本研究之目的為使用 Mori-Tanaka 模式模擬壓電壓磁橢球顆粒複合材料於不同母 材極化方向，與不同橢球顆粒內含物之旋轉或極化方向之等效材料性質，以找出最佳 磁電電壓係數之配置方式，並藉由 COMSOL Multiphysics 有限元素分析軟體之數據加 以驗證，證實微觀力學理論之準確性。本章將研究結果整理後提出結論，並闡述未來 之展望。
5-1 研究結論
1. 內含物形狀對於磁電耦合效應之影響
特殊極化方向下之 BTO/CFO 配置，球狀顆粒複合材料之最佳磁電電壓係數 𝛼E∗,33= -1.265 V/cmOe，纖維複合材料之最佳磁電電壓係數𝛼E∗,33= -5.821 V/cmOe，
後者提升了 4.6 倍。特殊極化方向下之 CFO/BTO 配置，球狀顆粒複合材料之最佳 磁電電壓係數𝛼E∗,33= -1.965 V/cmOe，纖維複合材料之最佳磁電電壓係數𝛼E∗,33= -6.232 V/cmOe，後者提升了 3.17 倍。考量內含物形狀對於磁電耦合效應之影響，
纖維複合材料之表現優於顆粒複合材料。
2. 母材與內含物配置對於磁電耦合效應之影響(BTO/CFO 與 CFO/BTO)
本文主要使用具 6mm 對稱性之壓電材料 BTO 與壓磁材料 CFO 進行研究。將 配置由 BTO[001]/CFO[001]改為 CFO[001]/BTO[001]，最佳磁電電壓係數𝛼E,11∗ = -1.265 V/cmOe 提升至-1.965 V/cmOe；最佳磁電電壓係數由𝛼E,33∗ = 1.149 V/cmOe 提升至𝛼E∗,33= 1.228 V/cmOe。由 BTO[100]/CFO[100]改為 CFO[100]/BTO[100]，最 佳磁電電壓係數𝛼E,11∗ = -0.5788 V/cmOe 提升至 0.8071 V/cmOe；最佳磁電電壓係數 由𝛼E∗,33= -5.821 V/cmOe 提升至𝛼E∗,33= -6.232 V/cmOe。結果顯示：在其餘條件相同 下，選擇 CFO/BTO 配置，磁電耦合效應將優於 BTO/CFO 配置。
3. 磁電耦合效應最佳化之成效
本文選擇橢球顆粒(a3=2)複合材料進行磁電耦合效應最佳化，並使用具 6mm 對稱性之壓電材料 BTO 與壓磁材料 CFO。固定橢球內含物之長軸方向，改變內 含物與母材之極化方向，可使得最佳磁電電壓係數獲得有效提升：BTO/CFO 的配 置下，𝛼E11∗ 由-0.5294 V/cmOe 增加至-1.3651 V/cmOe，𝛼E33∗ 由-0.0303V/cmOe 增加 至-2.262 V/cmOe，最佳磁電電壓係數提升了 4.27 倍；CFO/BTO 的配置下，𝛼E11∗ 由 -0.7057 V/cmOe 增加至-1.836 V/cmOe，𝛼E33∗ 由 0.971 V/cmOe 增加至-2.876 V/cmOe，
最佳磁電電壓係數提升了 2.96 倍。
4. 有限元素法分析數據誤差之比較
觀察 COMSOL Multiphysics 有限元素分析對照 Mori-Tanaka 模式所得數據，
橢球顆粒複合材料相較球狀顆粒及纖維複合材料，對於等效材料性質預測之誤差 較大，且橢球顆粒複合材料能夠模擬之體積百分比受限較多：球狀顆粒與纖維狀 模型之最大體積比為 0.7；橢球顆粒(長軸半徑為 2)之最大體積比為 0.5。相較橢球 顆粒複合材料，COMSOL Multiphysics 會更適用於球狀顆粒與纖維複合材料之分 析。
5-2 未來展望
1. 選用其他壓電及壓磁材料
目前較為人們熟知的壓電材料除 BaTiO3外，尚有 PZT、PbZrO3、LiNbO3、 NH4H2PO3及 SiO2等，而壓磁材料尚有 Terfenol-D 等可以用於研究，材料性質對 於磁電耦合效應之優劣有著決定性的影響，相信嘗試不同壓電與壓磁材料之配置，
能對磁電耦合效應之最佳化有所助益。
2. 非完美交界面對於磁電耦合效應之影響
過往討論複合材料的理論中，大多假設材料間的交界面為完美狀態，就彈性 力學的觀點而言，完美交界面即徹體力(Traction)與位移(Displacement)可以在相與 相之間完全被傳遞。若考量到應用層面，實際複合材料內部之交界面大多存在著 缺陷，使得交界面呈現非完美狀態，因此非完美交界面對於複合材料的影響值得 再深究。使用有限元素分析軟體建立完美交界面模型比非完美交界模型要來得直 覺與簡單許多，如何成功建立吻合實際情形之非完美交界模型仍需要嘗試。
3. 三相橢球顆粒複合材料
以往科學家曾經探討過雙層橢球顆粒內含物之反平面剪力問題(Ru et al., 1999)，
三相橢球顆粒複合材料之配置，除了使用雙層橢球顆粒之外，也可使用母材內同時含 有兩種不同材料之橢球顆粒。
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