Computational Homogenization in Micro‐Magneto‐Elasticity. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Sridhar, Ashish; Keip, Marc‐André; Miehe, Christian
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 363
• Page End: 364
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510172
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>The overall macroscopic response of magneto‐mechanically coupled materials stems from complex magnetization evolution and corresponding domain wall motion occurring on a lower length scale. In order to account for such effects we propose a computational homogenization approach that incorporates a <italic>ferromagnetic phase‐field formulation</italic> into a macroscopic Boltzmann continuum. This scale‐bridging is obtained by rigorous definition of <italic>rate‐type and incremental variational principles</italic>. An extended version of the classical Hill‐Mandel macro‐homogeneity condition is obtained as a consequence. In order to satisfy the unity constraint of the magnetization on the micro‐scale, an efficient <italic>operator‐split</italic> method is proposed. (© 2015 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>