Shear Crack Extension through an Incident Influence

SH motion is triggered by the nonuniform extension of a crack under an applied, general body force. The net incident force‐field along the fault plane converts into an incident influence which plays an important role in the source mechanism. With subsonic extension, fault plane perturbations ahead of a foremost crack‐emitted wavefront naturally originate entirely at the applied force. Nonetheless, they contribute to the incident influence everywhere behind such a wavefront. For a trailing mode of reception preceding the crack, repeated inversion of a governing inhomogeneous integral equation yields a displacement gradient that behaves singularly near the advancing crack edge. On invoking a Barenblatt type criterion, this singularity gets eliminated, essentially, because of the incident influence. A nonlinear integral equation governing that particular crack edge results. Another nonlinear integral equation can be formulated for an arrested advance. Besides the desingularized displacement gradient derived outside the crack, the displacement difference across the crack faces is also determined. A vital question throughout concerns the availability of bounded quantities.