Kyle D. Schulze

Meeting the Contact-Mechanics Challenge

This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

Self-assembled micro-organogels for 3D printing silicone structures

High-precision 3D printing of liquid silicone is achieved using a new oil-based microgel as a support medium. The widespread prevalence of commercial products made from microgels illustrates the immense practical value of harnessing the jamming transition; there are countless ways to use soft, solid materials that fluidize and become solid again with small variations in applied stress. The traditional routes of microgel synthesis produce materials that predominantly swell in aqueous solvents or, less often, in aggressive organic solvents, constraining ways that these exceptionally useful materials can be used. For example, aqueous microgels have been used as the foundation of three-dimensional (3D) bioprinting applications, yet the incompatibility of available microgels with nonpolar liquids, such as oils, limits their use in 3D printing with oil-based materials, such as silicone. We present a method to make micro-organogels swollen in mineral oil, using block copolymer self-assembly. The rheological properties of this micro-organogel material can be tuned, leveraging the jamming transition to facilitate its use in 3D printing of silicone structures. We find that the minimum printed feature size can be controlled by the yield stress of the micro-organogel medium, enabling the fabrication of numerous complex silicone structures, including branched perfusable networks and functional fluid pumps.

Real Area of Contact in a Soft Transparent Interface by Particle Exclusion Microscopy

Soft matter mechanics are characterized by high strains and time-dependent elastic properties, which complicate contact mechanics for emerging applications in biomedical surfaces and flexible electronics. In addition, hydrated soft matter precludes using interferometry to observe real areas of contact. In this work, we present a method for measuring the real area of contact in a soft, hydrated, and transparent interface by excluding colloidal particles from the contact region. We confirm the technique by presenting a Hertz-like quasi-static indentation (loading time > 1.4 hrs) by a polyacrylamide probe into a stiff flat surface in a submerged environment. The real contact area and width were calculated from in situ images of the interface processed to reduce image noise and thresholded to define the perimeter of contact. This simple technique of in situ particle exclusion microscopy (PEM) may be widely applicable for determining real areas of contact of soft, transparent interfaces.

Elastic modulus and hydraulic permeability of MDCK monolayers

The critical role of cell mechanics in tissue health has led to the development of many in vitro methods that measure the elasticity of the cytoskeleton and whole cells, yet the connection between these local cell properties and bulk measurements of tissue mechanics remains unclear. To help bridge this gap, we have developed a monolayer indentation technique for measuring multi-cellular mechanics in vitro. Here, we measure the elasticity of cell monolayers and uncover the role of fluid permeability in these multi-cellular systems, finding that the resistance of fluid transport through cells controls their force-response at long times.

Kinetics of aqueous lubrication in the hydrophilic hydrogel Gemini interface

The exquisite sliding interfaces in the human body share the common feature of hydrated dilute polymer mesh networks. These networks, especially when they constitute a sliding interface such as the pre-corneal tear film on the ocular interface, are described by the molecular weight of the polymer chains and a characteristic size of a minimum structural unit, the mesh size, ξ. In a Gemini interface where hydrophilic hydrogels are slid against each other, the aqueous lubrication behavior has been shown to be a function of sliding velocity, introducing a sliding timescale competing against the time scales of polymer fluctuation and relaxation at the surface. In this work, we examine two recent studies and postulate that when the Gemini interface slips faster than the single-chain relaxation time, chains must relax, suppressing the amplitude of the polymer chain thermal fluctuations.

