Scattering of torsional waves by a circular crack in a transversely isotropic solid

1990 ◽  
Vol 88 (4) ◽  
pp. 1975-1980 ◽  
Author(s):  
T. Kundu
Keyword(s):  
Circular Crack ◽  
Transversely Isotropic ◽  
Isotropic Solid ◽  
Torsional Waves

Axisymmetric Scattering of a Plane Longitudinal Wave by a Circular Crack in a Transversely Isotropic Solid

1991 ◽  
Vol 58 (3) ◽  
pp. 695-702 ◽  
Author(s):  
T. Kundu ◽  
A. Bostro¨m
Keyword(s):  
Integral Equation ◽  
Longitudinal Wave ◽  
Legendre Polynomials ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Edge Condition ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Isotropic Solid ◽  
Plane Longitudinal Wave

The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendicular to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.

Elastic waves through a simulated fractured medium

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 964-977 ◽  
Author(s):  
Chaur‐Jian Hsu ◽  
Michael Schoenberg
Keyword(s):  
Normal Stress ◽  
Stress Level ◽  
Elastic Waves ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Static Stress ◽  
Ultrasonic Velocities ◽  
Bulk Properties ◽  
Isotropic Solid ◽  
Fractured Medium

Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelengths much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, we inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describe the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.

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