Formulation of small-strain magneto-elastic problems

TL;DR

This paper develops a differential geometric formulation for small-strain magneto-elastic problems, revealing algebraic similarities with elasticity and magnetism, facilitating unified modeling and discretization approaches.

Contribution

It introduces a novel differential geometric framework for small-strain magneto-elastic problems, enabling unified algebraic modeling of magnetic, elastic, and magneto-elastic systems.

Findings

Algebraic similarity between small-strain elasticity and magnetism.

Unified modeling approach for magneto-elastic problems.

Framework suitable for discretization methods.

Abstract

Despite of the topical engineering need and all scientific investments, the mathematical formulation of modeling elastic deformations in magnetic systems is not yet fully established. Often, especially in electrical engineering applications, a model assuming small (infinitesimal) strains seems sufficient. To express such small-strain magneto-elastic problems in a suitable form for discretization methods, we present here a formulation in the framework of differential geometry. The given analysis shows algebraic similarity between small-strain elasticity and magnetism. This suggests that a class of magnetic, elastic, and magneto-elastic problems may be modeled in the same algebraic category, constituting suitable domain for discretizations.