TRANSPORT TREATMENT OF CRACK POPULATION SELF-SIMILARITY AND DAMAGE SCALING LAW

A self-similarity problem arising from our previous work on damage beh aviour 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 g eometrical similarity are formed by the radius extension or contractio n. It is found that the change of the length and of the time by the sa me factors a necessary and sufficient condition for self-similarity ph enomenon. As a consequence, the pressure-wave velocity, the crack velo city and the local pressure are invariant, in good agreement with the results of Refs [12,13]. A simple, hitherto unknown scaling law for th e damage is found. (C) 1997 Elsevier Science Ltd.