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Crack-equivalent sources

The correspondence between equations (4) and (2) permits an interesting observation on idealized cracks. The relationship between moment and volume is the same for an isolated crack-shaped body and for the moment-tensor equivalent of a crack (this is, a suitable distribution of moments in an unbroken full space). Thus, all of the moment is needed to dilate the crack filling, and no moment remains to push the surrounding medium away. Opening a crack in a full space requires no moment. This may sound paradox, but is not. The forces (stresses) opening the crack are finite for a finite crack but have a negligible moment when the crack is thin.

Erhard Wielandt