Müller, Stefan; Schlömerkemper, Anja Discrete-to-continuum limit of magnetic forces. (English. Abridged French version) Zbl 1038.74018 C. R., Math., Acad. Sci. Paris 335, No. 4, 393-398 (2002). 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. Cited in 7 Documents MSC: 74F15 Electromagnetic effects in solid mechanics 74A60 Micromechanical theories 82D40 Statistical mechanics of magnetic materials Keywords:magnetic dipoles; Bravais lattice; volume term; local surface term; singular sum; lattice regularization; hypersingular integral PDFBibTeX XMLCite \textit{S. Müller} and \textit{A. Schlömerkemper}, C. R., Math., Acad. Sci. Paris 335, No. 4, 393--398 (2002; Zbl 1038.74018) Full Text: DOI References: [1] Bobbio, S., Electrodynamics of Materials: Forces, Stresses, and Energies in Solids and Fluids (2000), Academic Press: Academic Press San Diego [2] Brown, W. F., Magnetoelastic Interactions (1966), Springer-Verlag: Springer-Verlag Berlin [3] DeSimone, A.; Podio-Guidugli, P., On the continuum theory of deformable ferromagnetic solids, Arch. Rational Mech. Anal., 136, 201-233 (1996) · Zbl 1002.74521 [4] Eringen, A. C.; Maugin, G. A., Electrodynamics of Continua, Vol. 1: Foundations and Solid Media, Vol. 2: Fluids and Complex Media (1990), Springer-Verlag: Springer-Verlag New York [5] James, R. D., Configurational forces in magnetism with application to the dynamics of a small-scale ferromagnetic shape memory cantilever, Continuum Mech. Thermodyn., 14, 55-86 (2002) · Zbl 1100.74549 [6] James, R. D.; Müller, S., Internal variables and fine-scale oscillations in micromagnetics, Continuum Mech. Thermodyn., 6, 291-336 (1994) · Zbl 0814.73054 [7] A. Schlömerkemper, Magnetic forces in discrete and continuous systems, Doctoral thesis, Leipzig, submitted; A. Schlömerkemper, Magnetic forces in discrete and continuous systems, Doctoral thesis, Leipzig, submitted This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.