臺灣博碩士論文加值系統

本研究利用3D列印技術製備二維高分子材料和三維金屬超材料，並利用共振超音波頻譜掃描(RUS)研究它們的等效性質。透過模擬軟體對超材料進行有限元素分析，用以解釋實驗數據，並確立了超材料的等效彈力模數和黏彈性阻尼。從實驗數據可以看出，二維手性材料的楊氏模數隨著手性的細胞數量增加而增加，其中，3x3和4x4手性結構材料的楊氏模數可達300MPa，比其他手性結構材料的楊氏模數高出5-10%。此外，三階手性材料比一階和二階手性材料具有更佳的等效性質。在三維手性材料的部分，骨幹厚度為5.466mm的楊氏模數比厚度為4.225mm 和2.708mm 分別高出35%和91%，且如同二維的結果，隨著手性細胞數量增加，三維手性的等效性質有很大的提升。透過實驗數據驗證了手性超材料的等效柏松比，我們發現所有手性結構材料都具有負柏松比的效益。除了手性結構體和層次結構體外，我們還研究了晶格結構及其複合材料的高阻尼和高剛度特性。從結果表示，梁柱型結合斜柱型的複合材料具有較強的等效性質且晶格-矽膠複合材料的黏彈消能性質比金屬晶格材料提高了10倍。在這項研究中，我們展示了RUS-有限元素分析來實驗確定二維和三維超材料的有效黏彈性質。

Polymeric two-dimensional (2D) and metallic three-dimensional (3D) metamaterials have been manufactured by using 3D printing technologies for studying their effective properties with resonant ultrasound spectroscopy (RUS). The finite element analysis (FEA) of the metamaterials have been performed for interpretation of experimental data to determine the effective elastic moduli and viscoelastic damping of the metamaterials. From the experimental data, we can find that the Young's modulus in 2D chiral structures increases along with the increasing number of chiral cells. The Young's modulus of 3x3 and 4x4 chiral structures can arrive 300 MPa and are 5 % to 10 % higher than others. Besides, third order chiral have better effective properties than one order and two order. In the part of 3D chiral, the Young's modulus of skeleton thickness 5.466 mm is 35 % and 91 % higher than thickness 4.225 mm and 2.708 mm. And as the two-dimensional result, the effective properties in 3D chiral have a great promotion with the number of chiral cells increasing. Effective negative Poisson's ratio is also identified in the chiral metamaterials from the RUS experimental data. We can find all chiral structures have good benefit in negative Poisson's ratio. In addition to the chiral or hierarchical structures, we also study the lattice structures and their composite materials for their potentials in high damping and high stiffness properties. It is found that the composites of beam-column and oblique column have a greater effective properties than each one, and the energy dissipation property of the lattice-rubber silicone composite materials enhance 10 times than the metal lattice materials. In this work, we demonstrate the RUS-FEA methodology to experimentally determine the effective viscoelastic properties of the 2D and 3D metamaterials.

CHINESE ABSTRACT i
ABSTRACT ii
ACKNOWLEDGMENTS iii
LIST OF TABLES vii
LIST OF FIGURES xi
NOMENCLATURE xv
1 Introduction 1
1.1 Goals and motivation 1
1.2 Literature review 2
1.2.1 Chiral structures 2
1.2.2 Resonant ultrasound spectroscopy 3
1.2.3 The inverse problem 3
1.3 Outline of this thesis 4
2 Theoretical aspects 5
2.1 Elasticity 5
2.1.1 Two-dimensional theory of elasticity 5
2.1.2 Solid mechanics theory in three dimensions 6
2.2 Theoretical foundation for RUS 8
2.2.1 Resonant Ultrasound Spectroscopy 8
2.2.2 Resonant frequency of a solid cube 8
2.2.3 Resonant frequency of a solid cylinder 8
2.2.4 The inverse problem 8
3 Numerical aspects 10
3.1 Finite element simulation 10
3.1.1 COMSOL simulation 10
3.1.2 Chiral structures in solid mechanical analysis 14
3.1.3 The calculation of effective properties 15
4 Experimental aspects 17
4.1 Sample description 17
4.1.1 Two dimensional chiral structure in different thickness 17
4.1.2 Two dimensional chiral structure in different rank 17
4.1.3 Two dimensional chiral structure in different hierarchy 18
4.1.4 Three dimensional chiral structure in different scale 20
4.1.5 Three dimensional chiral structure in different skeleton thickness 20
4.1.6 Three dimensional chiral structure in different hierarchy 21
4.1.7 3D metal printing materials 22
4.1.8 Metal microlattice-silicone rubber composite 23
4.1.8.1 Metal microlattice-silicone rubber composite making process 23
4.2 Manufacture of chiral structures by 3D printer 25
4.3 Experiment of Resonant ultrasound spectroscopy 27
4.3.1 The description of machine 27
4.3.2 The experiment steps of RUS 28
5 Results and discussion 30
5.1 Mechanical properties of 2D chiral structures in COMSOL simulation 30
5.1.1 Effective properties of chiral structures with different rank 30
5.1.2 Effective properties of chiral structures with different hierarchies 32
5.2 Mechanical properties of 3D chiral structures in COMSOL simulation 36
5.2.1 Effective properties of chiral structures with different rank 36
5.2.2 Effective properties of chiral structures with different hierarchies 39
5.3 Mechanical properties of 2D chiral structure with RUS experiment 39
5.3.1 Effective properties of chiral structures with different rank 40
5.3.1.1 Force in shear mode 40
5.3.1.2 Force in bending mode 46
5.3.2 Effective properties of chiral structures with different hierarchies 50
5.3.2.1 Force in shear mode 50
5.3.2.2 Force in bending mode 64
5.4 Mechanical properties of 3D chiral structure with RUS experiment 77
5.4.1 Effective properties of chiral structures with different skeleton thickness 77
5.4.2 Effective properties of chiral structures with different hierarchies 83
5.5 Comparison of the results with COMSOL simulation and RUS experiment 85
5.5.1 Error of effective properties in 2D chiral structures 85
5.5.2 Error of effective properties of 3D chiral structures 88
5.6 Mechanical properties of 3D metal printing microlattices in COMSOL simulation and RUS experiment 89
5.7 Mechanical properties of metal microlattice-silicone rubber composites in COMSOL simulation and RUS experiment 95
6 Conclusion and future work 101
6.1 Conclusion 101
6.2 Future work 103
LIST OF REFERENCES 104
APPENDICES 106
Appendix A: Matlab code 1: Inverse of the material properties using COMSOL Multiphysics 5.5 with MATLAB-main code 106
Appendix B: Matlab code 2: Inverse of the material properties using COMSOL Multiphysics 5.5 with MATLAB-objective function code 109
Appendix C: Presentation slides 112
Index 135
VITA 137

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