This work presents the analytical solution to the multi-fields in the whole domain of 3D multiferroic materials with an ellipsoidal inclusion/inhomogeneity induced by eigenfields and remote loads. It is a unified approach for the fully-coupled analysis of single-phase multiferroic materials and multiferroic composite materials, which are verified by comparing with available results in the literature and finite element analysis. It is found that, inside the inclusion, the magnetic field due to the spontaneous polarization and the electric field due to the spontaneous magnetization increase monotonically with the aspect ratio of the inclusion for single-phase multiferroic materials, but they first increase and then decrease with the aspect ratio of the inclusion for multiferroic composite materials with much larger maximum magnitudes. Moreover, in the matrix of the piezoelectric-piezomagnetic heterostructure, some components of the multi-fields change dramatically with the aspect ratio of the inhomogeneity, but other components vary insignificantly. Furthermore, although the generalized strain field is usually not uniform in the matrix, the uniformity condition could be still achieved by tuning the eigenfields and remote loads even regardless of the specific shape of the ellipsoidal inhomogeneity. These results could be helpful for the design of multiferroic materials.

中文翻译：

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特征场和远程负载引起的多铁材料中的多场

这项工作提出了 3D 多铁性材料整个域中多场的解析解，该材料具有由特征场和远程载荷引起的椭圆体夹杂物/不均匀性。它是单相多铁材料和多铁复合材料全耦合分析的统一方法，并通过与文献和有限元分析中的现有结果进行比较得到验证。研究发现，对于单相多铁材料，夹杂物内部自发极化产生的磁场和自发磁化产生的电场均随夹杂物长宽比单调增加，但随夹杂物长宽比的变化先增加后减少。具有更大最大值的多铁复合材料的夹杂物的纵横比。此外，在压电-压磁异质结构的矩阵中，多场的一些分量随着不均匀性的纵横比而发生显着变化，但其他分量变化不显着。此外，尽管广义应变场在矩阵中通常不均匀，但即使不考虑椭球不均匀性的具体形状，仍然可以通过调整特征场和远程载荷来实现均匀性条件。这些结果可能有助于多铁材料的设计。