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.

翻译：我们提出了基于Cosserat微极理论及其衍生偶应力理论的几何非线性（有限）挠曲磁连续介质模型。这些模型通过利用Lifshitz不变量将微极模型的微位错张量与磁化矢量耦合，从而引入磁-力学相互作用。与使用四阶张量将应变梯度与磁化耦合的传统公式不同，我们的方法依赖于三阶张量耦合，这是因为微位错本身是二阶张量。因此，该模型允许具有单一新挠曲磁常数的中心对称材料，更一般地允许具有两个此类常数的立方对称材料。我们建立了挠曲磁作用泛函，并分别使用标量和矢量磁势公式推导了相应的控制方程，同时给出了纳米梁结构的数值计算结果，验证了模型的物理合理性与计算可行性。