Infinite Isotropic Elastic Medium Research Articles

Interaction of elastic waves with a penny-shaped crack

The problem of the diffraction of normally incident longitudinal and torsional elastic waves by a penny-shaped crack located in an infinite isotropic elastic medium is considered. The associated integral equations are solved numerically for a range of values of the frequency of the incident waves. The dynamic stress intensity factors are computed as functions of the frequency. The displacement fields on the crack as well as at points far away from the crack are presented graphically.

Elastic wave excitation in piezoelectric slabs

A plane uniform electromagnetic wave traveling in a vacuum region and obliquely impinging on a piezoelectric slab bounded on the opposite side by an infinite isotropic elastic medium has been considered. The power carried by the elastic wave transmitted in this latter elastic medium has been compuftoerd various values of the geometrical parameters and the maxima determined.

Elastic self-energies of undissociated dislocation jogs

Abstract Analytic expressions are derived for the elastic energy of an undissociated jog lying perpendicular to an undissociated straight dislocation line of arbitrary Burgers vector in an otherwise perfect infinite isotropic elastic medium. These expressions are the most accurate which can presently be obtained, but the analysis still involves minor approximations. In particular, those associated with the contribution to the energy arising from the work done by core surface tractions at the corners in the dislocation are important for short jogs and are discussed in detail. Numerical results are presented and these and the analytic expressions are compared with those of previous workers, which involve major approximations. It is concluded that even the new expressions are not reliable for short jogs.

Stress distribution due to pressurized exterior crack in an infinite isotropic elastic medium with coaxial cylindrical cavity

The present work deals with the study of the stress field in an infinite homogeneous and isotropic medium containing a cylindrical cavity and an exterior crack (i.e. a crack occupying the region outside a circle) subject to internal pressure. The problem, considered within the framework of the infinitesimal theory of elasticity, is formulated in terms of a pair of dual integral equations involving Bessel functions of the first kind and the second kind. Similar equations have been discussed by the authors, Srivastav [1, 2] and Narain [3]. The techniques of these papers are suitably modified to reduce the dual equations to a single Fredholm's integral equation of the second kind. The integral equation of the Fredholm type is then solved numerically and the result is used to compare the crack energy corresponding to different crack sizes for a special type of internal pressure inside the crack.

A seismologist's Difficulties with some mathematical theory or the lack of it

The elastic‐wave theory is set up for an infinite isotropic elastic medium. Some work has been done on boundary‐waves at the interface of two semi‐infinite isotropic elastic media. Now most of such theory silently postulates that the elastic properties of a medium retain right up to its mathematical boundaries the same values which they have in its remote interior. We have all the assumptions of geometric optics that wave lengths are short with reference to the length of path in the medium, and that “discontinuities” are “sharp” with reference to wave length. An approach to the problem has been made in the paper “The effect of sharpness of discontinuities on the transmission and reflection of elastic waves,” by K. Sezawa and K. Kanai [see 1 of “References” at end of paper].