混凝土結構分析之三維等效單軸組成材料模型

3D Concrete Material Model with Concept of Equivalent Uniaxial Strain

賴昱儒(Yu-Ju Lai)

指導教授 ： 王仲宇 ； 王仁佐

國立中央大學/工學院/土木工程學系/碩士(2014年)

摘要

本研究主要為研究混凝土材料之非線性行為，透過前人所提出的等效單軸應變概念與混凝土材料亞塑性(hypoplastic)模型，將材料多軸行為轉化為多個單軸行為的方式，大幅簡化了混凝土塑性行為分析中複雜的數學計算。流動法則(flow rule)與硬化法則(hardening rule)等材料塑性行為分析中常用的理論，雖然在亞塑性材料模型中未出現，但其造成之影響亦直接表現於材料行為中，此種分析方式有別於傳統使用塑性力學來處理工程問題，並為研究混凝土開闢了一個新的方向。混凝土亞塑性材料模型主要分為兩個部分，分別為材料破壞曲面與等效單軸應力應變曲線，本論文研究了幾個發展至今較泛用的混凝土破壞模型，包括了Ottosen四參數模型、Hsieh-Ting-Chen四參數模型與Willam-Warnke五參數模型，最後選用由Menetrey 與Willam修正Willam-Warnke模型得到的Menetrey -Willam模型，同時，為了考慮材料之三維壓力強度極限，加入帽蓋(cap model)修正，提出封閉Menetrey -Willam模型(CMW model, Closed Menetrey &Willam Model)；單軸應力應變曲線部分則使用Saenz提出的單軸應力應變曲線公式，此公式以單一式子表示曲線中的上升段(硬化)與下降段(軟化)，在數值模擬的使用上非常方便。本文之數值算例，分別驗證了混凝土之單軸、雙軸與三軸之實驗行為。透過本研究的完成，可與有限元素法或向量式分析力學結合，預測混凝土結構之非線性動力行為。

關鍵字

混凝土結構 ； 塑性力學之亞塑性材料模型 ； 等效單軸應變 ； 破壞曲面 ； 非線性分析

並列摘要

Inelastic material model of concrete is a general used model for describing the behavior over the linear range. Based on concept of equivalent uniaxial strain proposed by Darwin and Pecknold, triaxial response can be de-coupled into three uniaxial relations. As this concept is used, calculation with plastic method including hardening rule and flow rule can be avoided. The effect of plastic behavior still be considered and appear in the stress-strain curve. On determination of current material strength, ultimate strength surface is used to complete the whole system with equivalent uniaxial strain. With combination of equivalent uniaxial strain and ultimate strength surface, “hypoplastic” is named to describe this systematized method. In this research, some failure surfaces is considered as the ultimate surface including Ottosen 4-parameter model, Hsieh-Ting-Chen 4-parameter model and Willam-Warnke 5-parameter model. Finally, Menetrey-Willam model which modified by Willam-Warnke 5-parameter model is used as ultimate strength surface in this research. Furthermore, the cap model is applied to describe the triaxial compressive ultimate strength and closed the ultimate strength surface. Combining Menetrey-Willam model and cap model together as a closed surface and named Closed Menetrey Willam model to attain the completeness and Closure of geometry. The equation of uniaxial envelope, proposed by Saenz, is convenient to use with only one equation describes ascending and descending branches. In case study, uniaxial, biaxial and triaxial experiments are applied to verify the analysis. By combining the hypoplastic model and finite element method, prediction of dynamic problems of nonlinear concrete structure are expected to be well.

並列關鍵字

Concrete structure ； hypoplastic ； equivalent uniaxial strain ； ultimate surface ； nonlinear analysis

參考文獻

[2] Balan, T.A., Spacone, E. and Kwon, M., “A 3D Hypoplastic Model for Cyclic Analysis of Concrete Structures,” Engineering Structures, 2001; 23:333-342.

[4] Menétrey, P.H., and Willam, K.J., ”Triaxial Failure Criterion for Concrete and Its Generalization,” ACI Structural Journal, 1995;92:311-8.

[7] Kolymbas, D. ”An outline of hypoplasticity” Arch Appl Mech 1991:6;143-51.

[9] Li, T., and Crouch, R., “A C2 Plasticity Model for Structural Concrete,” Computers and Structures, 2010;88:1322-1332.

[10] Pisano, A.A., Fuschi, P., and De Domenico, D., “A Kinematic Approach for Peak Load Evaluation of Concrete Elements,” Computers and Structures, 2013; 119:125-139.