1 Introduction |
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1 | (16) |
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1 | (3) |
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4 | (4) |
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8 | (3) |
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11 | (4) |
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1.5 Related Reviews and Books |
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15 | (2) |
2 Review of Continuum Mechanics |
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17 | (12) |
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17 | (3) |
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20 | (2) |
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22 | (4) |
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26 | (1) |
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2.5 Kinematic Compatibility |
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27 | (2) |
3 Continuum Theory of Crystalline solids |
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29 | (17) |
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29 | (3) |
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3.2 Deformation of Lattices and Symmetry |
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32 | (2) |
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3.3 Lattice-Continuum Link: The Cauchy-Born Hypothesis |
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34 | (2) |
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3.4 Energy Density in Crystalline Solids |
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36 | (2) |
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3.5 Symmetry of Deformable Lattices: Ericksen-Pitteri Neighborhood |
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38 | (5) |
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43 | (3) |
4 Martensitic Phase Transformation |
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46 | (20) |
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4.1 Martensitic Phase Transformation; Bain or Transformation Matrix |
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46 | (12) |
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58 | (2) |
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4.3 Material Symmetry: Variants of Martensite |
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60 | (2) |
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4.4 Frame-indifference: Energy Wells |
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62 | (2) |
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4.5 Summary of the Energy Density |
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64 | (1) |
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4.6 Multiple Transformations |
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65 | (1) |
5 Twinning in Martensite |
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66 | (20) |
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5.1 Deformation Involving One Variant |
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66 | (1) |
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5.2 Deformation Involving Two Variants |
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67 | (1) |
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5.3 Interpretation as a Twin |
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68 | (1) |
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5.4 Solution of the Twinning Equation and Classification of Twins |
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69 | (5) |
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5.5 Cubic to Tetragonal Transformation |
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74 | (1) |
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5.6 Cubic to Orthorhombic Transformation |
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75 | (3) |
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5.7 Cubic to Monoclinic-I Transformation |
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78 | (2) |
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80 | (1) |
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81 | (2) |
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83 | (3) |
6 Origin of Microstructure |
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86 | (19) |
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6.1 Simplified Example in One Dimension |
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87 | (2) |
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6.2 Simplified Example in Two Dimensions |
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89 | (4) |
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6.3 Example in Three Dimensions: Fine Twins |
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93 | (3) |
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6.4 Weakly Converging Sequences and Fine Microstructure |
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96 | (2) |
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6.5 Relaxed Energy Density |
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98 | (4) |
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6.6 Length-scale of the Microstructure |
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102 | (3) |
7 Special Microstructures |
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105 | (26) |
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7.1 Austenite-Martensite Interface |
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106 | (15) |
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7.1.1 Cubic to Tetragonal Transformation |
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114 | (3) |
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7.1.2 Cubic to Orthorhombic Transformation |
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117 | (1) |
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7.1.3 Cubic to Monoclinic-I Transformation |
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117 | (1) |
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118 | (3) |
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121 | (3) |
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7.3 Wedge-like Microstructure |
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124 | (7) |
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7.3.1 Cubic to Tetragonal Transformation |
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127 | (1) |
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7.3.2 Cubic to Orthorhombic Transformation |
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128 | (3) |
8 Analysis of Microstructure |
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131 | (12) |
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8.1 Average Compatibility Conditions or the Minors Relations |
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131 | (10) |
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8.2 Gradient Young Measure |
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141 | (2) |
9 The Shape-Memory Effect |
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143 | (16) |
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144 | (7) |
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146 | (2) |
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9.1.2 Tetragonal Austenite |
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148 | (2) |
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9.1.3 Self-accommodating Plate Group |
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150 | (1) |
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9.2 Recoverable Strains under Load Control |
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151 | (3) |
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151 | (2) |
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153 | (1) |
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9.3 Recoverable Strains under Displacement Control |
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154 | (5) |
10 Thin Films |
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159 | (19) |
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10.1 A Theory of Thin Films |
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161 | (4) |
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10.2 Deformations with One Variant or Phase |
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165 | (1) |
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10.3 Deformations with Two Variants or Two Phases: Interface Conditions |
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166 | (3) |
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10.4 Martensite-Martensite Interface |
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169 | (1) |
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10.5 Austenite-Martensite Interface |
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170 | (1) |
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171 | (7) |
11 Geometrically Linear Theory |
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178 | (26) |
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11.1 Linearized Kinematics |
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178 | (3) |
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11.2 Geometrically Linear Theory for Martensitic Phase Transformations |
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181 | (4) |
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11.3 Some Microstructures and Comparisons |
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185 | (9) |
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185 | (4) |
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11.3.2 Austenite-Martensite Interface |
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189 | (3) |
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11.3.3 Wedge-like Microstructure |
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192 | (1) |
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192 | (2) |
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11.4 Recoverable Strains under Displacement Control |
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194 | (6) |
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200 | (1) |
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11.6 Recoverable Strains under Load Control |
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201 | (1) |
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11.7 Accuracy of the Geometrically Linear Theory |
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202 | (2) |
12 Piecewise Linear Elasticity |
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204 | (20) |
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12.1 Piecewise Quadratic Energy |
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204 | (5) |
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12.2 Stress Due to Incompatible Phase Arrangement |
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209 | (4) |
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12.3 Relaxed Energy Density |
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213 | (6) |
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12.4 A Modified Variational Principle |
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219 | (3) |
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12.5 Connection to Homogenization Theory and Optimal Design |
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222 | (2) |
13 Polycrystals |
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224 | (43) |
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227 | (11) |
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227 | (7) |
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234 | (4) |
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238 | (2) |
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13.3 Recoverable Strains under Displacement Control |
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240 | (3) |
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13.4 Recoverable Strains under Load Control |
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243 | (4) |
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13.5 The Consequence of Symmetry |
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247 | (2) |
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13.6 The Consequences of Texture |
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249 | (12) |
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13.7 Energy Minimization and Recoverable Strain |
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261 | (6) |
Appendix |
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267 | (5) |
Bibliography |
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272 | (15) |
Index |
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287 | |