本研究提出一個基於微觀力學的本構模型方法，用於分析由主動磁致伸縮材料及黏彈性聚合物基質所組成的複合材料之整體非線性及時變響應。其中，磁致伸縮的加強材在施加大驅動磁場的情況下表現出明顯的非線性響應，而聚合物則表現出明顯的非線性黏彈性行為，特別是在高溫下操作。因此，磁致伸縮複合材料的整體響應可能具有明顯的時變性。為磁致伸縮複合材料制定了簡化的單位晶格微觀力學模型，用於求得微觀局部場變量及宏觀複合材料外加場變量的線性映射矩陣－concentration tensors。由於這些成分的材料非線性應用到線性的微觀力學關係式會有不相容的狀況，因此首先利用線性化的本構關係來獲得磁致伸縮複合材料總體響應的猜值，然後透過迭代方法來校正線性化非線性響應的誤差。本研究呈現了三種複合材料系統的數值模擬結果，分別是磁致伸縮薄板、長纖維和顆粒嵌入非線性黏彈基質中。將複合材料的預測響應與文獻中所提供的實驗數據進行比較，並進行參數研究，以探討加強材材料的幾何形狀、成分比例以及邊界條件對磁致伸縮複合材料整體時變性響應的影響。

A constitutive modeling methodology based on micromechanics for analyzing the overall nonlinear and time-dependent responses of a viscoelastic polymer medium reinforced by active magnetostrictive reinforcements is proposed in this study. The magnetostrictive fillers exhibit significant nonlinear response under large magnetic driving fields, while the polymer is experienced pronounced nonlinear viscoelastic behavior particularly operated under an elevated temperature. Therefore, the overall responses of the magnetostrictive composites can be significant time-dependent. A simplified unit-cell micromechanics model is formulated for the magnetostrictive composites in order to determine the concentration tensors that relate the local field variables to the prescribed loadings on the composites. Because of the material nonlinearity of these constituents, linearized constitutive relations are first utilized for obtaining the trial overall responses of the magnetostrictive composites followed by an iterative scheme in order to correct errors from linearizing the nonlinear responses. Numerical results are presented for three composite systems, i.e., magnetostrictive thin films, long fibers and particles embedded in a nonlinear viscoelastic matrix. The predicted responses of the composites are compared with the experimental data available in literatures, and parametric studies are also conducted in order to reveal the effect of inhomogeneity geometry and compositions, and prescribed boundary conditions on the overall time-dependent responses of the magnetostrictive composites.

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