Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations
This work addresses the problem of accurately modeling magneto-mechanical interactions in materials with flexomagnetic effects for researchers in continuum mechanics and materials science, representing an incremental advancement by introducing new tensor couplings.
The authors tackled the modeling of flexomagnetism at finite deformations by proposing Cosserat micropolar and couple-stress continuum models that couple micro-dislocation with magnetization using a Lifshitz invariant, resulting in models that allow centrosymmetric materials with a single flexomagnetic constant and cubic-symmetric materials with two constants, with numerical results confirming physical plausibility and computational feasibility.
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.