為保護軟性電子元件內部之脆性薄膜材料，設計堆疊薄膜元件時，將上述脆性材料層配置在中性軸位置附近，可藉此降低該薄膜層所承受之應力而免於破壞，提高軟性電子之長時可靠度壽命。基於此力學概念，若在軟性電子結構內部增加中性軸數量，則可使關鍵且易脆裂之薄膜層的配置有更多選擇，且該結構內之最大應力亦可顯著降低，進而提升軟性電子結構設計之多樣性。有鑑於此，本研究首先針對一不具軟性層之多層薄膜結構，推導其與厚度相依之水平方向應變值與中性軸位置。而後，分析一具軟性層之三層薄膜，藉由變分法求得其應變函數與中性軸位置。最後，針對含一軟性層之多層薄膜結構，將與軟性層相鄰之多層薄膜各自等效為單層，即可簡化多層薄膜系統之分析，用以獲得該系統之中性軸位置與數量。本研究由三層薄膜之理論模型延伸，推廣至多層薄膜之分析，完成多重中性軸之理論推導，探討多重中性軸發生的位置與所需之條件，並透過有限元素模擬分析進行驗證。本研究之理論推導能夠快速地預測多層薄膜結構之中性軸數量與位置。藉由本研究所呈現之力學模型與結果，可適當地配置中性軸之數量與位置，期作為下一世代改善軟性電子結構之重要設計參考準則。

In order to protect the brittle thin film material inside the flexible electronic devices, when designing the stacked film devices, the above-mentioned brittle material layer is arranged near the position of neutral axis, which can reduce the induced stress on the concerned film and avoid damage. Accordingly, the long-term reliability lifetime of soft electronics is boosted. Based on this concept of mechanics, more choices with regard to the arrangement of critical and brittle thin film can be provided when an increase in the number of neutral axes is taken into account. In this meanwhile, the maximum stress in the present configuration can be significantly reduced, thereby the diversity of design for the structures of soft electronics are promoted. For this reason, this research first derives the neutral axis position and the distribution of horizontal strain along the thickness direction of multi-layered thin film architecture without a soft layer. Afterwards, the variational method is utilized to acquire the strain function and the positions of neutral axes for a sandwich framework that a soft layer is embedded. Finally, for a stacked thin film structure containing a soft layer, the multi-layer films adjacent to the soft layer are needed to be an equivalent layer, respectively. Through this procedure, the analysis of multi-layered system can be simplified to obtain the position and quantity of the neutral axes within the concerned system.
This research extends and analyzes the theoretical model from three-layered to multi-layered system. The theoretical derivation regarding the locations of multiple neutral axes and the discussions for the necessary conditions of requirements are overall completed. All the estimated results from the present derivations are validated through finite element analysis. The theoretical derivation proposed by this research can quickly predict the number and positions of neutral axes for the designed multi-layered structure. With the mechanical model and analytic results presented in this research, the number and positions of the neutral axes can be appropriately configured, which is expected to be an important design reference for the next generation soft electronic architectures.

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