On Variationally‐Consistent Homogenization Approaches in Multi‐Phase Magnetic Solids

On Variationally‐Consistent Homogenization Approaches in Multi‐Phase Magnetic Solids It is well known that classical homogenization schemes, such as the Taylor/Voigt and Reuss/Sachs assumptions, can also be interpreted as energetic bounds. Furthermore, energy relaxation concepts have been established that determine stable effective material responses based on appropriate (convex, quasi‐convex, rank‐one) energy hulls for non‐convex energy landscapes associated with multi‐phase materials, see [1–3] and references therein. Our goal is to propose analogous relaxation based homogenization schemes for magnetizable solids. More specifically, we propose a magnetic potential perturbation scheme which yields relaxed effective free energy densities that simultaneously satisfy magnetic induction and magnetic field strength compatibility requirements—i.e. the magnetostatic Maxwell equations—at the phase boundary. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

On Variationally‐Consistent Homogenization Approaches in Multi‐Phase Magnetic Solids

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710228
Publisher site
See Article on Publisher Site

Abstract

It is well known that classical homogenization schemes, such as the Taylor/Voigt and Reuss/Sachs assumptions, can also be interpreted as energetic bounds. Furthermore, energy relaxation concepts have been established that determine stable effective material responses based on appropriate (convex, quasi‐convex, rank‐one) energy hulls for non‐convex energy landscapes associated with multi‐phase materials, see [1–3] and references therein. Our goal is to propose analogous relaxation based homogenization schemes for magnetizable solids. More specifically, we propose a magnetic potential perturbation scheme which yields relaxed effective free energy densities that simultaneously satisfy magnetic induction and magnetic field strength compatibility requirements—i.e. the magnetostatic Maxwell equations—at the phase boundary. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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