This work investigates a 2D vector field behavioral model to describe the anisotropic magnetic permeability and losses in Grain Oriented Electrical Steels (GOES) within quasi-static and magneto-harmonic working conditions. The model includes the an-hysteretic magnetic field driven by the total anisotropy, the coercive force responsible for the quasi-static hysteresis losses and the dynamic damping eddy field responsible for the extra losses. Each field contribution requires the definition of a tensor property whose diagonal and non diagonal coupling components are experimentally identified as a function of the flux density magnitude B and its angle  with the Rolling direction (RD). The static behavior is identified at low frequency and the dynamic one takes the frequency dependent field diffusion into account. Diagonalization tools reveal main characteristic magnetic axis for the separate properties with deflections at the macroscale.

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