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

TL;DR

This paper introduces nonlinear continuum models for flexomagnetism using Cosserat micropolar and couple-stress theories, coupling micro-dislocation tensors with magnetisation via third-order tensors, enabling analysis of centrosymmetric and cubic materials.

Contribution

The authors develop novel finite deformation flexomagnetic models based on micropolar and couple-stress theories with third-order tensor couplings, expanding the modeling capabilities for symmetric magnetic materials.

Findings

Models incorporate a single flexomagnetic constant for centrosymmetric materials.

Numerical simulations confirm the models' physical plausibility.

The approach simplifies coupling tensors compared to conventional strain-gradient methods.

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.