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研究生： 賴湘微
Lai, Hsiang-Wei
論文名稱： 二維負普松材料之彈性與非彈性分析
ELASTIC AND INELASTIC ANALYSIS OF 2D AUXETIC MATERIALS
指導教授： 王雲哲
Wang, Yun-Che
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 128
中文關鍵詞： 相場模擬 、裂紋 、彈性 、黏彈性 、塑性 、負普松 、負勁度 、階級材料
外文關鍵詞： Phase field modeling, Crack, Elasticity, Viscoelasticity, Plasticity, Negative stiffness (NS), Hierarchical material
相關次數： 點閱：70  下載：0 
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    • 具有負普松性質(NPR)之材料——所謂的拉脹結構材料，在於軸向拉伸時，其橫向尺寸增加，反之尺寸縮小。在材料之力學效應中，材料的微觀結構對於普松比而言具有相當的主導性。在本論文中，使用有限元素法對於具有星形單元之蜂巢結構於彈性及非彈性力學性質之面向進行研究及討論。於彈性性質之面相，進行了微結構材料之頻散曲線分析。在蜂巢結構骨幹比於0.095時在頻率介於33kHz至40kHz之間，有最佳的降低噪音及隔震效果。此外，被填充的負普松蜂巢材料可以增強約百分之20之負普松效應，亦可增強其黏彈特性，而此增強機制是由長度尺度之分層效應所造成。亦透過建立相場模型，研究負普松蜂巢結構對在裂紋擴張以及鐵彈相變換引起的負勁度(NS)效應下的行為，而在裂紋項場中可以發現增加骨幹大小0.1 cm可以增加材料最大應力之百分之十。於負普松材料中之非彈性性質之面向，將溫度相依之材料特性導入具內凹單元形狀之彈塑性分析中。在施加力學載重及溫度加載下，傳統外凸形的蜂巢單元結構可變形為內凹形狀，其中，力學載重用於主導單元變形，並於變形時給予溫度加載以協助釋放其應力，從而在卸載後保持內凹形狀，並進行參數研究，以建立製造條件及得到該模型之負普松比。

    Negative Poisson's ratio (NPR) materials, also known as auxetic materials, expand (reduce) their lateral dimensions under tension (compression). Microstructures of materials play a dominant role in affecting their effective Poisson's ratio. In this work, both elastic and inelastic aspects of honeycomb-like materials with star-shaped cells are studied with finite element methods. For elastic responses, dispersion curves of microstructured materials are analyzed. Bandgaps in certain frequency range are identified for possible applications in noise and vibration reduction. At the honeycomb structure skeletal ratio of 0.095, the frequency is between 33kHz and 40kHz, which has the best noise reduction and isolation effect. Filled NPR honeycombs may exhibit enhanced auxetic behavior, about 20% increase, as well as enhanced viscoelastic properties. The mechanism for such enhancement in auxeticity is due to length-scale hierarchical effects. With the phase-field modeling, crack propagation and ferroelasticity-induced negative stiffness (NS) effects in NPR honeycomb have been investigated. In the crack phase field model, it can be found that increasing the backbone size by 0.1 cm can increase the maximum stress of the material by 10%. For inelastic responses of the NPR materials, temperature-dependent material properties are incorporated in the elastoplastic analysis of the formation of reentrant cell shape. Under both the mechanical and thermal loading, conventional honeycomb cells can be transformed into reentrant shapes, where mechanical load serves as deforming the cells and thermal load relaxing the stresses in cell ribs, so that after unloading the reentrant shape can be maintained. Parametric studies are conducted for establishing manufacturing conditions and resultant negative Poisson's ratio.

    CHINESEABSTRACT.................................. i ABSTRACT ........................................ ii ACKNOWLEDGMENTS................................. iii LISTOFTABLES..................................... vi LISTOFFIGURES.................................... vii NOMENCLATURE.................................... xiii 1 Introduction...................................... 1 1.1 Goalsandmotivation ............................... 1 1.2 Literaturereview ................................. 1 1.2.1 Auxeticmaterials............................. 1 1.2.2 Fillermaterials .............................. 2 1.2.3 Phasefieldmodeling ........................... 3 1.3 Outlineofthisthesis ............................... 3 2 Theoreticalconsiderations .............................. 4 2.1 Elasticityanddispersioncurves.......................... 4 2.1.1 Floquet-Blochtheory........................... 5 2.2 Viscoelasticity................................... 8 2.3 Plasticity ..................................... 9 2.3.1 Thecriterionofisotropicsystem..................... 10 2.3.2 Thecriterionofanisotropicsystem.................... 11 2.4 Two-dimensionphasefieldmodel ........................ 14 2.4.1 Phasefieldmodelingofferroelasticsystem . . . . . . . . . . . . . . . 14 2.4.2 Phasefieldmodelingofcracksystem .................. 15 2.4.3 Weakformforferroelasticandcrack................... 17 3 Numericalconsiderations............................... 19 3.1 Finiteelementsolver ............................... 19 3.2 Modeldescription................................. 20 3.2.1 Phasefieldmodel............................. 20 3.2.2 Dispersioncurve ............................. 22 3.2.3 Effectsoffilled.............................. 25 3.2.4 Plasticitythermomechanics ....................... 28 3.2.5 Effectsofmicrostructurematerials.................... 31 4 Resultsanddiscussion ................................ 32 4.1 Effectsofauxeticfillermodel........................... 32 4.1.1 Effectsoffiller’smodulus ........................ 32 4.1.2 Effectsoffiller’sPoisson’sratio ..................... 36 4.1.3 Effectiveviscoelasticproperties ..................... 37 4.2 Microstructurematerialtest............................ 45 4.3 Phasefieldmodelingofferroelasticandcrackmodel . . . . . . . . . . . . . . 50 4.3.1 Phasefieldmodelingofcrackmodel................... 50 4.3.2 Phase field modeling of ferroelastic material with crack test . . . . . . 74 4.4 Dispersioncurve ................................. 76 4.4.1 Compositematerialtest ......................... 76 4.4.2 Microstructuematerialtest........................ 85 5 Conclusionsandfuturework............................. 90 5.1 Conclusions.................................... 90 5.2 Futurework.................................... 92 LISTOFREFERENCES................................. 93 APPENDICES Appendix A: Residual Stress Analysis of an Orthotropic Composite Cylinder under ThermalLoadingandUnloading ................... 96 AppendixB: Presentationslides........................... 107 Index ............................................ 128

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