A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

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Surface deformation due to shear and tensile faults in a half-space

Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Author(s): Vogel, Alfred; Venugopalan, Vasan | Abstract: The mechanisms of pulsed laser ablation of biological tissues were studied. The transiently empty space created between the fiber tip and the tissue surface improved the optical transmission to the target and thus increased the ablation efficiency. It was found that the structure and morphology also affect the energy transport among tissue constituents.

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Mechanisms of pulsed laser ablation of biological tissues.

Fault traces consist of numerous discrete segments, commonly arranged as echelon arrays. In some cases, discontinuities influence the distribution of slip and seismicity along faults. To analyze fault segments, we derive a two-dimensional solution for any number of nonintersecting cracks arbitrarily located in a homogeneous elastic material. The solution includes the elastic interaction between cracks. Crack surfaces are assumed to stick or slip according to a linear friction law. For an array of echelon cracks the ratio of maximum slip to array length significantly underestimates the difference between the driving stress and frictional resistance. The ratio of maximum slip to crack length slightly overestimates this difference. Stress distributions near right- and left-stepping echelon discontinuities differ in two important ways. For right lateral shear and left-stepping cracks, normal tractions on the overlapped crack ends increase and inhibit frictional sliding, whereas for right-stepping cracks, normal tractions decrease and facilitate sliding. The mean compressive stress between right-stepping cracks also decreases and promotes the formation of secondary fractures, which tend to link the cracks and allow slip to be transferred through the discontinuity. For left-stepping cracks the mean stress increases; secondary fracturing is more restricted and tends not to link the cracks. Earthquake swarms and aftershocks cluster near right steps along right lateral faults. Our results suggest that left steps store elastic strain energy and may be sites of large earthquakes. Opposite behavior results if the sense of shear is left lateral.

Mechanics of discontinuous faults

It is known that oscillatory singularities appear in problems involving interface cracks that are assumed to have open tips. An unsatisfacory aspect of the oscillatory singularities is that they lead to overlapping of the crack faces. The interface crack in a tension field, originially treated by England among others, is thus reconsidered on the basis that the crack is not completely open and that its faces are in frictionless contact near the tips. The formulation leads to a pair of coupled singular integral equations. The singularities, no longer oscillatory, exhibit some unusual features and indicate that the spreading of the interface crack in a tension field is intimately connected with failure in shear. A new stress-intensity factor is obtained and compared to the stress-intensity factors for the completely open crack. /Author/

The Interface Crack

The Interface Crack in a Combined Tension-Compression and Shear Field

The Interface Crack in a Shear Field

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.

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Maria Comninou

Papers

The Interface Crack

The Interface Crack in a Combined Tension-Compression and Shear Field

The Interface Crack in a Shear Field

The angular dislocation in a half space

Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibres