Analytical methods of solution to eddy current interaction problems
The eddy current method is used for nondestructive evaluation of conducting materials. To achieve a greater knowledge and insure safe and reliable evaluation methods, the use of mathematical models is needed. In this thesis analytical methods of solutions are applied to solve the eddy current interaction problem which essentially is a scattering problem. This involves a Green's function technique to generate integral relations between the surface fields and the fields everywhere else. Then the key is to use suitable basis functions to describe the surface fields. In the end numerical integration is used to get the solution, the change of impedance due to the scatterer. The scatterer in this case is a model of a defect and the source is a single conductor or a single coil. The solutions are compared to Finite Element solutions.
This thesis includes two papers where two different methods of solution have been used. In the first paper, the T matrix method is applied on a 2D problem with a subsurface defect. The second paper presents a boundary integral equation method solution to a problem with a surface-breaking flat crack.
Boundary integral equation