Eddy current model for nondestructive evaluation with thin cracks (Q2800430)

The forward problem of eddy current nondestructive evalutation for large steel structures with comprised interior cracks is studied. The thickness of cracks are very thin compared with the characteristic length of the system. To avoid meshing a thin structure, the authors propose an approximate eddy current model. It replaces the crack with an interior interface. The existence and uniqueness of the approximate solutions are presented. It is proved that the approximate solution convergences to the solution of the original problem as \(d\to 0\), where \(d\) denotes the thickness of cracks. An error estimate for constant conductivity is evaluated. The finite element approximation to the approximate eddy current model is studied. The well-posedness of the discrete problem is proved. To validate the approximation of the approximate eddy current model to the original eddy current problem, the authors consider two benchmark problems. The numerical experiments for both the original problem and the approximate problem are carried out. The presented results agree with each other.