Solving 3-D eddy current problem containing thin cracks using dual formulations and shell elements

The thin cracks in three-dimensional eddy current problems, frequently encountered in nondestructive testing applications, are modelled by surface domains of zero thickness. The double layer nodal and edge shell elements are employed in the dual eddy current formulations for the interpolation of scalar and vector potentials in the cracks. With the help of shell elements, the volume integrals corresponding to the magnetic energy and Joule losses in the cracks are transformed to surface integrals. This modelling allows consideration of the field jump across the thin cracks provided that the field continuity on the edge of the crack is correctly taken into account. An eddy current problem in presence of thin cracks is solved using the model and results are compared with those of conventional finite element modelling