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Variational modeling and homogenization in dissipative magneto‐mechanics
Author(s) -
Ethiraj Gautam,
Sridhar Ashish,
Miehe Christian
Publication year - 2015
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201510004
Subject(s) - homogenization (climate) , dissipative system , multiscale modeling , finite element method , continuum mechanics , macro , computer science , classical mechanics , statistical physics , mechanics , mathematics , physics , thermodynamics , chemistry , biodiversity , ecology , computational chemistry , biology , programming language
The aim of this work is to present new variational‐based modeling and homogenization approaches in dissipative magneto‐mechanics. On the modeling side, the presented constitutive models are motivated by the underlying physical phenomena at the micro‐ and nano‐scale that are embedded in appropriate variational‐based finite element frameworks. We discuss aspects that are characteristic to magneto‐mechanical problems such as the unity constraint on the magnetization, the inclusion of the surrounding free‐space, the micro‐mechanics of the coupled response etc. Following a hierarchical structure of scales, we present new variational principles for three model scenarios: (i) The modeling of magnetic domains at a micro‐level, (ii) the modeling of magnetorheological elastomers at a macro‐level and (iii) a homogenization‐based scale bridging scenario. Numerical simulations are outlined in each focus area in order to demonstrate the salient features of the variational‐based formulations. From the theoretical and computational standpoint, this work aims to contribute a building block to the ultimate goal of construction of a compatible hierarchy of computational models for magneto‐mechanically coupled materials. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)