WAVE-PROPAGATION IN ELASTIC MEDIA WITH CRACKS .1. TRANSIENT NONLINEARRESPONSE OF A SINGLE CRACK

The transient dynamic response of a single crack to an incident wave i n an infinite elastic medium is studied. Nonlinearity in the response due to contact between crack faces during the motion is taken into acc ount. A regularization of the hypersingular stress integral equation i s presented where the hypersingular integrals are isolated and transfo rmed into regular line integrals along the crack edge. This is made po ssible by giving a suitable form to the infinite-body elastodynamic Gr een tenser. In the case of a penny-shaped crack excited by a normally incident longitudinal wave, explicit formulae are given for a one-dime nsional formulation requiring a discretization only along the crack ra dius. Numerical examples showing the crack response to low-frequency a nd high-frequency incident waves are presented.