Stiffness of Contacts Between Rough Surfaces

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughnesses, system sizes and Poisson ratios can be collapsed using Persson's contact theory for continuous elastic media. The atomic scale response at the interface between solids has little affect on the area or normal stiffness, but can greatly reduce the lateral stiffness. The scaling of this effect with system size and roughness is discussed.Comment: 4 pages, 3 figure

Number and location of zero-group-velocity modes

The frequency-wavenumber spectra of laminated media often exhibit anomalous modes with descending branches whose group velocity is negative, and these terminate at a minimum point at which the group velocity transitions from negative to positive. These minima are associated with resonant conditions in the medium, which have been clearly observed in experiments and in the nondestructive testing of laminated plates. Starting from first principles, this paper provides a theoretical analysis on the number and location of such zero-group-velocity (ZGV) modes for horizontally layered media bounded by any arbitrary combination of external boundaries. It is found that these ZGV points are few in number and show up mostly in low-order modes which are characterized by a negative second derivative at the cutoff frequencies, a condition that can readily be tested. It is also shown that the effective number of ZGVs is small even when the ratio of the dilatational and shear wave velocity is a rational number and there exist coincidences in cutoff frequencies, a condition that at first would suggest that the number of ZGVs is infinite. Finally, it is shown that the number of ZGVs decreases with the Poisson’s ratio

Mechanistic analysis and computer simulation of impact breakage of agglomerates: Effect of surface energy

Agglomerates are ubiquitous as intermediate or manufactured products in chemical, pharmaceutical and food industries. During handling and processing they may suffer breakage if they are weak. On the other hand, if they are too strong, their dispersion and disintegration could be difficult. The control of their mechanical strength is therefore highly desirable. However, the analysis of agglomerate strength is complex due to the large number of parameters that influence agglomerate behaviour, such as the primary particle size, density and elastic modulus, and the interparticle bond strength. A simple mechanistic model is presented here which relates the number of broken contacts in agglomerate due to impact velocity, interparticle adhesion energy and the particle properties of the particles forming the agglomerate. The model is based on the hypothesis that the energy used to break contacts during impact is proportional to the incident kinetic energy of the agglomerate. The damage ratio defined as the ratio of broken contacts to the initial number of bonds is shown to depend on the dimensionless group, Δ, in the form (ρV2D5/3E2/3)/ Γ5/3, where V is the impact velocity, E the elastic modulus, D the particle diameter, ρ the particle density and Γ the interface energy. This dimensionless group, Δ, incorporates the Weber number, (ρDV2/Γ), which was previously shown to be influential in agglomerate breakage, and may be presented in the form, Δ=WeIe2/3 , where Ie = ED/ Γ. The predicted dependency of the damage ratio on the surface energy has been tested using Distinct Element Method (DEM). Four different agglomerates have been formed and impacted against a target for three different values of the surface energy of the primary particles. The simulation results show that the effect of surface energy is better described by the above mechanistic model than by the Weber number alone, as previously used to characterise the impact strength of agglomerates

Storyline description of Southern Hemisphere midlatitude circulation and precipitation response to greenhouse gas forcing

As evidence of climate change strengthens, knowledge of its regional implications becomes an urgent need for decision making. Current understanding of regional precipitation changes is substantially limited by our understanding of the atmospheric circulation response to climate change, which to a high degree remains uncertain. This uncertainty is reflected in the wide spread in atmospheric circulation changes projected in multimodel ensembles, which cannot be directly interpreted in a probabilistic sense. The uncertainty can instead be represented by studying a discrete set of physically plausible storylines of atmospheric circulation changes. By mining CMIP5 model output, here we take this broader perspective and develop storylines for Southern Hemisphere (SH) midlatitude circulation changes, conditioned on the degree of global-mean warming, based on the climate responses of two remote drivers: the enhanced warming of the tropical upper troposphere and the strengthening of the stratospheric polar vortex. For the three continental domains in the SH, we analyse the precipitation changes under each storyline. To allow comparison with previous studies, we also link both circulation and precipitation changes with those of the Southern Annular Mode. Our results show that the response to tropical warming leads to a strengthening of the midlatitude westerly winds, whilst the response to a delayed breakdown (for DJF) or strengthening (for JJA) of the stratospheric vortex leads to a poleward shift of the westerly winds and the storm tracks. However, the circulation response is not zonally symmetric and the regional precipitation storylines for South America, South Africa, South Australia and New Zealand exhibit quite specific dependencies on the two remote drivers, which are not well represented by changes in the Southern Annular Mode

