On slip pulses at a sheared frictional viscoelastic/ non deformable interface

We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a non-deformable one, to slide under shear via a periodic set of ``self-healing pulses'', i.e. a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.Comment: 23 pages, 3 figures. submitted to PR

Some consequences of the inequality conditions in contact and crack problems

The importance of the inequalities and related side conditions that must be incorporated in contact and crack problems is emphasized and the ensuing consequences explored. An asymptotic analysis of the transitions from slip to separation, stick to slip, and stick to separation is carried out. The inequalities in contact problems make the contact pressure continuous for all levels of friction. They also make a direct transition from stick to separation impossible, unless the combination of materials is special. The inequalities in crack problems are less stringent, but they preclude certain singularities that appear to have flourished in the literature previously. On appuie sur l'importance d'inéquations et d'autres conditions auxiliaires qui doivent être comprises dans les problèmes de contact et de fissure, et on en explore les conséquences. On emploie une analyse asympotique sur les transitions entre les zones glissement-décollement, adhérence-glussement et adhérence-décollement. Il s'ensuit que la contrainte normale du contact doit être continue pour toutes les valeurs du frottement. De plus, la transition directe adhérence-décollement est impossible, à moin que la combinaison des matériaux ne soit exceptionelle. Les inéquations dans les problèmes de fissure sont moins fortes, mais elles sont cependant suffisantes pour empêcher l'existence de certaines singularités qui apparaissent souvent dans les études précedentes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42689/1/10659_2004_Article_BF00040981.pd

On the super-Rayleigh/subseismic elastodynamic indentation problem

The elastodynamic super-Rayleigh/subseismic indentation paradox is examined in this paper. Both the Craggs/Roberts steady-state problem and the Robinson/Thompson transient problem are reconsidered. Certain features of these solutions are discussed from a new point of view, by considering asymptotics at the end of the contact region, the influence of contact inequalities, energetics of the process and existence/uniqueness.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42681/1/10659_2004_Article_BF00044967.pd

The interface penny-shaped crack reconsidered

The penny-shaped crack at the interface between two bonded dissimilar media is reconsidered on the basis of recent developments on the elimination of oscillatory singularities. This is accomplished by assuming an annular frictionless contact zone at the crack circumference and reducing the problem to a Fredholm integral equation. Expressions for the strain energy, crack opening force and bond stresses are obtained and numerical results given for specific material combinations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22767/1/0000322.pd

Spreading of slip from a region of low friction

Recent models of earthquake faults involve heterogeneous slip regions along the faults. Some of this work suggests the following problem: two solids of different material properties are pressed together and sheared. Then, slip propagates asymmetrically from a region of low friction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41713/1/707_2005_Article_BF01176501.pd

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

An experimental study of stress singularities at a sharp corner in a contact problem

The photoelastic method was used to investigate the nature of the local stress field at a sharp corner of a wedge that was compressed against a larger body. Planar wedge specimens made of photoelastic material were compressed against a half plane (larger body) of identical material at various load levels. Several wedge angles were studied. The nature of the singular stress field postulated by linear elastic analysis was verified and the strength of the singularity was obtained by plotting the variation of fringe order as a function of radial distance from the sharp corner on a logarithmic scale. The experimental results were found to be in good agreement with the theoretical predictions. The effect of interface friction and the effect of rounding off the sharp edge are brietly discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43931/1/11340_2006_Article_BF02322823.pd

Reduction of contact stress by use of relief notches

The photoelastic method is used to investigate the possibility of relieving the large local stresses that develop in the corners of a right angled indenter compressing a semi-infinite body by inducing geometric changes to the indenter/semi-infinite body configuration. It is shown that a circular notch cut along the free edges of the indenter can totally eliminate the large corner stresses. The notch, if placed along the interface edge of the half plane, can reduce the stress concentration, but never eliminate it. The results obtained have wide practical application.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43932/1/11340_2006_Article_BF02326071.pd