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研究生：	楊長運 Yang, Chang-Yun
論文名稱：	孔隙材料降伏面演化的有限元分析 Finite element analysis on yield surface evolution of cellular materials
指導教授：	劉立偉 Liu, Li-Wei
學位類別：	碩士 Master
系所名稱：	工學院 - 工程科學系 Department of Engineering Science
論文出版年：	2022
畢業學年度：	110
語文別：	英文
論文頁數：	90
中文關鍵詞：	孔隙材料、蜂巢、填充材、小梁骨、有限元素法、降伏面、接續降伏面、降伏後行為
外文關鍵詞：	Cellular material, Honeycomb, Inclusions, Trabecular bone, Finite element method, Yield surface, Subsequent yield surface, Post yield behaviour
相關次數：	點閱：57 下載：0
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在塑性力學相關研究的降伏面為彈性區域的邊界，因此降伏面的面積大小與形狀可視為材料性能與其在應力空間中所能承受的狀態，而降伏面用由無數個降伏點構成。本研究運用有限元分析研究了 2 維孔隙材料-六角形蜂巢材料的降伏點和降伏面。根據金屬實驗中決定降伏點的方式，使用有限元分析模擬單軸拉伸試驗，得出蜂巢材料的等效塑性應變，從而選擇在模擬上合適的蜂巢降伏點決定方式。本研究擴展了一維應力空間降伏點的決定方式，以探測蜂巢材料在軸向剪切應力空間中的降伏面。考慮有限尺寸和不同長寬比的蜂巢來探測初始降伏面，降低邊界效應。應用四種不同位移的預加載路徑後，探測蜂巢材料的接續降伏面，觀察降伏面的演化。在本研究中發現，相對密度對於蜂巢材料的降伏面演化行為有著顯著的相關性。由於在模擬上必須選定代表區塊尺寸，而結果顯示代表區塊尺寸對於蜂巢材料所能承受的預加載量在降伏面演化的行為上有差異性。本研究不僅確立了觀察六角形蜂巢材料的降伏面演化應用，也將此方法擴展至研究更多形式的孔隙材料，如 Voronoi 蜂巢、帶有填充材的孔隙材料與小梁骨。藉由分析具有擾動幾何的 Voronoi 蜂巢在相同預加載狀態下的降伏面演化行為，進一步延伸至討論使用 Voronoi 蜂巢進行建模的小梁骨仿生孔隙材料。建立不同擾動狀態的 Voronoi 蜂巢並分別設定不同的等向性與異向性材料觀察孔隙材料幾何與材料對小梁骨降伏面演化結果的影響。觀察 Voronoi 蜂巢的結果可發現孔隙形狀的不規則擾動對於孔隙材料的降伏面行為影響較不顯著，而對於孔隙的鬆弛擾動狀態較為顯著，並且小梁骨的降伏面演化結果表明孔隙材料的降伏面行為與幾何和材料模型有關。為了強化孔隙材料藉由分別填充軟硬材在孔隙材料中，結果表明填充材能有效的強化孔隙材料剛性及改變降伏面演化行為。

The yield surface is an elastic region boundary in the theory of plasticity, wherefore the area size and shape of the yield surface can represent the capability of honeycomb materials in stress space. The yield point and the yield surface of one kind of 2 D cellular materials, hexagonal honeycombs is investigated in this study via the finite element analysis. According to determinations of yield point for metals in the experi- ment, a finite element analysis is conducted to simulate the uniaxial tension test and show the equivalent plastic strain of the honeycomb materials, then the proper deter- mination of yield point for the honeycombs is selected. The present study extends the selected determination of yield point in 1D stress space into yield surface detection of honeycombs in the axial-shear stress space. Honeycombs with finite size and different length-to-width ratio of the cell wall are considered to detect the initial yield surface with the reduction of the boundary effect. After the four different preloading paths of displacement were applied, the subsequent yield surfaces of honeycombs were detected and the evolution of yield surface was observed. The simulation shows a significant correlation between the relative density with the yield surface evolution of the hon- eycomb materials. The representative-block size must be selected in simulation, and results show that representative-block size has a significant relation to the yield surface evolution of cellular materials. This study not only establishes the application of this method in observing the yield surface evolution of hexagonal honeycomb materials but also extends this method to study more cellular materials, such as Voronoi honeycombs, cellular material with inclusions, and trabecular bone. By analyzing the yield surface evolution of the Voronoi honeycombs in the same preloading paths, we investigated the yield surface evolution of the trabecular bone. Voronoi honeycombs with different perturbed types were established and different isotropic and anisotropic materials were assigned to simulate trabecular bone. The results of Voronoi honeycombs show that the perturbed type of cellular shape has a less significant effect on the behavior of the shape of yield surfaces while the perturbed type of the cellular relaxation is more significant, and the results of the yield surface evolution of the trabecular bone also show that the influence of cellular shape is less significant. The material model assigns to trabecular bone has a significant influence on yield surface evolution. To reinforce the cellular materials, the soft and stiff inclusions were assigned to cellular materials as cellular composites. The observation results show that the inclusions can effectively strengthen the stiffness and change the yield surface evolution.