Eliminating the surface location from soft matter contact mechanics measurements

Abstract The material properties of soft materials can be measured with rheometers and tensile testing instruments whenever there exist few limitations on sample volume, fixturing and general sample preparation, where samples often need to be prepared specifically to work with the hardware of a given instrument. By contrast, indentation methods are well suited for measuring material properties when sample preparation and geometry are highly constrained, as is the case with living cells, confluent cell layers, tissue samples, hydrogel coatings or soft objects with defined shapes like contact lenses. For example, indentation can be performed directly on cells grown in a Petri dish, without modifying typical cell culture protocols or materials. However, the low elastic modulus of these soft materials make it extremely difficult to determine when an indentation instrument first makes contact with a sample, which is critically important to know if material properties are to be determined with confidence. Here, we present an analysis method that eliminates the need to identify when an instrument makes contact with a sample. The method recasts the traditional force–displacement models of contact mechanics in terms of the first derivative of applied normal force with respect to indenter position, which automatically removes the unknown point of contact. This approach enables the selection of appropriate theoretical models for a given data-set and allows the measurement of sample material properties with the only fitting parameter being the elastic modulus.

Challenges and opportunities in soft tribology

Abstract Despite the ubiquitous use of soft materials in everything from transportation to biomedicine, there remain tremendous opportunities for fundamental studies on the governing principles behind their tribological performance. One of the greatest challenges in performing tribological studies of friction and wear on soft materials is the low modulus, which necessitates low forces for convenient and accessible contact areas widely used in experimental tribology. Many excellent and established tribological instruments that have been optimized over the years for use with hard materials are essentially unusable for low modulus materials like soft elastomers, hydrogels, tissues, and cells. This critical need for fundamental measurements of soft contacts has led to a growing field of instrumentation development, stronger connections between tribology and rheology, increased in situ studies of contact deformation using optical microscopy, and new models for rate-dependent effects on friction and wear. Improvements in the ability to measure the real area of contact, assess time-dependent responses of soft interfaces, and reduce uncertainty in shear stress measurements are critical for friction measurements on soft materials. Some recent efforts in soft tribology are outlined herein with an eye towards performing non-destructive experiments on living cell layers to foster stronger interactions with biology and biomedicine.

The Role of Microstructure in Ultralow Wear Fluoropolymer Composites

Abstract Past studies have shown that the inclusion of fillers in a polytetrafluoroethylene (PTFE) matrix can improve wear resistance by nearly four orders of magnitude. These discoveries have prompted several tribological experiments over the past decade that have highlighted the importance of particle size, tribofilm formation, filler percentage, and environment. To evaluate the effect that microstructure plays on a composite’s tribological performance, PTFE-filled polyamide-imide (PAI) composites were made and tested. To investigate the role of microstructure on the tribological performance of fluoropolymer composites, 12 composite formulations of PTFE and PAI over a range of 0 to 100 vol% PAI were tested. PTFE–PAI composite samples were slid against a stainless steel countersample using a linear reciprocating tribometer under a nominal 6.35 MPa contact pressure at 50.8 mm/s sliding speed. Of the samples tested, the 25 vol% PAI showed a remarkable mean steady-state wear rate of k = 3 × 10−9 mm3/Nm over an extreme distance of 360 km. A serial imaging investigation revealed that a mechanical interlocking of the two polymers occurred during the sintering process, which possibly contributed to the ultralow wear rates observed in this polymer–polymer composite.

Lessons from the Lollipop: Biotribology, Tribocorrosion, and Irregular Surfaces

Abstract Biotribology and tribocorrosion are often not included in numerical or computational modeling efforts to predict wear because of the apparent complexity in the geometry, the variability in removal rates, and the challenge associated with mixing time-dependent removal processes such as corrosion with cyclic material removal from wear. The lollipop is an accessible bio-tribocorrosion problem that is well known but underexplored scientifically as a tribocorrosion process. Stress-assisted dissolution was found to be the dominant tribocorrosion process driving material removal in this system. A model of material removal was described and approached by lumping the intrinsically time-dependent process with a mechanically driven process into a single cyclic volumetric material removal rate. This required the collection of self-reported wear data from 58 participants that were used in conjunction with statistical analysis of actual lollipop cross-sectional information. Thousands of repeated numerical simulations of material removal and shape evolution were conducted using a simple Monte Carlo process that varied the input parameters and geometries to match the measured variability. The resulting computations were analyzed to calculate both the average number of licks required to reach the Tootsie Roll® center of a Tootsie Roll® pop, as well as the expected variation thereof.