The expressions of the material derivative of differential forms in the language of vector analysis are introduced. These formulae allow us to describe naturally the electromechanical coupling, and the coupling term appears to be a volume integral. A general approach to compute forces is then proposed, which takes that fact into consideration. The method is applicable in 2D and 3D with dual formulations. Numerical evidences of its efficiency are given.
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Henrotte et al. (2004) studied this question.