometry of the AFM tip and mESC interaction. With the choice of appropriate contact model, we can determine the accurate modulus of the cell membrane. The experimental results confirmed our research hypothesis that the mechanical property of undifferentiated mESC is different from differentiating (6th day) mESC.

Stick slip contact mechanics between dissimilar materials: effect of charging and large friction

Measurements of the contact radius as a function of applied force between a mica surface and a silica surface (mica/silica) in air are reported. The load/unload results show that the contact radius generally increases with applied force. Because of the presence of charging due to contact electrification, both a short-range van der Waals adhesion force and longer-range electrostatic adhesive interaction contribute to the measured force. The results indicate that approximately 20% of the pull-off force is due to van der Waals forces. The contact radius versus applied force results can be fit to Johnson-Kendall-Roberts (JKR) theory by considering that only the short-range van der Waals forces contribute to the work of adhesion and subtracting a constant longer-range electrostatic force. Also, an additional and unexpected step function is superimposed on the contact radius versus applied force curve. Thus, the contact diameter increases in a stepped dependence with increasing force. The stepped contact behavior is seen only for increasing force and is not observed when symmetric mica/mica or silica/silica contacts are measured. In humid conditions, the contact diameter of the mica/silica contact increases monotonically with applied force. Friction forces between the surfaces are also measured and the shear stress of a mica/silica interface is 100 times greater than the shear stress of a mica/mica interface. This large shear stress retards the increase in contact area as the force is increased and leads to the observed stepped contact mechanics behavior.