On a class of constitutive relations for ferromagnetic hysteresis
This paper deals with a very detailed analysis of the first order ordinary piecewise linear differential equation which describes the phenomenon of unidimensional, rate independent, ferromagnetic hysteresis by relating the magnetic flux density to the magnetic field. This constitutive relation is rather general in that it contains quite arbitrary material functions subject only to some minimal restrictions imposed by physical, mainly thermodynamical, requirements. The authors show that a unique primitive hysteresis loop can be attained and the energy expended in a single complete transversal of that loop is positive. Finally they deduce conclusions about the asymptotic behaviour under oscillatory magnetic fields which prove that primitive loop with specified extreme values of the magnetic field can be realized in practice as a limit of repeated oscillations.
first order ordinary piecewise linear differential equation
scientific article; zbMATH DE number 4026983