Preface |
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ix | |
Introduction |
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xiii | |
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Chapter 1 Literature Survey |
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1 | (14) |
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1.1 Random heterogeneous material |
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1 | (1) |
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1.2 Two-point probability functions |
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2 | (2) |
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1.3 Two-point cluster functions |
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4 | (1) |
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4 | (1) |
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4 | (7) |
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1.5.1 X-ray computed tomography (experimental) |
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4 | (2) |
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1.5.2 X-ray computed tomography (applications to nanocomposites) |
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6 | (1) |
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1.5.3 FIB/SEM (experimental) |
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6 | (4) |
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1.5.4 Reconstruction using statistical descriptor (numerical) |
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10 | (1) |
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1.6 Homogenization methods for effective properties |
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11 | (1) |
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1.7 Assumption of statistical continuum mechanics |
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12 | (1) |
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1.8 Representative volume element |
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13 | (2) |
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Chapter 2 Calculation of Two-Point Correlation Functions |
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15 | (28) |
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15 | (2) |
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2.2 Monte Carlo calculation of TPCF |
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17 | (2) |
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2.3 Two-point correlation functions of eigen microstructure |
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19 | (2) |
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2.4 Calculation of two-point correlation functions using SAXS or SANS data |
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21 | (7) |
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2.4.1 Case study for structural characterization using SAXS data |
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24 | (4) |
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2.5 Necessary conditions for two-point correlation functions |
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28 | (2) |
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2.6 Approximation of two-point correlation functions |
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30 | (12) |
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2.6.1 Examination of the necessary conditions for the proposed estimation |
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34 | (5) |
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2.6.2 Case study for the approximation of a TPCF |
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39 | (3) |
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42 | (1) |
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Chapter 3 Approximate Solution for N-Point Correlation Functions for Heterogeneous Materials |
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43 | (24) |
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43 | (2) |
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3.2 Approximation of three-point correlation functions |
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45 | (6) |
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3.2.1 Decomposition of higher order statistics |
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45 | (1) |
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3.2.2 Decomposition of two-point correlation functions |
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46 | (1) |
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3.2.3 Decomposition of three-point correlation functions |
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47 | (4) |
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3.3 Approximation of four-point correlation functions |
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51 | (5) |
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3.4 Approximation of N-point correlation functions |
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56 | (4) |
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60 | (6) |
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3.5.1 Computational verification |
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60 | (2) |
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3.5.2 Experimental validation |
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62 | (4) |
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66 | (1) |
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Chapter 4 Reconstruction of Heterogeneous Materials Using Two-Point Correlation Functions |
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67 | (36) |
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67 | (2) |
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4.2 Monte Carlo reconstruction methodology |
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69 | (17) |
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72 | (3) |
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75 | (2) |
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77 | (2) |
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4.2.4 Optimization of the statistical correlation functions |
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79 | (1) |
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79 | (2) |
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4.2.6 Three-phase solid oxide fuel cell anode microstructure |
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81 | (1) |
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4.2.7 Reconstruction of multiphase heterogeneous materials |
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82 | (4) |
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4.3 Reconstruction procedure using the simulated annealing (SA) algorithm |
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86 | (5) |
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4.4 Phase recovery algorithm |
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91 | (5) |
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4.5 3D reconstruction of non-eigen microstructure using correlation functions |
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96 | (5) |
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4.5.1 Microstructure reconstruction using Monte Carlo methodology |
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96 | (1) |
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97 | (1) |
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4.5.3 Monte Carlo calculation of a two-point correlation function |
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98 | (1) |
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4.5.4 Microstructure optimization |
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99 | (1) |
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4.5.5 Results and discussion |
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99 | (2) |
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101 | (2) |
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Chapter 5 Homogenization of Mechanical and Thermal Behavior of Nanocomposites Using Statistical Correlation Functions: Application to Nanoclay-based Polymer Nanocomposites |
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103 | (30) |
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103 | (1) |
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5.2 Modified strong-contrast approach for anisotropic stiffness tensor of multiphase heterogeneous materials |
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104 | (8) |
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5.3 Strong-contrast approach to effective thermal conductivity of multiphase heterogeneous materials |
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112 | (5) |
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5.4 Simulation and experimental verification |
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117 | (10) |
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5.4.1 Computer-generated model |
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118 | (2) |
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5.4.2 Thermal conductivity |
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120 | (2) |
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122 | (3) |
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125 | (2) |
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5.5 Results and discussion |
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127 | (3) |
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5.5.1 Thermal conductivity |
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127 | (1) |
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5.5.2 Thermo-mechanical properties |
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128 | (2) |
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130 | (3) |
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Chapter 6 Homogenization of Reconstructed RVE |
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133 | (36) |
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133 | (1) |
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6.2 Finite element homogenization of the reconstructed RVEs |
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134 | (7) |
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6.2.1 Reconstruction of FIB-SEM RVEs |
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134 | (4) |
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6.2.2 Finite element analysis of RVEs |
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138 | (3) |
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6.3 Finite element homogenization of the statistical reconstructed RVEs |
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141 | (8) |
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6.3.1 FEM analysis of reconstruction RVE using statistical correlation functions |
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141 | (2) |
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6.3.2 Finite element analysis of RVEs |
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143 | (6) |
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6.4 FEM analysis of debonding-induced damage model for polymer composites |
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149 | (17) |
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6.4.1 Representative volume element (RVE) |
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150 | (2) |
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6.4.2 Cohesive zone model |
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152 | (5) |
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6.4.3 Material behavior and FE simulation |
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157 | (1) |
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6.4.4 The effect of the GNP's volume fraction and aspect ratio in perfectly bonded nanocomposite |
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158 | (2) |
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6.4.5 Comparing the effect of the GNP's volume fraction and aspect ratio in perfectly bonded and cohesively bonded nanocomposites |
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160 | (3) |
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6.4.6 The effect of the GNP's aspect ratio and volume fraction in weakly bonded nanocomposite |
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163 | (3) |
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6.5 Conclusion and future work |
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166 | (3) |
Appendices |
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169 | (2) |
Appendix A |
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171 | (4) |
Appendix B |
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175 | (4) |
Bibliography |
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179 | (6) |
Index |
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185 | |