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To study the magnetic shielding and the losses of non‐linear, hysteretic multilayered shields by using fast to evaluate analytical expressions.

In order to evaluate the shield in the frequency domain, the non‐linear shield is divided into a sufficient number of piecewise linear sublayers. Each sublayer has a permeability that is constant (space independent) and complex (to model hysteresis). This expression for the permeability is found from the Preisach model by a Fourier transform. Once H is known in the entire shield, analytical expressions calculate the eddy current losses and hysteresis losses in the material. The validity of the analytical expressions is verified by numerical experiments.

In the Rayleigh region, the shielding factor of perfectly linear material is better than the one of non‐linear metal sheets, but also the eddy current losses are higher. The results of the optimization show that steel is only a useful shielding material at low frequencies.

The analytical method is valid for infinitely long shields and for weak imposed fields in the Rayleigh region.

As the analytical expressions can be evaluated very fast (in comparison with slow finite elements models), many magnetic shields can be compared in parametric studies.

Analytical expressions exist for the shielding factor and the losses of linear materials. In this paper, the method is extended for non‐linear hysteretic materials. The effects of several parameters (material parameters, incident fields parameters) on the shielding and the losses are shown.

Mechanical stress can heavily affect the magnetic behaviour law in ferromagnetic materials. This paper, aims to take into account the effect of mechanical stress into a hystreresis model. This model is implemented in a finite element analysis code and tested in the case of a simple system.

A simple extension of the classical Preisach model is proposed, in which a function linked to the Preisach density is parameterized using the mechanical stress as a supplementary parameter. The methodology is based on experimental measurements for identifying the required function. As a first approach, a linear interpolation is used between the measurements in order to have a continuous evolution of the magneto‐mechanical behaviour. This model has been tested in the case of a steel sheet in which width is not constant in order to obtain a non‐uniform distribution of stress and magnetic flux density.

The model can predict the magneto‐mechanical behaviour with a good accuracy in the case of tensile stress. Implementation of the model in finite element analysis has shown that the model can predict the behaviour of steel sheet subject to a non‐uniform stress distribution.

This paper shows that a classical hysteresis model can be extended to take into account the magneto‐mechanical behaviour. This is useful for the design of electrical machines which are subject to non‐negligible mechanical stress.