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Thermodynamically-Consistent Modeling of Ferromagnetic Hysteresis.

Claudio Giorgi1, Angelo Morro2

  • 1Dipartimento di Ingegneria Civile Ambiente Territorio Architettura e Matematica, Università di Brescia, Via Valotti 9, 25133 Brescia, Italy.

Materials (Basel, Switzerland)
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Summary

This study models ferromagnetic hysteresis using thermodynamics, ensuring constitutive properties obey the second law. The research details how entropy production explains distinct loading and unloading behaviors in magnetic materials.

Keywords:
ferromagnetic hysteresismagnetic susceptibilitymagnetizationrate equationsthermodynamic consistency

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Area of Science:

  • Thermodynamics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Ferromagnetic hysteresis is a key phenomenon in magnetic materials.
  • Understanding hysteresis is crucial for applications in data storage and magnetic devices.
  • Existing models often lack a rigorous thermodynamic foundation.

Purpose of the Study:

  • To develop a thermodynamic model for ferromagnetic hysteresis.
  • To incorporate the second law of thermodynamics (Clausius-Duhem inequality) into hysteresis modeling.
  • To explain the origin of distinct loading and unloading behaviors in hysteresis loops.

Main Methods:

  • A thermodynamic approach was employed, adhering to Euclidean invariance.
  • Entropy production was treated as a non-negative constitutive function.
  • A nonlinear ordinary differential system was solved to obtain hysteresis cycles.

Main Results:

  • A constitutive framework was established for ferromagnetic hysteresis based on thermodynamic principles.
  • The model demonstrates that entropy production is essential for capturing asymmetric loading/unloading behavior.
  • A detailed one-dimensional model for magnetization was derived, validated with simulations for soft iron.

Conclusions:

  • The thermodynamic approach provides a robust framework for modeling ferromagnetic hysteresis.
  • The proposed model successfully accounts for the observed hysteretic behavior in magnetic materials.
  • This work offers a foundation for developing more accurate predictive models for magnetic materials.