Mathematics and Mechanics of Solids· 2026Q2
On the single-field formulation in magnetostatics
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- 2026year
Short summary
A single-field formulation for magnetostatics using only magnetic induction is shown to be equivalent to dual formulations involving magnetization and magnetic field, even when coupled with elasticity.
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Key points
- Equivalence established between single-field (magnetic induction) and dual-field (magnetization/magnetic field) magnetostatic formulations.
- Equivalence is maintained when magnetostatics is coupled with elasticity.
- Legendre–Fenchel transforms can compute energy densities, but functionals lack standard convex duality.
- Convexity and coercivity of functionals are not prerequisites for the transformation and are not always preserved.
AI-generated from the title and abstract; the full text is not read.
Abstract
We systematically discuss the equivalence of two variational formulations of magnetostatics, in terms of magnetization and magnetic field, on the one hand, and the single-field formulation using only magnetic induction. To demonstrate that this link is stable also when the magnetic laws are coupled with other variational static models, elasticity is included in the models as well. Interestingly, even though the corresponding magnetoelastic energy densities in the material can be computed via Legendre–Fenchel transform in the magnetic state variables, the two formulations are not linked by standard convex duality on the level of the functionals. In addition, convexity and coercivity of the given functional are neither required for the transformation nor always preserved by it.
The authors' abstract, as published at the source. Mathematics and Mechanics of Solids, 2026 · DOI ↗
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Field: Electronic, Optical and Magnetic Materials
Electronic, Optical and Magnetic MaterialsMaterials Science