SCATTERING OF TRANSIENT WAVES BY FINITE CRACKS IN AN ANTI-PLANE STRAIN ELASTIC SOLID

The transient problem of finite cracks with vanishing thickness in an anti-plane strain solid is investigated by finite element method. The infinitesimally thin crack with traction free on both faces of the crack is simulated by the energy-sharing-node technique. The following cases are considered: (a) One finite line crack in a whole space subjected to (i) a concentrated line source and (ii) an inclined incident SH plane wave. (b) Two cracks in a whole space subjected to an inclined incident SH plane wave. Emphasis has been laid on the quantitative evaluation of the dynamic disturbances for the problem in the interference stage, which is generally difficult to be obtained by analytical approaches. The synthetic seismograms for displacements along the crack surfaces, which cover a period up to an instant of time during which the second order scattering from crack tips can be observed, are presented. Snapshots of the scattered displacement field for each case are also displayed so that the generations of the scatterings and the processes of the wave propagations can be clearly visualized. The two-dimensional wave propagation for transient acoustic problem and electromagnetic problem with the same nature of boundaries can be analogously obtained.