Abstract
A self-similarity problem arising from our previous work on damage behaviour is treated here by a non-linear integro-differential transport equation for spherical geometry. New cracks are created by an outgoing pressure wave originating in spherical bore-hole and returning to the center after reflection at the outer boundary. Spherical samples of geometrical similarity are formed by the radius extension or contraction. It is found that the change of the length and of the time by the same factors a necessary and sufficient condition for self-similarity phenomenon. As a consequence, the pressure-wave velocity, the crack velocity and the local pressure are invariant, in good agreement with the results of Refs [12, 13]. A simple, hitherto unknown scaling law for the damage is found.
Published Version
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