On two-dimensional dynamical dislocations

Abstract

The problem of a two-dimensional dynamical dislocation in an isotropic, homogeneous, unbounded, elastic medium is discussed at length. Beginning with the known solution for a line force, the field due to a displacement dislocation is obtained through the Volterra relation. It is shown that the field due to a dip-slip source of arbitrary dip can be expressed in terms of the field due to a vertical dip-slip source and that due to a 45° dip-slip source. The representations of the two-dimensional dynamical sources are obtained in terms of the vector solutions of the Navier equation and in terms of the source potentials. The potential representation is used to get the field due to an arbitrary line source buried in a uniform half-space.