摘 要 本論文提出一新的混凝土塑性模型─雙荷載函數混凝土模型，以兩個不同的函數形式分別考慮了混凝土因微裂縫拓展所造成的體積改變，以及因錯動所造成的形狀變化，同時將混凝土進入塑性後的硬化法則，亦分別依形狀改變與體積改變分開，並在隨動式硬化法則移動後的應力空間中，建立起硬化參數和應力函數的關係。將此兩個荷載函數經過適當的組合後，可以證明與體積變化相關的材料塑性行為，符合非相關性流動法則，而其相對應的塑性勢能函數(plastic potential)恰是兩個荷載函數之和。 將此一雙荷載函數混凝土模型與向量式有限元結合，將混凝土結構的分析以宏觀裂縫的形成為分界，區分為宏觀裂縫形成前的連續體行為，與宏觀裂縫形成後的不連續體行為兩部分。前者主要的工作在處理混凝土材料的彈塑性與不可逆的非線性行為﹔後者因裂縫的形成，材料變成非等向性，計算上著重在單一連體碎裂成多個連體，各個連體之間接觸判斷與接觸力等互致作用的處理。 以此一程序分析混凝土結構在承受靜載重和動態載重下的行為。首先，以一考慮因裂縫造成混凝土體積變化效應雙荷載函數模型，與現有單軸、雙軸和三軸實驗結果比較，驗證本方法在模擬混凝土宏觀裂縫形成前的連續體行為上，是目前最適用的材料模型。同時在重複加卸載的情況下，此一雙荷載函數模型可模擬材料非線性與不可逆的特性，可作為分析混凝土動態行為的基礎。其次，在靜荷載作用下，以本方法模擬混凝土結構承受剪力的行為，驗證了混凝土宏觀裂縫發生後本文所提的混凝土開裂模式，與單一連體碎裂成多連體後的開裂計算法、多連體間的碰撞互制等現象的計算方法，已經具備分析混凝土結構物的基礎。 在混凝土的動態行為模擬方面，首先以一維的混凝土桿承受衝擊荷載之分析，驗證本文所發展的材料模型與計算方法適用於混凝土承受衝擊載重下的行為。接著驗證本方法在模擬混凝版承受高速衝擊的穿孔現象，承受中速衝擊的彈坑現象與承受低速衝擊的剝離現象的效果。在確立了本方法在定性分析上，可以模擬混凝土結構受衝擊載重下的行為之後，再分別以混凝土版承受撞擊試驗以及鋼筋混凝梁承受撞擊試驗結果和計算結果比較，顯示本論文所提之計算方法，在混凝土結構承受衝擊載重下的定量分析上，也已經有初步理想的結果。 Nonlinear Discontinuous Deformation Analysis of Concrete Structures ABSTRACT In this thesis, a dual loading functions plasticity (DLFP) model that is capable to characterize the elastic-plastic behaviors of concrete material under various multi-axial stress state is proposed. The dilatation effect due to the formation of micro cracks and the shape change effect due to dislocation are taken into account by individual loading function to guide the plastic behavior of concrete. The hardening parameter of each loading function is determined based on series of worldwide-recognized experimental data. It is shown that the presented dual loading functions model can predict the plastic behavior of concrete material at various stress state. This incremental type model can be adapted into numerical code to simulate the irreversible behavior of concrete material during any loading –unloading process. The numerical algorithm for applying this DLFP model is also presented. Although associated flow rule is applied to individual loading function during the derivation, but it is proved that the overall format of the flow rule within this concrete plasticity model is non-associated. We combine DLFP with Vector Form Intrinsic Finite Element, VFIFE, to analysis concrete structures. The procedure is mainly divided into two major parts by the formation of macro crack: the continuum behavior before macro crack forming and multi-bodies behavior after macro crack forming. The major work of the former is to establish a concrete constitutive relation. In this thesis, DLFP is adapted. The major work of the latter is to handle crack of concrete, which contains new nodes generation, detection of contact and contact force. With such procedure, we analyze concrete structure under static and dynamic load. Comparing with uni-axial, bi-axial and tri-axial experiment data, DLFP represent a better choice of all the concrete models. This DLFP can handle cyclic behavior of concrete without difficulties. We also analyze a concrete structure that is under shear to verify the procedure of post failure behavior of concrete. Finally, we use this tool to analyze the concrete structure under dynamic loading. In qualitative analysis, we analyze the concrete slab under impact of low, medium and high velocities to verify the procedure. The results show the trends are admit with experiments though quantitative analysis still needs more efforts to put on.
