In electromagnetism and materials science, the Jiles–Atherton model of magnetic hysteresis was introduced in 1984 by David Jiles and D. L.
[1] This is one of the most popular models of magnetic hysteresis.
Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material.
[2] Jiles–Atherton model enables calculation of minor and major hysteresis loops.
[1] The original Jiles–Atherton model is suitable only for isotropic materials.
[1] However, an extension of this model presented by Ramesh et al.[3] and corrected by Szewczyk [4] enables the modeling of anisotropic magnetic materials.
: Original Jiles–Atherton model considers following parameters:[1] Extension considering uniaxial anisotropy introduced by Ramesh et al.[3] and corrected by Szewczyk [4] requires additional parameters: Effective magnetic field
However, measurements of anhysteretic magnetization are very sophisticated due to the fact, that the fluxmeter has to keep accuracy of integration during the demagnetization process.
As a result, experimental verification of the model of anhysteretic magnetization is possible only for materials with negligible hysteresis loop.
is determined on the base of Boltzmann distribution.
In the case of isotropic magnetic materials, Boltzmann distribution can be reduced to Langevin function connecting isotropic anhysteretic magnetization with effective magnetic field
is also determined on the base of Boltzmann distribution.
[3] However, in such a case, there is no antiderivative for the Boltzmann distribution function.
In the original publication, anisotropic anhysteretic magnetization
It should be highlighted, that a typing mistake occurred in the original Ramesh et al.
), the presented form of anisotropic anhysteretic magnetization
Physical analysis leads to the conclusion that the equation for anisotropic anhysteretic magnetization
was confirmed experimentally for anisotropic amorphous alloys.
[4] In Jiles–Atherton model, M(H) dependence is given in form of following ordinary differential equation:[6] where
[7] This model is especially suitable for finite element method computations.
It uses the Runge-Kutta algorithm for solving ordinary differential equations.
[8] The two most important computational problems connected with the Jiles–Atherton model were identified:[8] For numerical integration of the anisotropic anhysteretic magnetization
In GNU Octave this quadrature is implemented as quadgk() function.
For solving ordinary differential equation for
It was observed, that the best performing was 4-th order fixed step method.