A Homogenized Energy Framework for Ferromagnetic Hysteresis
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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In this paper, we develop a macroscopic framework quantifying the hysteresis and constitutive nonlinearities inherent to ferromagnetic materials. In the first step of the development, we construct Helmholtz and Gibbs energy relations at the mesoscopic or lattice level based on the assumption that magnetic moments or spins are restricted to two orientations. Direct minimization of the Gibbs energy yields local average magnetization relations appropriate for operating regimes in which relaxation mechanisms are negligible, whereas the balance of the Gibbs and relative thermal energies through Boltzmann principles provides local models which incorporate mechanisms such as thermal after-effects. To construct macroscopic relations that incorporate material nonhomogeneities, poly-crystallinity, and variable effective fields, we employ stochastic homogenization techniques based on the assumption that parameters such as local coercive and interaction fields are manifestations of underlying distributions. The resulting framework quantifies in a natural manner the anhysteretic magnetization provided by decaying AC fields and guarantees the closure of biased minor loops once transient accommodation and after-effects are complete. Furthermore, noncongruency is achieved with certain choices for the energy functionals. Hence the framework provides an energy basis for certain extended Preisach models and the relation of the framework to several macroscopic hysteresis models is detailed. The behavior of both the nonlinear anhysteretic relations and full hysteresis model are validated through comparison with experimental steel and nickel data.
- Properties of Metals and Alloys
- Numerical Mathematics
- Electricity and Magnetism