在這項研究中，考慮了磁致伸縮-壓電顆粒複合材料的有效磁電效應，包括定向和非定向的情況。本研究提出了一個著名的微觀力學模型，Mori-Tanaka模型，用於分析磁電複合材料。由於單相磁電材料如Cr2O3對於工程領域上的應用來說太小，因此近期的研究著重於將磁致伸縮化合物嵌入壓電基質中形成兩相複合材料，旨在增強磁電效應。當複合材料受到外部磁場作用時，磁電複合材料中的磁致伸縮材料的應變導致對壓電相的應變，從而引起電極化。然而，由於壓電基質中的磁致伸縮顆粒可能不會在同一方向上排列，因此採用離散能量平均模型，能夠描述任意晶體方向的單相磁致伸縮材料，以解決基材中的顆粒方向問題。這個獨特的本構模型在複合材料受到加載或磁場作用時，能夠準確捕捉非線性行為並以封閉形式的方程式來表示。與現有文獻相比，該模型可以直接在本構層面考慮顆粒方向，從而得到方向無關的剛度矩陣，從而提高了計算效率。微觀力學的預測將與現有文獻中的實驗數據進行比較，以驗證數值結果的可行性，然後將呈現有關體積分率、預應力和細長比影響的參數研究。

In this research, the effective magnetoelectric effect of magnetostrictive-piezoelectric particle composites, both oriented and non-oriented, is considered. A well-known micromechanics model, Mori-Tanaka, is proposed for the analysis of magnetoelectric composites. Since single-phase magnetoelectric materials such as Cr2O3 are too small for practical engineering applications, recent research has focused on embedding magnetostrictive compounds into piezoelectric matrix to form two-phase composites, aiming to enhance the magnetoelectric effect. The magnetoelectric effect in the two-phase composite is caused from the strain of the magnetostriction material when the composite is subjected to the external magnetic field, strain transmits to piezoelectric phase led to induces electrical polarization. However, because magnetostrictive particles in the piezoelectric matrix may not align in the same direction, the discrete anergy averaged model, capable of describing monolithic magnetostrictive materials with arbitrary crystal orientations, is employed to address particle orientation in the matrix. This distinctive constitutive model accurately captures the nonlinear behavior in closed-form equations when the composite is subjected to loading or a magnetic field. In comparison with existing studies, this model can directly consider particles orientation at the constitutive level, resulting in orientation-independent stiffness and thus improving computational efficiency. The micromechanics prediction will comparison with experiment data to verify the feasibility of the numerical results. Then, the parameter studies about the influence of the volume fraction, prestress and aspect ratio will be presented.

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