Antiplane Elastic Wave Scattering From a Curved Randomly Rough Crack

Abstract

The problem of scattering of antiplane elastic waves from a rough crack is solved by means of an extension of the null field approach. The extension consists of the expansion of certain matrix elements in terms of a small parameter followed by an analytical ensemble averaging. The geometry is taken to be two-dimensional, and the scatterer is a curved crack with a small random roughness. Both effects due to overall curvature and effects due to surface roughness are thus included in the analysis. It is assumed that the roughness is one where the height has less effect on the scattering than does the gradient (this is satisfied whenever the correlation length of the surface roughness is much smaller than the curvature of the crack), and some numerical results are given for this case. However, it is a straightforward extension of the analysis to consider cases where the height effects are included.