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

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

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

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

Granular Packings: Nonlinear elasticity, sound propagation and collective relaxation dynamics

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.Comment: 21 pages, 13 figure

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

Jamming transition in emulsions and granular materials

We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find that the construction history parametrized by the compression rate during the preparation protocol has a strong effect on the micromechanical properties of granular materials but not on emulsions. This leads the granular system to jam at different volume fractions depending on the histories. Isostaticity is found in the packings close to the jamming transition in emulsions and in granular materials at slow compression rates and infinite friction. Heterogeneity of interparticle forces increases as the packings approach the jamming transition which is demonstrated by the exponential tail in force distributions and the small values of the participation number measuring spatial localization of the forces. However, no signatures of the jamming transition are observed in structural properties, like the radial distribution functions and the distributions of contacts.Comment: Submitted to PR

A Ball in a Groove

We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to the vertical, we identify two regimes of static equilibrium for the ball. In the first of these, at large opening angle or low tilt, the ball rolls at both contacts as it is loaded. This is an analog of the "elastic" regime in the mechanics of granular media. At smaller opening angles or larger tilts, the ball rolls at one contact and slides at the other as it is loaded, analogously with the "plastic" regime in the mechanics of granular media. In the elastic regime, the stress indeterminacy is resolved by the underlying kinetics of the ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps