深度神經網路應用於短纖維複合材及仿生階層複合結構的應力應變曲線預測

Abstract

本研究針對短纖維複合材及仿生階層複合結構建立了一套以深度神經網絡預測應力應變曲線的流程。從古至今，材料的發展一直都在帶領著人類生活不斷地進步。近年來，因為電腦計算模擬技術、3D列印及機器學習等先進技術的蓬勃發展，材料的設計得以更加深入地探討，能拓展的層面也越來越廣。因此，透過機器學習輔助，在廣大的設計空間中藉由預測應力應變曲線來更加了解材料性質，找尋符合需求的材料，是本研究主要的宗旨。 短纖維複合材料的材料性質受許多因素影響，如纖維形狀、纖維含量、纖維的的方向性及基體材料與纖維之間的介面的品質等。三維的有限元素分析能精準的預測短纖維複合材料的材料性質；然而，計算需耗費相當大的計算資源及成本。因此，本研究利用主成分分析（PCA）降維後訓練了深度神經網絡（DNN）預測模型，建立材料組成物的性質以及由有限元素分析（FEA）得來的應力應變曲線的關係，以預測短纖維複合材料的應力應變曲線，再由應力應變曲線求得其各應變下的應力與勁度。此預測模型材料性質的決定係數（R2）皆高達0.9以上，而預測之應力應變曲線與真實值之應力應變曲線比較下的相對最大誤差大部分都小於10%。此外，本研究亦提出應用理論引導之機器學習（TGML）以及兩階段機器學習（two-phase learning）之方法來提升預測模型之準確度。而上述方法可延伸應用於其他具非線性材料性質之複合材料分析。 另外，自然環境中生物材料具有相當好的機械性質與多功能性，因此值得我們作為設計材料時的參考。本研究的仿生階層複合結構是啟發自骨頭的拓墣與竹子的階層密度分佈。本研究運用主成分分析降維後訓練了另一個深度神經網絡預測模型，建立複合材各階層之體積分率與來自二維三角晶格彈簧模型（LSM）模擬得到的應力應變曲線的關係，以預測具破壞行為之仿生階層複合結構的應力應變曲線，再由其應力應變曲線求得最大強度及韌性。此部分預測模型韌性的決定係數高達0.85，而強度的決定係數亦達0.8。因此可驗證此預測模型可以準確且有效地預測材料的應力應變曲線，在廣大的設計空間中能夠更快速地了解材料性質，更進一步去促進材料設計的發展與最佳化。

In recent years, attributed to the advancement in computational simulations and 3D printing experiments, the development of materials has made considerable progress. Despite these material analysis methods providing highly accurate predictions of material properties, they are not feasible to explore the colossal design space of structural materials due to the high cost and time consumption. Therefore, in this research, machine learning techniques are utilized to predict stress-strain curves of different composite materials and further understand the mechanical behaviors of composites. Firstly, this study predicts the mechanical response of short fiber-reinforced composites (SFRCs). The properties of SFRCs greatly depend on several factors, such as fiber shape, fiber content, fiber orientation, and the interphase quality between fiber and matrix materials. Three-dimensional finite element analyses (FEA) for the SFRCs predict composite properties accurately; however, the tremendous consumption of computational cost and time is a critical disadvantage. With the aid of machine learning techniques, the predictions of the composite properties can be produced effectively and accurately at the same time when having a sufficient amount of data. In this research, we propose a machine learning approach via training a deep learning network with the FEA dataset to predict the nonlinear mechanical response of short fiber-reinforced composites. Moreover, theory-guided machine learning (TGML) and two-phase learning approaches are adopted to enhance predictive performances. Our results show that TGML and two-phase learning methods can capture more information on the data and thus improve predictive performances. The proposed method can be extended to other composite analyses with nonlinear mechanical behavior. Secondly, the mechanical responses of bio-inspired layered structural composites are predicted in this work. Biological materials evolve extraordinary protective systems to survive the competitive environment, thus having outstanding mechanical properties and multifunctionality. For instance, bone and bamboo are both bio-composites with superior mechanical properties. In this research, the composite structures are inspired by the topology of bone and the density distribution of bamboo. To explore the vast design space of structural materials, we developed a machine learning-based surrogate model using a combination of principal component analysis (PCA) and deep neural networks (DNN) and predicted the entire stress-strain behavior of the bio-inspired layered composite structures. The results show that the surrogate model is accurate and efficient for investigating the design space. The proposed approach in this work can be extended to other composite structures to accelerate material design and optimization.