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研究生： 柯智欽
Ko, Chih-Chin
論文名稱： 負勁度複合材料極端黏彈與耦合場性質
Extreme viscoelastic and coupled-field properties of negative-stiffness composite materials
指導教授： 王雲哲
Wang, Yun-Che
學位類別： 博士
Doctor
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2015
畢業學年度： 103
語文別： 英文
論文頁數： 220
中文關鍵詞： 黏彈性複合材料 、負勁度 、穩定性 、有限元素法 、耦合場性質
外文關鍵詞： Viscoelastic composite, Negative stiffness, Stability, Finite element analysis, Coupled-field properties
相關次數： 點閱：107  下載：2 
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    • 本論文所研究的負勁度複合材料，是假設一純彈等向之內含物，令其中一個彈性模數為負，埋入正勁度基材中，且假設彼此間的相界面為完美。實驗證明，含鐵彈性內含物之複合材料，如鈦酸鋇，在其固-固相變化附近時，產生負勁度效應，可使得整體複合材料展現極端等效性質，例如極大或極小的等效黏彈模數、阻尼與耦合場性質，此結果突破複合材料的上下界理論。除了使用古典複合材料理論預測負勁度對整體有效性質的影響，本論文亦使用有限元數值分析方法，計算負勁度複合材料的等效耦合場性質。此類複合材料之穩定性可使用拉普諾夫Lyapunov的穩定理論分析，亦可由熱力學、應變能之正定與強橢圓性等理論進行分析，本論文使用數值方法於時間域探討其穩定性，其判定方式為分析邊界受正弦微擾刺激下，其內部物理場量隨時間的發散與否而決定，藉此以數值穩定性推估材料穩定性的方法論。本論文提出此類複合材料之負勁度值的穩定邊界，包含等效黏彈與耦合場性質。其結果顯示，除了壓電與熱膨脹係數的等效性質，其他場量的極端性質都出現在不穩定區域。在多重物理場影響下，負勁度內含物為絕緣體時，體積比越大越穩定。此外，基材為黏彈系統的負勁度複合材料，藉由阻尼機制，提供優於基材為純彈系統的穩定性。在時間域下，複合材料系統中的阻尼，可減緩不穩定現象的發散速率，因此、負勁度複合材料的極端性質可歸類於亞穩態，亦即極端性質可於短時間存在。除了負勁度複合材料之研究，本論文亦探討傳統的複合材料，以”微結構”的型式，結合軟金屬與高分子材料，同時展現高勁度與高阻尼。在軟金屬進入塑性變形前，此複合材料藉由高分子的黏彈性質提供阻尼。在軟金屬進入塑性變形後，軟金屬藉由塑性變形提供能量消散的能力。在合適的設計下，此黏彈複合材料可應用於土木工程中之樑柱接頭。

    Negative-stiffness (NS) composite materials consist of inclusions with negative bulk modulus, Young’s modulus or shear modulus, that are embedded in positive matrix. Elastic isotropy is assumed for the inclusion. Experimental evidence from composites having ferroelastic inclusions, such as barium titanate, in the vicinity of solid-solid phase transformation supports the use of negative stiffness in theoretical and numerical modeling. Extreme effective properties, such as extremely large or small effective viscoelastic moduli, damping and coupled-field coefficients, of the composite materials can be realized if negative stiffness in inclusions is allowed, hence bounds of composite materials can be broken. Stability of the NS composites requires considerations in thermodynamics, continuum mechanics and coupled-field theories, as well as the Lyapunov stability analysis. In addition to using the theory of composite materials to predict their effective properties under the effects of negative stiffness in this dissertation, numerical calculations based on finite element methods are employed to study the effective elastic, viscoelastic, thermoelastic, piezoelectric and dielectric properties of the NS composite systems. Furthermore, their stability is determined through monitoring divergence of field variables when the system is under small sinusoidal perturbation on the boundary in the time domain analysis. Connections between material stability and numerical stability are established in the finite element time-domain analysis. Stability boundaries, in terms of allowable amounts of negative stiffness, are identified for all of the studied effective properties, including the coupled-field properties. It is found that all of the extreme properties occur in the unstable regime, except for the piezoelectric and thermal expansion properties. The multiphysics effects in the coupled-field properties may provide a stabilizing mechanisms when inclusion volume fraction is large, and inclusions are electrically insulated. In addition, stability of the NS viscoelastic systems is superior to their purely elastic counterparts due to damping mechanisms. When time-dependent material properties are considered, the divergent rate of the instability phenomena can be controlled by damping in the composite systems. Hence, the extreme properties of the NS composites may be considered as metastable. In addition to research in the negative-stiffness composite materials, conventional composite materials that simultaneously exhibit high stiffness and high damping are studied through the combination of ‘microstructured’ soft metal and polymer. In small deformation, the composite exhibits large damping due to the viscoelasticity of polymer. In large deformation, the soft metal provides energy-dissipation capabilities through plastic deformation. Through suitable design, the viscoelastic composite material may be used as a beam-column connector in civil engineering.

