磁場、機械場與環境溫度之耦合一直以來在智慧材料的應用上扮演著很大的優勢，其中鐵磁材料響應之研究對於智慧材料的發展有著非常重要的影響。因此，多尺度分析一直是研究鐵磁材料的耦合響應的方法，藉由發展一個能夠描述鐵磁材料響應的本構方程式是我們本研究的目的，本研究提出一套完整的非線性三維本構方程式來描述上述所提及之耦合現象，同時，引入材料因為內部缺陷而體現在巨觀下的能量損失而造成之遲滯現象也將近一步被描述。我們以連續體力學下的假設和現象化的觀點提出描述鐵磁合金的吉普斯自由能 (Gibb’s free energy)，而伴隨以泰勒展開 (Taylor’s series expansion) 來描述物理場近似行為。由文獻回顧之實驗結果來驗證本研究所提出物理模型在不同外加物理場，如磁場或外加應力之加載下，來評估響應的可靠性。由結果可顯示本研究所提出的模型與實驗結果有著高度相關性。最後，參數之研究特別是在極端環境下實驗無法得出的結果進行模型之模擬，可以進一步理解特殊情況下之參數指定之整體響應。

Magneto-mechanical coupling behavior plays an important role in active devices, and thermal effects from surrounding environments has significant influence on the responses of ferromagnetic alloys. In order to design the smart devices containing the ferromagnetic constitutes, it is necessary to have a reliable constitutive law to accurately describe the multi-physics coupling behavior for the ferromagnetic alloys. This study presents a three-dimensional nonlinear constitutive model for predicting magnetostriction and magnetization of giant ferromagnetic alloys subject to magnetic intensity as well as undergo the mechanical loadings. The thermo-magneto-mechanical coupling constitutive law is derived based on a phenomenological approach within continuum mechanics. A Gibb’s free energy function is firstly formed and then it is followed by its Taylor series expansion in order to obtain characteristic material parameters for the ferromagnetic alloys. The experimental data obtained from available literatures on the hysteretic behavior operating under both magnetic fields and prestressed conditions are used to evaluate the accuracy of the proposed constitutive model. Results show that the model can adequately predict the nonlinear strain responses and magnetization in wide regime. Parametric studies are also conducted to examine the effect of loading rates, temperature and coupled magneto-mechanical stimuli on the overall performance of the ferromagnetic alloys.

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