Erweiterung eines halbunendlichen Risses durch eine antisymmetrische, quasigleichf�rmige Volumskraft

Abstract

A semiinfinite crack extends nonuniformly against a body force that is antisymmetric about the fault plane but independent of the distance from the latter. Conversion of the inhomogeneous wave equation for SH motion into a radiation equation incorporates fault plane distributed mechanisms. An integral equation is then formulated for fault plane observations preceding the crack. Both the body force and the stress drop are assumed to be bounded over finite histories. Multiple inversion yields a formal exterior solution which behaves singularly near the crack edge. An analogy with a Barenblatt postulate cancels the singularity through a nonlinear integral equation governing the edge coordinate. The resultant non-singular displacement gradient turns out to be continuous at the crack edge; here, the force-induced contribution vanishes. The interior problem is also solved for the displacement along either crack face. An application is illustrated for an impulsive body force; this leads to an interesting corollary with totally uniform results. Finally, if the body force exists within a half-space away from which extension occurs, it contributes nothing to the exterior solution; furthermore, the interior solution can be evaluated in terms of only the stress drop and the edge locus, i.e. without explicit prescription of such a body force.