An efficient numerical algorithm for crack reconstruction in elastic media by the circular US scanning

In the present work, a direct numerical reconstruction algorithm is proposed, which is applied to the identification of the position and shape of cracks detected in elastic solid samples, in the case when the input data available for the reconstruction is provided by a circular ultrasonic (US) scanner. The US probe gives the far-field back scattered pattern over the full interval of the incident polar angle. The problem is first reduced to a system of basic boundary integral equations. Then the inverse reconstruction problem is formulated as a minimization problem for a certain strongly nonlinear functional. The proposed numerical algorithm is tested on some examples of complex-shaped cracks. Then the influence of the error in the input data on the precision of the reconstruction is studied in detail.