金屬精微成形技術是一項正在發展中的重要精密工業技術，具有生產效率高、成本低和產品可具複雜之幾何外形等優點，但是在微觀尺度下，成形參數與材料性質會與傳統巨觀尺度有所不一樣，這種現象我們稱為尺寸效應（size effect）。
本文遵循Prandtl-Reuss塑流法則與von Mises之降伏條件，結合有限變形理論及updated Lagrangian formulation (ULF)之觀念建立一增量型彈塑性大變形三維有限元素分析程式。並利用以四邊形四節點之退化殼元素(degenerated shell element)所推導之形狀函數耦合入剛性矩陣，組成三維有限元素之分析模式，並且使用廣義 法則處理金屬板材在成形時，包含元素之降伏判斷、最大容許應變增量、最大容許旋轉增量、料片與模具間節點之接觸與分離判斷等問題。
本文將探討厚度分別為0.2mm、0.1mm、0.075mm、0.05mm的純鐵薄板材，經由不同溫度與時間的再結晶退火後，其微拉伸成形(micro stretching forming)之成形性變化，並與數值模擬分析結果做比較，探討其中的沖頭負荷與位移關係、破裂沖程、應力分佈與厚度分佈等，以獲得目前塑性理論可適用的最小尺度範圍，並探討在微觀尺度下之準確性與適用性。

Metal microforming process is a developing technology in precision manufacturing. This technology has many advantages, such as high producing efficiency, low cost, and the ability to produce products with complicated geometrical shape. But when the dimensions reduce to the micro scale, the forming parameters and material properties change due to the reduction of dimensions. This is called the “size effect”.
A methodology of formulating an elastic-plastic three-dimensional finite element model to simulate sheet metal forming process is developed using Prandtl-Reuss flow rule and von Mises yield criterion respectively in association with an updated Lagrangian formulation. The shape function derived from a four-node quadrilateral degenerated shell element was combined into the stiffness matrix to constitute the finite element model. An extended algorithm was proposed to formulate the boundary condition, such as nodal penetration and separation, strain increment and rotation increment, and altered elasto-plastic state of material.
This study will discuss thickness respectively the pure iron sheet of 0.2mm, 0.1mm, 0.075mm, 0.05mm, after different temperature and time recrystallization annealing, its micro stretch forming the formability change, and compare with the analysis result of numerical simulation, the relationship between punch load and punch stoke, the breakage stroke, the distribution of stress, the distribution of thickness. In order to obtain the minimum suitable range of plasticity theory at present, and discuss the accuracy and suitability in micro scale.

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