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arXiv · 2511.22756

Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations

Adam Sky·David Codony·Stephan Rudykh·Andreas Zilian·Stéphane P. A. Bordas·Patrizio Neff
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Abstract

We propose geometrically nonlinear (finite) continuum models of flexomagnetism based on the Cosserat micropolar and its descendent couple-stress theory. These models introduce the magneto-mechanical interaction by coupling the micro-dislocation tensor of the micropolar model with the magnetisation vector using a Lifshitz invariant. In contrast to conventional formulations that couple strain-gradients to the magnetisation using fourth-order tensors, our approach relies on third-order tensor couplings by virtue of the micro-dislocation being a second-order tensor. Consequently, the models permit centrosymmetric materials with a single new flexomagnetic constant, and more generally allow cubic-symmetric materials with two such constants. We postulate the flexomagnetic action-functionals and derive the corresponding governing equations using both scalar and vectorial magnetic potential formulations, and present numerical results for a nano-beam geometry, confirming the physical plausibility and computational feasibility of the models.

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Adam Sky, David Codony, Stephan Rudykh, Andreas Zilian, Stéphane P. A. Bordas, Patrizio Neff. 2025-11-27. Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations. https://arxiv.org/abs/2511.22756

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