Percolation and Reynolds Flow in Elastic Contacts of Isotropic and Anisotropic, Randomly Rough Surfaces

In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds fow through the gap between the two contacting solids. We fnd the percolation threshold to depend on the fuid fow direction when the Peklenik number indicates anisotropy unless the system size clearly exceeds the roll-of wave length parallel to the easy fow direction. A critical contact area near 0.415 is confrmed. Heuristically corrected efective-medium treatments satisfactorily provide Reynolds fuid fow conductances, e.g., for isotropic roughness, we identify accurate closed-form expressions, which only depend on the mean gap and the relative contact area

On the adhesion between thin sheets and randomly rough surfaces

Thin, elastic sheets are well known to adapt to rough counterfaces, whereby adhesive interactions and pull-off stresses σp can be significant, yet no generally applicable, quantitative guideline has been suggested hitherto as to when a sheet should be considered thin enough to be sticky. Using computer simulations, we find that the dependence of σp on surface energy γ has a high and a low-pull-off-stress regime. For randomly rough surfaces, we locate the dividing line at the point, where γ is approximately half the elastic energy per unit area needed to make conformal contact, which is the same ratio as for semi-infinite elastic solids. This rule of thumb also applies to a certain degree for single-wavelength roughness, in which case the transition from low to high stickiness occurs when at the moment of maximum tension contact is not only broken at the height maxima but also at the saddle points

Contact-Patch-Size Distribution and Limits of Self-Affinity in Contacts between Randomly Rough Surfaces

True contact between solids with randomly rough surfaces tends to occur at a large number of microscopic contact patches. Thus far, two scaling regimes have been identified for the number density n(A) of contact-patch sizes A in elastic, non-adhesive, self-affine contacts. At small A, n(A) is approximately constant, while n(A) decreases as a power law at large A. Using Green’s function molecular dynamics, we identify a characteristic (maximum) contact area Ac above which a superexponential decay of n(A) becomes apparent if the contact pressure is below the pressure pcp at which contact percolates. We also find that Ac increases with load relatively slowly far away from contact percolation. Results for Ac can be estimated from the stress autocorrelation function Gσσ(r) with the following argument: the radius of characteristic contact patches, rc, cannot be so large that Gσσ(rc) is much less than p2cp. Our findings provide a possible mechanism for the breakdown of the proportionality between friction and wear with load at large contact pressures and/or for surfaces with a large roll-off wavelength

Predicting the Lifetime of Superlubricity

The concept of superlubricity has recently called upon notable interest after the demonstration of ultralow friction between atomistically smooth surfaces in layered materials. However, the energy dissipation process conditioning the sustainability of superlubric state has not yet been well understood. In this work, we address this issue by performing dynamic simulations based both on full-atom and reduced Frenkel-Kontorova models. We find that the center-of-mass momentum autocorrelation of a sliding object can be used as an indicator of the state of superlubricity. Beyond a critical value of it, the sliding motion experiences catastrophic breakdown with a dramatically high rate of energy dissipation, caused by the inter-vibrational-mode coupling. By tracking this warning signal, one can extract heat from modes other than the translation to avoid the catastrophe and extend the lifetime of superlubricity. This concept is demonstrated in double-walled carbon nanotubes based nanomechanical devices with indicator-based feedback design implemented

Modeling Adhesive Hysteresis

When an elastomer approaches or retracts from an adhesive indenter, the elastomer’s surface can suddenly become unstable and reshape itself quasi-discontinuously, e.g., when smallscale asperities jump into or snap out of contact. Such dynamics lead to a hysteresis between approach and retraction. In this study, we quantify numerically and analytically the ensuing unavoidable energy loss for rigid indenters with flat, Hertzian and randomly rough profiles. The range of adhesion turns out to be central, in particular during the rarely modeled approach to contact. For example, negligible traction on approach but quite noticeable adhesion for nominal plane contacts hinges on the use of short-range adhesion. Central attention is paid to the design of cohesive-zone models for the efficient simulation of dynamical processes. Our study includes a Griffith’s type analysis for the energy lost during fracture and regeneration of a flat interface. It reveals that the leading-order corrections of the energy loss are due to the finite-range adhesion scale at best, with the third root of the linear mesh size, while leading-order errors in the pull-off force disappear linearly

How Thermal Fluctuations Affect Hard-Wall Repulsion and Thereby Hertzian Contact Mechanics

