磁電效應指的是在施加的磁場下產生的電極化強度，反之亦然在施加的電場下產生的磁化強度。三相磁電彈複合材料為彈性層中嵌入壓電層和壓磁層，並展現磁場，電場和機械場之間的耦合。這種類型的複合材料比壓電和壓磁材料直接結合的兩相磁電複合材料具有更好的延展性和可塑性。壓電和壓磁材料本身具有脆性和不順應性，因此包含這兩個相的複合材料會受到脆性斷裂的影響。因此本研究採用廣義版單位晶格模型來介紹三相磁電彈複合材料的有效磁電效應。為了進行比較，我們還建立了完善的 Mori – Tanaka 模型。這些基於代表性體積元素的微觀力學模型用於預測連續多相複合材料的有效響應。廣義版單位晶格模型可以辨別每個相的特殊排列方式及相體積分數等等。因此他可以呈現出應用中多相複合材料的真實反應。三相電磁彈性複合材料的非線性本構方程和隨時間變化的行為是必須考慮。這是因為聚合物材料在機械負載，溫度等的共同作用下會產生時間依賴性。由於材料的非線性和非線性本構方程式可以良好地捕獲實驗數據，因此考慮非線性行為是必不可少的。為了使線性本構方程式能獲得整體響應，使用定點迭代法來減少線性化非線性磁電效應及時間相關行為所造成的誤差。實驗結果與微觀力學模型所預測的有效響應有良好的一致性。呈現出具有纖維，顆粒和層板連接性的三相電磁彈性複合材料的參數研究。

The magnetoelectric effect is defined as the electric polarization produces under an applied magnetic field or vice versa as the magnetization produces under an applied electric field. A three phase magneto-electro-elastic composite which consists of piezomagnetic reinforcement and piezoelectric reinforcement embedded with elastic matrix reveals the coupling between the magnetic field, the electric field and mechanical field. This type composite would has more excellent ductility malleability and formability than a two phase magneto-electric composite which is bonded directly with piezoelectric and piezomagnetic material. The piezoelectric and piezomagnetic material are inherently brittle and noncompliant, hence a composite which contains these two phases would impact on brittle fracture. As a result, this study introduces the effective magneto-electric effect of magnetoelectric-elastic three-phase composites with the micromechanical generalized method of cells model. For the comparison, we also build the well-established Mori–Tanaka model. These micromechanical models which are based on averaging of a representative volume element is employed for the prediction the effective responses of continuous multiphase composites. The generalized method of cells model recognizes the special arrangements for each phase, phase volume fractions and so on. Therefore, it can present true reflector of the multiphase composite applied on applications. It is essential that consider the nonlinear constitutive equations and time-dependent behavior for three-phase magneto-electric-elastic composites. This is because the time-dependent behaviors of polymeric materials under combination of mechanical loading, temperature, and so on. Due to the material nonlinearity and the nonlinear constitutive equations which can capture well the experimental results, it is essential to consider the nonlinear behaviors. In order that linear constitutive laws are used to attain the overall behaviors, a fixed-point iteration is applied to decrease errors from linearizing the nonlinear magneto-electric effect and time-dependent behaviors. The effective responses of the prediction are validated with the experimental results. Parametric studies are presented for three-phase magneto-electric-elastic composites with fiber-, particle- and lamina- connectivity.

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