Shakedown in elastic contact problems with Coulomb friction

AbstractElastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e., that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down.In this paper, we prove this result for ‘complete’ contact problems in the discrete formulation (i) for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions and (ii) for certain two-dimensional problems in which the friction coefficient at each node is less than a certain critical value. We also present counter-examples for all systems that do not fall into these categories, thus giving a definitive statement of the conditions under which Melan’s theorem can be used to predict whether such a system will shake down

HD 179949b - a close orbiting extrasolar giant planet with a stratosphere?

The original article can be found at: http://www3.interscience.wiley.com Copyright Blackwell Publishing. DOI: 10.1111/j.1365-2966.2008.13831.xWe have carried out a search for the 2.14-μm spectroscopic signature of the close orbiting extrasolar giant planet, HD179949b. High-cadence time-series spectra were obtained with the Cryogenic high-resolution InfraRed ´ Echelle Spectrograph at Very Large Telescope, Unit 1 on two closely separated nights. Deconvolution yielded spectroscopic profiles with mean signal-to-noise ratios of several thousand, enabling the near-infrared contrast ratios predicted for the HD179949 system to be achieved. Recent models have predicted that the hottest planets may exhibit spectral signatures in emission due to the presence of TiO and VO which may be responsible for a temperature inversion high in the atmosphere.We have used our phase-dependent orbital model and tomographic techniques to search for the planetary signature under the assumption of an absorption line dominated atmospheric spectrum, where T and V are depleted from the atmospheric model, and an emission line dominated spectrum, where TiO and VO are present. We do not detect a planet in either case, but the 2.120–2.174-μm wavelength region covered by our observations enables the deepest near-infrared limits yet to be placed on the planet/star contrast ratio of any close orbiting extrasolar giant planet system. We are able to rule out the presence of an atmosphere dominated by absorption opacities in the case of HD179949b at a contrast ratio of Fp/F∗ ∼ 1/3350, with 99 per cent confidence.Peer reviewe

The distortion of a cylinder with non-uniform axial heat conduction

Closed form expressions are developed for the thermoelastic curvature of the initially plane end faces of a traction free cylinder subjected to arbitrary axisymmetric heat flux, the curved surfaces being assumed insulated. The solution is developed from a potential function representation of displacement and temperature for an elastic layer. The reciprocal theorem is invoked to show that the tractions at the curved surface of the cylinder vary linearly along the axis and they are removed by superposition of biaxial bending. It is found that the curvature of the plane ends depends on the local heat flux and the mean heat flux, whilst the cylindrical face distorts into a cone.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42669/1/10659_2004_Article_BF00042521.pd

Stability of thermoelastic contact for a rectangular elastic block sliding against a rigid wall

In this note, we determine the stability boundary for the thermoelastic contact of a rectangular elastic block sliding against a rigid wall in the presence of a pressure-dependent thermal contact resistance. This geometry can be seen as intermediate between the idealized ‘Aldo’ rod model and continuum solutions for the elastic half-plane.The solution is obtained by comparing the expression for the perturbed boundary condition including frictional heating with that for purely static loading, already solved by Yeo and Barber (1995). The critical sliding speed is obtained as a function of the temperature difference imposed between the wall and the free end.In most cases, frictional heating tends to destabilize the system. However, for certain forms of the resistance-pressure law, the opposite conclusion is reached and the system can be stable for all sliding speeds

Contact transmission of wave motion between two solids with an initial gap

The paper treats the tranmission of wave motion from one solid to another when the bodies are initially separated by a small gap. If a pulse of elastic waves strikes the surface of one of the solids and the amplitude of the pulse is large enough, the solids can come into contact and interact locally. The dynamic interaction is treated using Coulomb's friction law, and a method is presented for finding the slip and stick zones in the contact region when the incidence angle of the pulse is subcritical. Unusual results are encountered for large friction coefficients.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24135/1/0000392.pd

Nature of Sonoluminescence: Noble Gas Radiation Excited by Hot Electrons in "Cold" Water

We show that strong electric fields occurring in water near the surface of collapsing gas bubbles because of the flexoelectric effect can provoke dynamic electric breakdown in a micron-size region near the bubble and consider the scenario of the SBSL. The scenario is: (i) at the last stage of incomplete collapse of the bubble the gradient of pressure in water near the bubble surface has such a value and sign that the electric field arising from the flexoelectric effect exceeds the threshold field of the dynamic electrical breakdown of water and is directed to the bubble center; (ii) mobile electrons are generated because of thermal ionization of water molecules near the bubble surface; (iii) these electrons are accelerated in ''cold'' water by the strong electric fields; (iv) these hot electrons transfer noble gas atoms dissolved in water to high-energy excited states and optical transitions between these states produce SBSL UV flashes in the trasparency window of water; (v) the breakdown can be repeated several times and the power and duration of the UV flash are determined by the multiplicity of the breakdowns. The SBSL spectrum is found to resemble a black-body spectrum where temperature is given by the effective temperature of the hot electrons. The pulse energy and some other characteristics of the SBSL are found to be in agreement with the experimental data when realistic estimations are made.Comment: 11 pages (RevTex), 1 figure (.ps

Stresses in a half space due to Newtonian gravitation

An efficient general solution is obtained for the problem of the elastic half space z > 0 with a traction-free surface experiencing gravitational attraction to an arbitrarily shaped body located in z < 0. Many components of the stress field can be written down immediately if the potential of the attracting body is known. Results are given for the case of attraction to a uniform sphere.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42687/1/10659_2005_Article_4105.pd

Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation

We explore the initial conditions in short-time critical dynamics to propose a new method to evaluate the dynamic exponent z. Estimates are obtained with high precision for 2D Ising model and 2D Potts model for three and four states by performing heat-bath Monte Carlo simulations.Comment: Latex paper, 2 eps figure