三維等效單軸應變與應力之材料組成模型

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林佑倫(You-Lun Lin) 查詢紙本館藏

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土木工程學系

論文名稱

三維等效單軸應變與應力之材料組成模型
(A Three-Dimensional Equivalent Uniaxial Strain and Stress Constitutive Model)

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摘要(中)

本研究提出之三維等效單軸應變組成模型，目的是用來模擬材料多軸非線性行為，並引用Darwin和Pecknold所提出之等效單軸應變概念分離材料多軸受力之柏松效應；本模型數值計算過程中皆以全量應變形式而非傳統塑性力學分為彈性應變與塑性應變兩部分，且將材料多軸行為以單軸實驗結果預測，跳脫傳統塑性力學繁瑣之數學推導。除此之外，本研究將此組成模型應用範圍由混凝土材料延伸至岩石材料以及金屬材料，進一步驗證本研究理論之正確性以及廣義性。
本研究於混凝土及岩石材料中，提出軟化模型(Softening model)與動態帽蓋模型(Kinematic cap model)之理論，解決了先前Darwin 和 Pecknold與Elwi和Murray模型中軟化段下降過快，以及無法探討應力路徑有變動之問題。而金屬材料中以硬化模型(Hardening model)之理論，定義出金屬材料通過降伏點後塑性硬化之程度，且將此金屬硬化模型結合循環加卸載(Cyclic loading)，可模擬塑性力學中定義之動態硬化(Kinematic hardening)、等向硬化(Isotropic hardening)以及獨立硬化(Independent hardening)等現象，且包辛格效應(Bauschinger effect)將透過硬化模型於硬化過程中是否有形變產生來定義。
本研究以不同時刻下之應力狀態於材料破壞模型上定義當前時刻之極限強度參數(Ultimate strength parameters)，藉由此極限強度參數調整單軸應力-應變模型來預測多軸情況下真實之材料參數如：材料勁度模數(Stiffness modulus)與泊松比(Poisson’s ratio)。本研究所開發之模型維持一貫之數值計算流程，只需修改對應之材料破壞模型以及描述材料單軸行為之單軸應力-應變模型即可，混凝土材料使用Menetrey和Willam所提出之三參數破壞準則、岩石材料使用Drucker-Prager破壞準則、金屬材料則使用von-Mises破壞準則。

摘要(英)

This research presents a three-dimensional constitutive model of material based on the concept of equivalent uniaxial strain in order to decouple Poisson’s effect in multiaxial loading condition. 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. The characteristics of uniaxial stress-strain model which defined by the ultimate strength parameters are obtain from material failure surface and the ultimate strength parameters varies with current stress or strain state.
This research contains not only concrete material but also rock material and metal material, exerted by monotonic loading, proportional loading non-proportional loading and cyclic loading. A hypothesis of kinematic cap model is proposed to reflect the influence of the non-proportional loading path. Further, a hypothesis of softening model is applied on concrete and rock material not only to simulate post-peak branch behavior but to reflect the transition between brittle softening and ductile softening under different confining pressure.
In concrete material established closed Menetrey-Willam (CMW) failure model which combined with Menetrey-Willam meridian and the cap model in concrete material and replaced Menetrey-Willam meridian with Drucker-Prager criterion in rock material. Saenz stress-strain model is applied and adjusted by the ultimate strength parameters from material failure model to reflect the latest stress or strain condition in both concrete and rock material. von-Mises criterion is applied to build material failure model for metal material as well. Correlation studies with available experimental tests are presented to valid the performance of proposed three d constitutive of materials.

關鍵字(中)

★ 多軸加載
★ 不等比例加載
★ 循環加載
★ 等效單軸應變
★ 材料破壞模型
★ 非線性分析
★ 混凝土材料
★ 岩石材料
★ 金屬材料
★ 動態帽蓋模型
★ 軟化模型
★ 硬化模型

關鍵字(英)

★ Tri-axial behavior
★ Non-proportional loading
★ Cyclic behavior
★ Equivalent uniaxial strain
★ Material failure model
★ Nonlinear analysis
★ Concrete
★ Rock
★ Metal
★ Kinematic cap moel
★ Softening mdoel
★ Hardening model

論文目次

第一章、前言 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究方法與內容 3
第二章、三維等效單軸應變與應力組成模型 4
2.1 三維增量組成關係 4
2.2 等效單軸應變 5
2.3 單軸應力-應變關係模型 7
2.4 材料破壞準則 9
2.4.1 Haigh-Westergaard坐標系統 10
2.4.2 極限強度參數定義 14
2.5 動態材料破壞模型 16
2.5.1 軟化模型與硬化模型 18
2.5.2 動態帽蓋模型 24
第三章、普通強度混凝土三維等效單軸應變模型 29
3.1 普通強度混凝土材料單軸應力-應變關係 29
3.2 普通強度混凝土三參數破壞準則 31
3.3 普通強度混凝土破壞模型修正 35
第四章、高強度混凝土三維等效單軸應變模型 51
4.1 高強度混凝土單軸應力-應變關係 53
4.2 高強度混凝土三參數破壞準則 55
4.3 高強度混凝土破壞模型修正 58
4.4 高強度混凝土軟化模型理論 76
4.5 高強度混凝土動態帽蓋模型理論 83
第五章、岩石材料三維等效單軸應變模型 94
5.1 岩石材料單軸應力-應變關係模型 96
5.2 岩石材料Drucker-Prager 破壞準則 98
5.3 岩石材料破壞模型修正： 100
5.4 岩石材料動態帽蓋模型理論： 117
5.5 岩石材料非等向性假設 123
5.6 岩石材料帽蓋模型斜率之修正 127
第六章、金屬材料三維等效單軸應變模型 136
6.1 金屬材料 von-Mises 破壞準則 137
6.2 金屬材料單軸應力-應變模型 140
6.3 金屬材料極限強度參數定義修正 141
6.4 金屬材料硬化模型理論 143
第七章、數值算例與實驗比對 149
7.1 普通強度混凝土雙軸等比例加載 149
7.2 普通強度混凝土三軸等比例加載 152
7.3 高強度混凝土三軸不等比例加載 154
7.4 岩石三軸不等比例加載 161
7.5 鋁合金雙軸拉力實驗 169
7.6 鋼材雙軸拉力實驗 173
7.7 金屬三軸加卸載 175
結論與建議 182
參考文獻 184

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2017-7-24

推文