摘要 I
Abstract II
致謝 IV
List of figures IX
List of tables XIV
Introduction 1
1  Motivation 1
2  Background 1
3  Outlines 4
Yield surface detection by finite element method 7
1  Six experimental approaches of yield point determination 7
1.1  Review the determinations of yield surface in metal 8
1.2  Finite element analysis on the yield stress of standard specimens 8
1.3  Finite element analysis on the yield stress of honeycombs 9
2  Detection of initial yield surface and subsequent yield surface 13
2.1 Arrangements of finite element analysis 13
2.2 Probing and preloading paths 13
3  Convergence analysis of mesh generation 15
4  Boundary effect reduction 15
5  Boundary condition verification 16
 Yield surface evolution of cellular materials 23
1  Objective 23
2  Geometry of honeycombs 23
3  Influence of relative density 24
3.1  Initial yield surfaces 24
3.2  Yield surface evolution of honeycombs with ρ = 40% 25
3.3  Yield surface evolution of honeycombs with ρ = 32.6% 27
3.4  Yield surface evolution of honeycombs with ρ = 21.4% 28
3.5  Yield surface evolution of honeycombs with ρ = 6.9% 29
3.6  Comparisons 31
4  Influence of the representative-block size 31
4.1  Initial yield surfaces 32
4.2  Yield surface evolution of honeycomb with ρ = 40%, l = 13 32
4.3  Yield surface evolution of honeycomb with ρ = 40%, l = 7 33
4.4  Yield surface evolution of honeycomb with ρ = 40%, l = 3 34
4.5  Comparisons 34
 Yield surface evolution of trabecular bone 49
1 Objective 49
2  Trabecular bone modeling 49
2.1  Geometry of Voronoi honeycombs 50
2.2  The anisotropic material model for trabecular bone 50
2.3  The isotropic material model for trabecular bone 51
3  Yield surface evolution of Voronoi honeycombs 51
3.1  Yield surface evolution of Voronoi honeycomb with perturbed 
shape type 51
3.2  Yield surface evolution of Voronoi honeycomb with perturbed  relaxation type 53 
3.3  Comparisons 54
4  Yield surface evolution of trabecular bone 54
4.1  Yield surface evolution of trabecular bone in symmetry geometry with anisotropic material model 54
4.2  Yield surface evolution of trabecular bone in asymmetry geometry with isotropic material model 55
4.3  Summary 56
Yield surface evolution of cellular composite 66
1  Objective 66
2  Geometry 67
3  Influence of inclusions on honeycombs with ρ=40% 67
3.1  Stress-strain curve 67
3.2  Initial yield surfaces 68
3.3  Yield surface evolution of stiff honeycomb with soft inclusions 69
3.4 Yield surface evolution of soft honeycomb with stiff inclusions 70
4  Influence of inclusions on Voronoi honeycomb with ρ = 42% 70
4.1  Stress-strain curve 71
4.2  Initialyieldsurfaces 71
4.3  Yield surface evolution of stiff Voronoi honeycomb with soft inclusions 72
4.4  Yield surface evolution of ρ = 42% soft Voronoi honeycomb with stiff inclusions 72
5  Summary 73
Conclusions and future works 82
Reference 85
                                    

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