動態加載下的等效單軸應變與 應力材料組成模型

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顏昱丞(Yu-Cheng Yen) 查詢紙本館藏

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土木工程學系

論文名稱

動態加載下的等效單軸應變與應力材料組成模型
(Equivalent Uniaxial Strain And Stress Material Constitutive Model Under Dynamic Loading)

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摘要(中)

本研究提出的動態加載下的三維等效單軸應變與應力組成模型，目的是研究混凝土材料動態加載下的行為，因為日常生活中結構物大多數都是受到動態加載如地震、撞擊和爆炸等現象。
本研究引用Darwin & Pecknold提出的等效單軸應變概念，分離材料多軸受力時的柏松比效應(Poisson’s ratio)，且透過單軸行為預測多軸行為，在本研究的
數值模擬方法中以全量應變做計算，而非傳統塑性力學中分為塑性應變和彈性應變，簡化了混凝土在塑性行為分析中許多積分及複雜的數學計算。材料模型中主要分為兩個部分，分別為材料破壞模型(Ultimate failure model)，及單軸應力應變曲線(Uniaxial stress strain model)。
單軸應力應變模型採用Saenz所提出的單軸應力應變公式，此公式僅需定義極限強度參數即可描述混凝土行為中之硬化段與軟化段，在數值模擬的使用上相當簡潔且方便。
本研究提出動態材料破壞模型，採用Menetrey和Willam所提出之三參數破壞準則與Balan等人所提出的帽蓋模型結合形成了Close-Menetrey-Willam模型。並透過動態增量因子(Dynamic Increase Factor)使破壞模型擴張，建立不同應變率加載狀態下之動態破壞模型，將不同時刻下之應力狀態於動態材料破壞模型上定義當前時刻之極限強度參數(Ultimate strength parameters)。
本研究提出老劣化模型，採用杜建民提出的劣化強度公式與Close-Menetrey-Willam模型結合使得模型縮減，建立不同損傷程度下的劣化破壞模型，定義在劣化模型上的極限強度參數，將其帶入單軸應力應變模型中進行預測。
本研究之模型維持一貫之數值計算流程，只需修改動態材料破壞模型以及單軸應力-應變破壞模型即可，本研究之數值算例分別驗證了混凝土高應變率和低應變率加載的情形、冰塊低應變率加載的情形且考慮不同溫度下的冰塊應變率加載和混凝土硫酸鹽劣化的加載。

摘要(英)

This research presents a dynamic three-dimensional constitutive model of material equivalent uniaxial strain and stress. The purpose is to study the behavior of concrete materials under dynamic loading, because most of the structures in daily life are subject to dynamic loading such as earthquakes, impacts and explosions.
This research uses the equivalent uniaxial strain concept proposed by Darwin & Pecknold to separate the Poisson′s ratio of multi-axial forces. The equivalent uniaxial strain is a fictitious material index which is invented to compute the parameters such as material stiffness modulus and Poisson’s ratio.
This research proposes a dynamic material failure model, which combines the three-parameter failure criterion proposed by Menetrey and Willam with the cap model proposed by Balan et al. to form the Close-Menetrey-Willam model. The dynamic failure model is expanded by the DIF (Dynamic Increase Factor). The dynamic failure model under different strain rate loading states is established, and the stress state at different moments on the dynamic material failure model to define the ultimate strength parameters at the current moment.
Using the uniaxial stress-strain model proposed by Saenz, this formula only needs to define the ultimate strength parameters to describe the hardened and softened sections in concrete behavior. It is quite simple and convenient to use in numerical simulation.
This study proposes a concrete deterioration model. The combination of the concrete deterioration strength formula proposed by Du Jian-min and the Close-Menetrey-Willam model, establishes a deterioration model with different damage levels, defines the ultimate strength parameters of deterioration model.
The numerical examples in this study verify the high strain rate, low strain rate loading of concrete, low strain rate loading of ice, the low strain rate loading of ice at different temperatures and concrete deterioration.

關鍵字(中)

★ 等效單軸應變
★ 非線性分析
★ 混凝土動態加載
★ 材料破壞模型
★ 冰塊材料
★ 動態模型
★ 劣化模型

關鍵字(英)

★ Equivalent uniaxial strain
★ nonlinear analysis
★ dynamic loading of concrete
★ material failure model
★ ice material
★ dynamic model
★ deterioration model

論文目次

第一章前言 1
1.1研究動機與目的 1
1.2研究方法與內容 2
第二章文獻回顧 5
2.1靜態混凝土材料組成律模型 6
第三章三維高應變率模型 27
3.1高應變率混凝土動態試驗 27
3.2高應變率混凝土動態破壞模型修正 36
第四章三維低應變率模型 46
4.1混凝土材料低應變率下單軸應力-應變關係 46
4.2混凝土材料低應變率下材料破壞模型修正 49
4.3混凝土材料低應變率下應變率影響修正 62
第五章冰塊材料的等效單軸應變模型 68
5.1冰塊材料的特性 68
5.2冰塊材料單軸應力應變模型 71
5.3冰塊溫度對壓力強度的影響 82
第六章不同水養護時間和劣化的混凝土破壞模型 86
6.1不同水養護天數的混凝土單軸應力-應變關係 87
6.2劣化的混凝土 93
6.3受到硫酸鹽侵蝕後的混凝土退化模型 99
6.4混凝土退化模型的多軸預測 105
結論與建議 110
參考文獻 112
附錄A 一維波傳效應 116
附錄B 軟化模型 119
附錄C 動態帽蓋模型 127

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2018-11-27

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