Homogenized eddy current model for non‐destructive testing of metallic cables

Valdemar Melicher (Research Group for Numerical Analysis and Mathematical Modelling, Department of Mathematical Analysis, Ghent, Belgium)
Peter Sergeant (Department of Electrical Energy, Systems and Automation, Ghent University and Department of Electrotechnology, Faculty of Applied Engineering Sciences, University College Ghent, Ghent, Belgium)



This paper aims to derive a simple and effective but still a reasonably accurate model for electromagnetic problems with hysteretic magnetic properties and/or induced currents in heterogeneous regions in 2D, meant particularly for non‐destructive testing (NDT) of steel cables by eddy‐currents.


It is assumed that the diffusion of electromagnetic fields in a heterogeneous cable, which consists of many strands, can be described by the Maxwell equations with periodically oscillating coefficients. A computationally efficient model can then be derived. The idea behind this is to replace the heterogeneous material in the cross‐section by a fictitious homogeneous one, whose behaviour at the macroscopic level is a good approximation of the one of the composite material. Such a homogenized model is obtained by employing the two‐scale convergence.


The model is validated based on experimental electromagnetic data from a steel cable (measured magnetic hysteresis loops) to show that the model is applicable for NDT of cables. The model is useful for studying NDT of cables, both for excitation at low frequency (where changes in magnetic properties are investigated) and at higher frequency (eddy current testing). It is valid for a wide range of amplitudes and frequencies.


From the mathematical point of view the model incorporated a non‐local boundary condition that has to be included in the analysis. From the engineering point of view, by solving an inverse problem based on this model and on measured hysteresis loops at several frequencies, a broader range of defects in the cable can be detected.



Melicher, V. and Sergeant, P. (2012), "Homogenized eddy current model for non‐destructive testing of metallic cables", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 31 No. 6, pp. 1656-1680. https://doi.org/10.1108/03321641211267056

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