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Arrivals associated with a class of self-similar problems in elastodynamics

Abstract A systematic method is given for finding all of the singularities in the stress fields associated with self-similar elastodynamic problems for half-spaces, directly from representations developed in (1). No particular symmetry is assumed, and both two- and three-dimensional problems are discussed for arbitrarily anisotropic half-spaces. Expressions for body wave arrivals are obtained, reproducing results given in (1), and head wave arrivals, not discussed in (1), are found. Arrivals produced by interfacial dislocations and cracks are found by the same method. As an example, an account of the first arrival produced by a penny-shaped crack expanding under shear on an interface is completed, by finding the head wave that precedes the body wave, already found in (1), in a region exterior to a cone in one of the half-spaces.