An old elasticity problem in a unilateral setting

A limiting case of the Michell problem involving an elastic wedge is the unbounded solid with a semi-infinite cut, the tip of which is subjected to a concentrated force. For the limiting case, the classical solution leads to overlapping of material whenever the component of the force along the axis of symmetry is directed away from the cut, and the problem must be solved anew using unilateral boundary conditions. The required mathematics is simple, and the subject is suitable for classroom discussion. Two examples are solved explicitly, and additional exercise problems are suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42668/1/10659_2004_Article_BF00042218.pd

Stress singularity at a sharp edge in contact problems with friction

The paper discusses the nature of the singularity that arises at a sharp edge in contact problems with friction. The theoretical treatment is based on the Mellin transform of the elastic fields. The results regarding the power singularities confirm the previous work of Gdoutos and Theocaris, but it is shown that logarithmic singularities are always present. Some experimental observations in photoelasticity are also presented. Die Art der Spannungssingularität, die an einer scharfen Ecke in Berührungsproblemen erscheint, ist für den Fall mit Reibung untersucht. Die theoretische Behandlung stützt sich auf die Mellin-Transformation der elastischen Felder. Die Ergebnisse bezüglich der Potenzsingularitäten bestätigen die früheren Resultate von Gdoutos und Theocaris. Es wird jedoch gezeigt, daß logarithmische Singularitäten stets anwesend sind. Auch einige Beobachtungen von photoelastischen Versuchen sind dargestellt.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43357/1/33_2005_Article_BF01594906.pd

Interface slip caused by a surface load moving at constant speed

Slip at the interface between a layer and a substrate caused by a slowly moving tangential force on the surface of the layer is considered. The solution shows a significant departure from the stationary load case. In particular, a permanent tangential displacement is left behind the moving load, symmetry is lost, and the shear tractions have continuous derivatives at the trailing edge of the transition zone.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25349/1/0000796.pd

The angular disclination

Similarly to the angular dislocation introduced by Yoffe, the angular disclination is a basic configuration that is suitable for generating polygonal loops by superposition. The displacements in an unbounded elastic material are given and the generation of closed loops discussed. La disclinaison angulaire est une configuration fondamentale la plus facile à construire des disclinaisons en polygone, tout comme dans le cas de la dislocation angulaire introduite par Yoffe. Nous donnons ici les déplacements dans un milieu élastique infini et discutons la méthode de construction des disclinaisons en polygone.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42686/1/10659_2004_Article_BF00041129.pd

The angular dislocation in a half space

The solution for an angular dislocation allows one to construct the fields for any polygonal loop by superposition. The paper presents the displacements induced by the angular dislocation in an elastic half space. In view of potential applications in geophysics, particular attention is paid to the elastic fields at the free surface. The surface data are seen to exhibit a very simple dependence on the elastic constants. On peut construire les champs élastiques associés à une dislocation en polygone par superposition de solutions au problème d'une dislocation angulaire. Nous présentons les déplacements induits par une dislocation ingulaire dans un demi-éspace élastique. En vue des applications géophysiques, les champs élastiques sur la surface libre sont étudiés en particulier. Nous montrons que les champs élastiques sur la surface dépendent des constantes élastiques d'une facon très simple.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42683/1/10659_2004_Article_BF00126985.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

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