Fretting wear of Ti(CxNy) PVD coatings under variable environmental conditions

Fretting wear as a specific type of degradation is defined as an oscillatory motion at small amplitude between two nominally stationary solid bodies in mutual contact. Under external stresses the interface is being damaged by debris generation and its successive ejections outside the contact area. A potential protection against fretting damage by means of hard coatings is being offered by different surface engineering techniques. For this study TiC, TiN and TiCN hard coatings manufactured by a PVD method have been selected and tested against smooth polycrystalline alumina ball. A fretting test programme has been carried out at the frequency of 5Hz, 100N normal load, 100µm displacement amplitude and at three values of a relative humidity: 10, 50 and 90% at 295-298K temperature. It turned out that the intensity of wear process was depending not only on loading conditions but on environmental ones as well. A significant impact of RH on wear rate and friction behaviour of the coatings under investigation has been observed. Two different damage mechanisms have been identified and related to the phenomena of debris oxidation and debris adhesion to the counterbody surface. In the latter case the debris deposited onto the surface of the alumina ball lead to a change of stress distribution at the interface and as a result to accelerated wear. In this work experiments with variable relative humidity increasing from 10% to 90% within 1 a single fretting test have been completed. It follows from these experiments that there exists an intermediate value of the RH at which the friction coefficient changes rapidly. Finally a dissipated energy approach has been applied in the work in order to quantify and compare fretting wear rates of different hard coatings

Unsymmetrical shear loading and its influence on the frictional shakedown of incomplete contacts

Published versio

Nonlinear Interaction of Transversal Modes in a CO2 Laser

We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The pattern dynamics near this codimension two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.Comment: 16 pages, 0 figure

Preface - Personal perspectives in nonlinear science : Looking back, looking forward

Peer reviewedPublisher PD

Gravity-driven Dense Granular Flows

We report and analyze the results of numerical studies of dense granular flows in two and three dimensions, using both linear damped springs and Hertzian force laws between particles. Chute flow generically produces a constant density profile that satisfies scaling relations suggestive of a Bagnold grain inertia regime. The type of force law has little impact on the behavior of the system. Bulk and surface flows differ in their failure criteria and flow rheology, as evidenced by the change in principal stress directions near the surface. Surface-only flows are not observed in this geometry.Comment: 4 pages, RevTeX 3.0, 4 PostScript figures (5 files) embedded with eps

Probing the mechanical properties of graphene using a corrugated elastic substrate

The exceptional mechanical properties of graphene have made it attractive for nano-mechanical devices and functional composite materials. Two key aspects of graphene's mechanical behavior are its elastic and adhesive properties. These are generally determined in separate experiments, and it is moreover typically difficult to extract parameters for adhesion. In addition, the mechanical interplay between graphene and other elastic materials has not been well studied. Here, we demonstrate a technique for studying both the elastic and adhesive properties of few-layer graphene (FLG) by placing it on deformable, micro-corrugated substrates. By measuring deformations of the composite graphene-substrate structures, and developing a related linear elasticity theory, we are able to extract information about graphene's bending rigidity, adhesion, critical stress for interlayer sliding, and sample-dependent tension. The results are relevant to graphene-based mechanical and electronic devices, and to the use of graphene in composite, flexible, and strain-engineered materials.Comment: 5 pages, 4 figure