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Discrete-to-continuum limit of magnetic forces. (English. Abridged French version) Zbl 1038.74018

Summary: We derive a formula for forces within a magnetized body, starting from a discrete configuration of magnetic dipoles on a Bravais lattice. The resulting force consists of the usual (nonlocal) volume term and an additional local surface term, whose coefficients involve a singular sum over the lattice. The force thus obtained is different from the usual continuum expression, reflecting the different characters of lattice regularization of the underlying hypersingular integral.

MSC:

74F15 Electromagnetic effects in solid mechanics
74A60 Micromechanical theories
82D40 Statistical mechanics of magnetic materials
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