A Multi‐Field Coupled Multiphase Hybrid Finite Element Method for the Piezoelectric Fiber‐Reinforced Composite

The piezoelectric effect in piezoelectric materials facilitates the transformation of mechanical energy into electrical energy, with significant applications in energy generation, aerospace, biomedical engineering and other sophisticated technologies. In this study, a Multi‐field coupled Multiphase hybrid finite element method (MFCMHFEM) is discovered. The multiphase composite material enhances material properties while reducing fracture and fatigue characteristics. In the multiphase material element, independent force and electric displacement fields are established. For each phase, corresponding stress and electric displacement functions are constructed to analyze the piezoelectric composite material. Based on the principle of minimum complementary energy and using the Lagrange multiplier to implement several constraints, the modified complementary energy functional of the multiphase hybrid finite element is derived. The accuracy of the proposed method is ultimately validated by comparing the computational results of the piezoelectric MFCMHFEM model with those from the ABAQUS software through several numerical examples. The model is further employed to investigate the macroscopic equivalent physical and mechanical properties of piezoelectric composites in relation to microstructural details, including the volume ratio of the inclusion to the matrix, the number of inclusions, and the orientation of polarization. This method offers an effective approach to studying the micro‐ and macro‐electromechanical coupling of piezoelectric composites with numerous inclusions.