Modeling of thin structures in eddy current testing with shell elements

Abstract

Abstract. The modeling and design of eddy currents sensors for non-destructive testing applications, generally, requires numerical methods. Among these methods, the finite element method is one of the most used. Indeed, it presents a great capability to treat a large variety of configurations. However, in the study of eddy current testing problems, the existence of structures that have a geometrical dimension smaller than the others (thin air gaps, coatings...) will lead to difficulties related to the meshing process. The introduction of particular elements such as shell elements allows to simplify the modeling of these problems. In this paper, the shell elements are used in two different 2D axisymmetric formulations, the electric formulation a * and the magnetic formulation t-φ in order to simulate the behaviour of the electromagnetic fields. The results obtained with the two formulations are compared with analytical solutions.PACS. 81.70.-q Methods of materials testing and analysis -07.05.Tp Computer modeling and simulation

A simple integral formulation for the modeling of thin conductive shells

“…In order to take into account the surrounding air region, it remains to couple both equations. In [2][3][4][5][6][7][8], the authors choose to use the finite-element method (FEM), thus they need to mesh the air region. In [1], a boundary element method (BEM) is preferred but the authors have to manage the coupling on both sides of the shell and have to determine if both sides of the shell are interfaced with a single region or with two different ones.…”

“…Equations ( 2) and ( 3) are written on the averaged surface Γ of the thin region. Subtracting equations ( 3) and (2) leads to:…”

“…Furthermore, when frequency is high, skin depth can become much thinner than thickness e, leading to an increase of the size of the mesh if this effect has to be properly modeled. Shell element formulations have been developed to overcome such difficulties, e.g., with the boundary element method (BEM) [1], with the finite-element method (2D formulation [2] and 3D formulation [3][4][5][6][7][8]), and with an integral method recently, proposed by the authors of this paper [9].…”

“…In [9], a general shell element formulation for modeling thin conductive regions has been proposed (δ e or δ ≈ e or δ e). Like in [1][2][3][4][5][6][7][8], this element takes into account the field variation through depth due to skin effect. The shell is modeled by an integral formulation avoiding the mesh of air region.…”