Theory of scattering of elastic waves from flat cracks of arbitrary shape

• Published in: Wave motion 1983, Vol.5 (1), p.15-32
• Main Author: Visscher, William M.
• Format: Article
• Language: English
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/0165-2125(83)90003-3

A method, based on a boundary-integral representation of the elastic displacement, for calculating crack-opening-displacements on a flat crack of arbitrary shape and for incident elastic waves of arbitrary direction, polarization, and wavelength is developed and illustrated by application to Rayleigh scattering from two families of crack shapes. The crack-opening-displacement is expanded in a truncated complete set of functions on the crack surface. This transforms the boundary-integral representation into a matrix equation with rank three times the order of the truncation. This matrix equation has the properties that it can be expressed as the result of an extremum principle with respect to variations of the expansion coefficients of the crack-opening-displacement (thus converges as the truncation order increases) and the matrix kernel (which must be inverted) is positive definite. A conclusion drawn is that only very accurate experiments can distinguish a flat crack of general shape from a penny-shaped crack by long-wavelength elastic-wave scattering.