Coupling Magneto-Electro-Elastic Multiscale Finite Element Method for Transient Responses of Heterogeneous MEE Structures

Magneto-electro-elastic (MEE) materials are widely utilized across various fields due to their multi- field coupling effects. Consequently, investigating the coupling behavior of MEE composite materials is of significant importance. The traditional finite element method (FEM) remains one of the primary approaches for addressing such issues. However, the application of FEM typically necessitates the use of a fine finite element mesh to accurately capture the heterogeneous properties of the materials and meet the required computational precision, which inevitably leads to a reduction in computational efficiency. To enhance the computational accuracy and efficiency of the FEM for heterogeneous multi-field coupling problems, this study presents the coupling magneto-electro-elastic multiscale finite element method (CM-MsFEM) for heterogeneous MEE structures. Unlike the conventional multiscale FEM (MsFEM), the proposed algorithm simultaneously constructs displacement, electric, and magnetic potential multiscale basis functions to address the heterogeneity of the corresponding parameters. The macroscale formulation of CMMsFEM was derived, and the macroscale/microscale responses of the problems were obtained through up/downscaling calculations. Evaluation using numerical examples analyzing the transient behavior of heterogeneous MEE structures demonstrated that the proposed method outperforms traditional FEM in terms of both accuracy and computational efficiency, making it an appropriate choice for numerically modeling the dynamics of heterogeneous MEE structures.