Contact problems as they occur in tribology and colloid science are often solved with the assumption of hard-wall and hard-disk repulsion between locally smooth surfaces. This approximation is certainly meaningful at sufficiently coarse scales. However, at small scales, thermal fluctuations can become relevant. In this study, we address the question how they render non-overlap constraints into finite-range repulsion. To this end, we derive a closed-form analytical expression for the potential of mean force between a hard wall and a thermally fluctuating, linearly elastic counterface. Theoretical results are validated with numerical simulations based on the Green’s function molecular dynamics technique, which is generalized to include thermal noise while allowing for hard-wall interactions. Applications consist of the validation of our method for flat surfaces and the generalization of the Hertzian contact to finite temperature. In both cases, similar force-distance relationships are produced with effective potentials as with fully thermostatted simulations. Analytical expressions are identified that allow the thermal corrections to the Hertzian load-displacement relation to be accurately estimated. While these corrections are not necessarily small, they turn out surprisingly insensitive to the applied load

Tactile perception of randomly rough surfaces

Most everyday surfaces are randomly rough and self-similar on sufficiently small scales. We investigated the tactile perception of randomly rough surfaces using 3D-printed samples, where the topographic structure and the statistical properties of scale-dependent roughness were varied independently. We found that the tactile perception of similarity between surfaces was dominated by the statistical micro-scale roughness rather than by their topographic resemblance. Participants were able to notice differences in the Hurst roughness exponent of 0.2, or a difference in surface curvature of 0.8 mm−1 for surfaces with curvatures between 1 and 3 mm−1. In contrast, visual perception of similarity between color-coded images of the surface height was dominated by their topographic resemblance. We conclude that vibration cues from roughness at the length scale of the finger ridge distance distract the participants from including the topography into the judgement of similarity. The interaction between surface asperities and fingertip skin led to higher friction for higher micro-scale roughness. Individual friction data allowed us to construct a psychometric curve which relates similarity decisions to differences in friction. Participants noticed differences in the friction coefficient as small as 0.035 for samples with friction coefficients between 0.34 and 0.45

Tactile perception of randomly rough surfaces

Most everyday surfaces are randomly rough and self-similar on sufficiently small scales. We investigated the tactile perception of randomly rough surfaces using 3D-printed samples, where the topographic structure and the statistical properties of scale-dependent roughness were varied independently. We found that the tactile perception of similarity between surfaces was dominated by the statistical micro-scale roughness rather than by their topographic resemblance. Participants were able to notice differences in the Hurst roughness exponent of 0.2, or a difference in surface curvature of 0.8 mm−1 for surfaces with curvatures between 1 and 3 mm−1. In contrast, visual perception of similarity between color-coded images of the surface height was dominated by their topographic resemblance. We conclude that vibration cues from roughness at the length scale of the finger ridge distance distract the participants from including the topography into the judgement of similarity. The interaction between surface asperities and fingertip skin led to higher friction for higher micro-scale roughness. Individual friction data allowed us to construct a psychometric curve which relates similarity decisions to differences in friction. Participants noticed differences in the friction coefficient as small as 0.035 for samples with friction coefficients between 0.34 and 0.45

On the adhesion between thin sheets and randomly rough surfaces

Thin, elastic sheets are well known to adapt to rough counterfaces, whereby adhesive interactions and pull-off stresses σp can be significant, yet no generally applicable, quantitative guideline has been suggested hitherto as to when a sheet should be considered thin enough to be sticky. Using computer simulations, we find that the dependence of σp on surface energy γ has a high and a low-pull-off-stress regime. For randomly rough surfaces, we locate the dividing line at the point, where γ is approximately half the elastic energy per unit area needed to make conformal contact, which is the same ratio as for semi-infinite elastic solids. This rule of thumb also applies to a certain degree for single-wavelength roughness, in which case the transition from low to high stickiness occurs when at the moment of maximum tension contact is not only broken at the height maxima but also at the saddle points

The development characteristics and mechanisms of the Xigou debris flow in the Three Gorges Reservoir Region

Debris flow is a common geological hazard in mountainous areas of China, often causing secondary disasters and seriously threatening residents and infrastructure. This paper uses the Xigou debris flow in the Three Gorges Reservoir Region (TGRR) as an example case study, the development characteristics and initiation pattern of which were analyzed based on field investigation. The disaster dynamics software DAN-W was then used to simulate the entire initiation-movement-accumulation process of the debris flow and conduct the debris flow dynamics analysis. The paper also simulated and predicted the movements of landslides in the formation area of a debris flow after its initiation. The results show that the movement duration of the Xigou debris flow was approximately 40 s, the maximum velocity was 37.1 m/s, the maximum thickness of the accumulation was 18.7 m, and the farthest movement distance was 930 m, which are consistent with the field investigation. When the volumes of landslide transformed into a new source material of debris flow are 5 × 104, 10 × 104, 15 × 104, 20 × 104, and 26 × 104 m3, the movement distances of the debris flows are 250, 280, 300, 340, and 375 m, respectively. When the volume of the source material exceeds 20 × 104 m3, debris flow movement can seriously impact the residential houses at the entrance of the gully. This paper can provide a scientific basis for the prevention and mitigation of the Xigou debris flow