Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. Part I: Analysis

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• 作者：Nikola Popovi? ; Dirk Praetorius and Anja Schl?merkemper
• 关键词：Magnetostatics ; Magnetic force formulae ; Potential theory ; Partial differential equations ; Lattice ; to ; continuum limit
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2007
• 出版时间：June, 2007
• 年：2007
• 卷：19
• 期：1-2
• 页码：67-80
• 全文大小：209 KB
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Engineering Thermodynamics and Transport Phenomena
  Mechanics, Fluids and Thermodynamics
  Structural Materials
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0959

文摘

The mathematical and physical analysis of magnetoelastic phenomena is a topic of ongoing research. Different formulae have been proposed to describe the magnetic forces in macroscopic systems. We discuss several of these formulae in the context of rigid magnetized bodies. In case the bodies are in contact, we consider formulae both in the framework of macroscopic electrodynamics and via a multiscale approach, i.e., in a discrete setting of magnetic dipole moments. We give mathematically rigorous proofs for domains of polygonal shape (as well as for more general geometries) in two and three space dimensions. In an accompanying second article, we investigate the formulae in a number of numerical experiments, where we focus on the dependence of the magnetic force on the distance between the bodies and on the case when the two bodies are in contact. The aim of the analysis as well as of the numerical simulation is to contribute to the ongoing debate about which formula describes the magnetic force between macroscopic bodies best and to stimulate corresponding real-life experiments.