An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations

The applications of fixed-point theorem in optimisation problems

“…The model is readily applied by engineers working on coupled phenomena in ferromagnetic cores [3,12,13,17,19,24]. One of the drawbacks of the description is the difficult and error-prone method of estimation of optimal model parameters, as proposed by one of model developers [15].…”

“…For a step-by-step derivation of the relationship (11) the Readers are referred to [24]. The instant values of magnetic field strength H corresponding to the values of magnetisation M are determined from the constitutive relationship H(t) = B(t)/: 0 !…”

Numerical analysis of hysteresis loss in pulse transformer

“…In order to formulate equation (6) of the discrete model of electromagnetic phenomena it has been assumed that the magnetic properties of a ferromagnetic material are described by the equation H = B/: 0 -M, whereas the magnetization M is determined on the basis of magnetic induction from the inverse Jiles-Atherton model [4,9]. In order to solve the system of non-linear coupled equations (11) and (12), the block relaxation method and the NewtonRaphson algorithm were used.…”

Comparison of macroscopic descriptions of magnetization curves

“…A step-bystep derivation is provided e.g. in [29][30], whereas the differences between subsequent versions and their consequences are discussed in [31].…”

“…all definitions of respective quantities are rigorously followed, it is instructive to follow the logical scheme of calculations for the case of the so-called inverse model, i.e. when in the calculations the input quantity is magnetic flux density B [30,35,43]. The toned for using the inverse model stems from the fact that in magnetic measurements, carried out in accordance with international standards IEC 60404, the shape of magnetic flux density waveform should be kept sinusoidal.…”