Anti-plane Waves Research Articles

Elastic wave scattering by a surface-breaking or subsurface planar crack

A boundary integral representation of the displacement field is developed and solved for the crack-opening displacement by expressing the latter on the crack surface as an expansion in localized functions, whose parametrization is determined by fitting exactly-known cross sections. Numerical results are presented for scattering of antiplane (SH) waves as a function of frequency from surface-breaking and buried 2D cracks for a variety of crack inclinations and burial depths. The theory and the method apply to the 3D case. Its numerical implementation will be straightforward but tedious.

Transient scattering of a piezoelectric wave from a crack

The problem of the scattering of transient antiplane shear electroelastic waves from a crack in a piezoelectric medium possessing 6-mm symmetry is solved by determining the electric dipole density induced on the crack by the incident wave. An integral equation satisfied by the Laplace-transformed dipole distribution is derived by appealing to the piezoelectric reciprocity relation. The solution of the integral equation is accomplished by expanding the dipole distribution in a series of first-order spline functions with unknown coefficients and then applying the method of moments to transform the problem to a vector-matrix one, which is readily handled by a computer. Inversion back into the time domain is effected by an efficient numerical method of inverting Laplace transforms. Results are given for the cases of normal and oblique incidence of the wave onto the crack.

Extension of a cut-induced crack under antiplane loading

The extension of a crack formed by cutting at a high velocity into the surface of an elastic solid is investigated. The solid is assumed to be in a state of uniform antiplane shear before the cut is induced. The anti-plane wave motion which is generated by the cutting process is analyzed through a Green's function technique. This technique leads to an integral equation for the stress in the plane of the crack. The stress intensity and velocity intensity functions are obtained, and the propagation of the crack after the cutting process has been terminated is analyzed by means of the balance-of-rates-of-energy criterion. It is shown that the proclivity towards propagation beyond the length of the cut-induced crack shows a significant dependence on the speed of cutting.

Axisymmetric Slipless Indentation of an Infinite, Elastic Cylinder

Axisymmetric Slipless Indentation of an Infinite, Elastic Cylinder