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Application de la méthode des éléments finis pour la modélisation de configurations de contrôle non destructif par courants de Foucault

Abstract : The works presented in this thesis deal with the modelling of Eddy Current Testing (ECT) configurations using the Finite Element Method (FEM). A FEM solver code programmed in the C++ language, based on the 3D discretization of the Maxwell's equations in harmonic mode has been developed. Two dual magnetodynamic combined potentials formulations "a − psi " and "t − phi" have been implemented. First order tetrahedral Whitney elements have been used. The scalar potentials are discretized at the nodes of the elements and the vector potentials at their edges. The work presented in this thesis addresses a precise case but with a great importance among the ECT applications. It consists in the defects having a weak opening (cracks), which are frequently encountered in ECT. Their detection allows to prevent the destruction of the parts under operation and to increase the reliability of the industrial products. Taking into account cracks in the finite element method can be delicate because their mesh led to a strong density of elements or deformed ones. In this context, a model has been developed to simplify the modelling of this type of defects. The idea consists in considering the crack as a non-conducting surface impermeable to the current. To ensure the good behaviour of the electromagnetic field, appropriate boundary conditions are applied at the crack surface. These conditions are taken into account by the electric formulation a − psi by duplicating the degrees of freedom (electric scalar potential) attached to the nodes of the crack surface and by the magnetic formulation t − phi by setting to zero the circulation of the electric potential vector on the edges belonging to the crack surface. The simultaneous resolution of the two formulations a − psi and t − phi by the FEM allows to verify all the Maxwell's equations strongly. The results obtained are supplemented and the numerical errors due to the discretization appear in the form of a non-verification of the behaviour laws. This has allowed, by using this property of complementarity of the two formulations, to define error indicators in order to develop an automatic mesh adaptation procedure. Several type of error estimators were defined and were studied on different problems.
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Contributor : Yahya Choua <>
Submitted on : Wednesday, February 10, 2010 - 11:45:15 AM
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  • HAL Id : tel-00455379, version 1


Yahya Choua. Application de la méthode des éléments finis pour la modélisation de configurations de contrôle non destructif par courants de Foucault. Modélisation et simulation. Université Paris Sud - Paris XI, 2009. Français. ⟨tel-00455379⟩



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