本研究探討了磁電複合材料的有效非線性和時間相依的磁電行為。磁電耦合響應是由磁致伸縮相和壓電相之間的相互作用引起的。根據複合材料的結構，耦合可以通過應變介導或電荷介導的效應發生。特別關注磁電複合材料中的柔性壓電陶瓷和壓電聚合物，觀察到這些複合材料的響應隨時間呈現的黏彈性行為。為了預測磁電複合材料的有效響應，採用了簡化的unit-cell微觀力學模型。將微觀結構表示為立方體subcells的週期陣列，通過分析代表性體積元素的行為來表徵宏觀行為。使用非線性和時間相依的本構方程，需要應用增量形式將非線性關係線性化。為了驗證數學預測，與現有文獻中的實驗數據進行了比較。所提出的數學模型涵蓋了關於粒子增強和纖維增強磁電複合材料的全面的參數研究。這些研究調查了材料非線性、體積分率、磁場加載速率、施加預應力和施加磁場方向的影響。這些參數研究有助於了解磁電複合材料，特別強調了柔性壓電材料的作用以及其對時間相依響應的影響。研究結果對於設計和工程磁電複合材料具有實際意義，可以實現其性能的定制和優化。

This study investigates the effective nonlinear and time-dependent magnetoelectric behavior of magnetoelectric composites. The magnetoelectric coupling response arises from the interaction between the magnetostrictive and piezoelectric phases. Depending on the composite architecture, the coupling can occur through strain-mediated or charge-mediated effects. Special attention is given to flexible piezoelectric ceramics and piezoelectric polymers in magnetoelectric composites. It is observed that the response of these composites can exhibit viscoelastic behavior over time. To predict the effective response of magnetoelectric composites, a simplified unit-cell micromechanical model is employed. The microstructure is represented as a periodic array of cubic subcells, enabling the characterization of macroscopic behavior by analyzing representative unit cells. Nonlinear and time-dependent constitutive equations are used, requiring the application of incremental formulations to linearize the nonlinear relations. To validate the mathematical predictions, experimental data available in the literature are compared. The proposed mathematical model encompasses a comprehensive set of parametric studies on particle-reinforced and fiber-reinforced magnetoelectric composites. These studies investigate the influence of material nonlinearity, constituent volume fraction, magnetic field loading rate, applied prestress, and applied magnetic field direction. The parametric studies contribute to the understanding of magnetoelectric composites, particularly emphasizing the role of the soft piezoelectric material and its impact on time-dependent responses. The findings have practical implications for the design and engineering of magnetoelectric composites, allowing for the tailoring and optimization of their properties.

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