在固體力學的理論中，絕大多數的材料於外部承受均勻壓力時，會在所有方向上發生收縮，然而有一些材料被發現會在壓力下沿一個或兩個方向膨脹，我們稱此材料在該方向上具有負線性模量。在自然界中，絕大部分的材料其線性模量都為正值，只有極少數量的材料具有負的線性模量，而這種特殊的材料性質在工程應用上具有相當之發展潛力，因此我們希望能夠藉由微結構設計的技術製造出具有負線性模量特性之人工材料，即四角星形超材料。經由彈性模數的計算，我們發現此超材料不僅僅具有負線性模量，還同時展現了負柏松比的特性，而且此四角星形超材料具有優越的可調性，可以藉由桿長比和角度的調整將系統的負線性模量和負面積壓縮模量最大化。除此之外，我們藉由計算結果去探究不同方向上負壓縮模量的發生時機，並且對柏松比與線性模量之間的關係進行探討。除了理論上的推導，本文於最後利用3D列印機來印製本文模型做為實驗試體，透過材料試驗機進行實驗，並藉由應力應變關係圖計算其楊氏模數，希望藉此更貼近真實的應用，並歸納出現實與理想之間的差異，提供具有負線性模量材料的一些初步設計概念與實際應用上的建議。

In the last few decades we have seen significant advancements in the field of mechanical metamaterials. In contrast to other mechanical properties, there are relatively few studies on the design and fabrication of material systems with negative compressibility. In this thesis, we present a new type of mechanical metamaterial referred to as “quadrangular star cellular structures”. In an attempt to derive the mechanical properties and compressibility of this cellular structure, based on the idealized wine-rack mechanism model, we show that the structure exhibits negative Poisson's ratios, as well as negative linear and area compressibility. Furthermore, we demonstrate the tunability of the microstructure and the occurrence of negative linear compressibility. Lastly, we obtain the Young's modulus of this material through experimental tests, which facilitates a discussion on the disparities between experimental results and theoretical derivations.

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