On a class of constitutive relations for ferromagnetic hysteresis
type: Item
instance of: scholarly article
title: On a class of constitutive relations for ferromagnetic hysteresis
zbMATH Open document ID: 0631.73093
DOI: 10.1007/BF00282052
author: Bernard D. Coleman
author: Marion L. Hodgdon
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 4026983
zbMATH Keywords: stability of loops
zbMATH Keywords: general oscillations
zbMATH Keywords: first order ordinary piecewise linear differential equation
zbMATH Keywords: unidimensional
zbMATH Keywords: rate independent
zbMATH Keywords: ferromagnetic hysteresis
zbMATH Keywords: magnetic flux density
zbMATH Keywords: magnetic field
zbMATH Keywords: constitutive relation
zbMATH Keywords: unique primitive hysteresis loop
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
cites work: A mathematical foundation for thermodynamics
cites work: On thermodynamics and elastic-plastic materials
cites work: On thermodynamics and intrinsically equilibrated materials
cites work: A constitutive relation for rate-independent hysteresis in ferromagnetically soft materials
full work available at URL: https://doi.org/10.1007/bf00282052
OpenAlex ID: W2012382108
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description: scientific article; zbMATH DE number 4026983