    CHINESE ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 What is negative stiffness? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Negative-Stiffness Vibration Isolators . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Conventional composite upper and lower bound . . . . . . . . . . . . . . . . . 8 1.4 Conventional method for high damping and high stiffness . . . . . . . . . . . . 10 1.5 What are composite materials? . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Dynamical phase-field modeling of one-dimensional ferroelastics under negativestiffness influences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 The phase-field model for 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Numerical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.1 Quasi-static energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.2 Initial step-function polarization . . . . . . . . . . . . . . . . . . . . . 20 2.4.3 Initial random polarization . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.4 Initial square polarization with temperature cycling . . . . . . . . . . . 27 2.4.5 Initial square polarization with triangular-wave temperature cycling and sinusoidal loading . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 2D viscoelastic continuum with negative-stiffness inclusions . . . . . . . . . . . 39 3.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Viscoelastic finite element calculatons . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Hashin-Shtrikman 2D viscoelastic composites . . . . . . . . . . . . . . . . . . 45 3.4 Hashin-Shtrikman 3D viscoelastic composites . . . . . . . . . . . . . . . . . . 46 3.5 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.5.1 Time-domain viscoelastic finite element analysis . . . . . . . . . . . . 47 3.5.2 Two-dimensional and three-dimensional composite analyses . . . . . . 56 3.5.3 Examination of stress at inclusion-matrix interface . . . . . . . . . . . 56 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4 Anomalous effective viscoelastic, thermoelastic, dielectric and piezoelectric properties of negative-stiffness composites. . . . . . . . . . . . . . . . . . . . . . . . . 62 4.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Coupled-field properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.3 Numerical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3.1 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.2 Numerical models and settings . . . . . . . . . . . . . . . . . . . . . . 69 4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.4.1 Viscoelastic properties - effective properties . . . . . . . . . . . . . . . 74 4.4.2 Viscoelastic properties - inclusion shape effects . . . . . . . . . . . . . 80 4.4.3 Thermoelastic properties . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.4.4 Dielectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.4.5 Piezoelectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4.6 Effects of inclusion geometric arrangements . . . . . . . . . . . . . . . 89 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5 Stability of negative-stiffness composites . . . . . . . . . . . . . . . . . . . . . . 94 5.1 Classical stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.1.1 Lyapunov’s theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.1.2 Single-phase isotropic elastic continuum . . . . . . . . . . . . . . . . . 98 5.1.3 Stability criteria from Drugan and Kochmann . . . . . . . . . . . . . . 99 5.2 Comments on the low frequency behavior . . . . . . . . . . . . . . . . . . . . 102 5.3 Stability of coupled-field properties . . . . . . . . . . . . . . . . . . . . . . . 106 5.4 Stabilization by extra degrees of freedom at material points . . . . . . . . . . . 117 5.4.1 Cosserat model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.4.2 Micromorphic model . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.5 Stabilization by driving frequency . . . . . . . . . . . . . . . . . . . . . . . . 128 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 APPENDICES Appendix A: Beam-column connector . . . . . . . . . . . . . . . . . . . . . . . . 147 Appendix B: The phase-field model for 2D and 3D . . . . . . . . . . . . . . . . . 172 Appendix C: Related numerical methods used in this research . . . . . . . . . . . 177 Appendix D: Strong form to weak form for a 1D problem . . . . . . . . . . . . . 182 Appendix E: Averaged physical quantities . . . . . . . . . . . . . . . . . . . . . 184 Appendix F: Linear viscoelastic model and energy dissipation . . . . . . . . . . . 188 Appendix G: Relationship among elastic constants of isotropic materials . . . . . 190 Appendix H: Presentation slides . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

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