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EDDY CURRENT MODEL FOR NONDESTRUCTIVE EVALUATION WITH THIN CRACKS
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DOI：10.1137/15M1015492.png)
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In this paper, we propose an approximate eddy current model for nondestructive evaluation. Interior cracks of large steel structures are very thin compared with the characteristic length of the system. Numerical methods usually necessitate very fine meshes to characterize the small thickness of cracks, and thus yield a very large number of degrees of freedom. The proposed model neglects the thickness of cracks and treats them as interior surfaces. The existence and uniqueness are established for the approximate solution upon introducing proper gauge conditions. The convergence of the approximate solution to the solution of the original eddy current problem is proved as the thickness of cracks tends to zero, and an error estimate is presented for homogeneous conducting materials. A coupled finite element method is proposed to solve the approximate problem. The well-posedness and the error estimate are proved for the discrete solution. Numerical experiments are carried out for engineering benchmark problems to validate the approximate eddy current model and to demonstrate the efficiency of the finite element method.
Keyword:
eddy current problem
Maxwell's equations
finite element method
nondestructive evaluation
thin crack
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