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1 | (44) |
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1.1 Definition of Poisson's Ratio |
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1 | (1) |
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1.2 History of Poisson's Ratio |
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2 | (1) |
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1.3 Definition of Auxetic Materials |
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3 | (2) |
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1.4 History of Negative Poisson's Ratio |
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5 | (1) |
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1.5 Naturally Occurring Auxetic Materials |
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6 | (1) |
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7 | (25) |
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1.7 Auxetic Yarns and Textiles |
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32 | (5) |
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1.8 Auxetic Liquid Crystalline Polymers |
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37 | (1) |
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38 | (7) |
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40 | (5) |
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2 Micromechanical Models for Auxetic Materials |
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45 | (62) |
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45 | (1) |
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2.2 Re-entrant Open-Cell Microstructure |
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45 | (3) |
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2.3 Nodule Fibril Microstructure---Hinging, Flexure and Stretching Modes of Fibrils |
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48 | (10) |
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2.4 Generalized 3D Tethered-Nodule Model |
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58 | (4) |
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2.5 Rotating Squares and Rectangles Models |
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62 | (10) |
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2.6 Rotating Triangles Models |
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72 | (4) |
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2.7 Tetrahedral Framework Structure |
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76 | (3) |
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2.8 Hard Cyclic Hexamers Model |
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79 | (2) |
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81 | (7) |
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2.10 Chiral and Anti-chiral Lattice Models |
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88 | (9) |
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2.11 Interlocking Hexagons Model |
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97 | (6) |
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103 | (4) |
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103 | (4) |
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3 Elasticity of Auxetic Solids |
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107 | (40) |
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3.1 Constitutive Relationships |
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107 | (6) |
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3.2 Bounds in Poisson's Ratio for Isotropic Solids |
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113 | (4) |
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3.3 Constitutive Relationships for Isotropic Solids |
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117 | (3) |
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120 | (2) |
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3.5 Density-Modulus Relation in Auxetic Foams |
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122 | (3) |
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3.6 Large Elastic Deformation of Auxetic Solids |
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125 | (3) |
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3.7 Anisotropic Auxetic Solids |
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128 | (14) |
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3.8 Elastoplasticity of Auxetic Solids |
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142 | (2) |
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3.9 Viscoelasticity of Auxetic Solids |
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144 | (3) |
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144 | (3) |
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4 Stress Concentration, Fracture and Damage in Auxetic Materials |
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147 | (24) |
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147 | (1) |
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4.2 Stress Concentration in Auxetic Solids with Cavities |
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148 | (1) |
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4.3 Stress Concentration in Auxetic Solids with Rigid Inclusions |
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149 | (2) |
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4.4 Stress Concentration in Auxetic Plates |
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151 | (1) |
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4.5 Stress Concentration in Auxetic Rods |
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152 | (4) |
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4.6 Fracture Characteristics of Auxetic Solids |
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156 | (2) |
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4.7 Stress and Displacement Fields Around Notches in Auxetic Solids |
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158 | (3) |
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4.8 Mode I Dimensionless Displacement Fields |
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161 | (1) |
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4.9 Mode II Dimensionless Displacement Fields |
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162 | (3) |
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4.10 Mode III Dimensionless Displacement Field |
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165 | (1) |
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4.11 Damage in Auxetic Solids |
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166 | (1) |
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4.12 Fatigue in Auxetic Materials |
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167 | (4) |
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168 | (3) |
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5 Contact and Indentation Mechanics of Auxetic Materials |
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171 | (30) |
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171 | (1) |
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5.2 Line Contact on Auxetic Materials |
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171 | (9) |
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5.3 Point Contact on Auxetic Materials |
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180 | (5) |
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5.4 Effect of Indenter Shape on Auxetic Materials |
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185 | (6) |
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5.5 Contact Between Auxetic Spheres |
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191 | (4) |
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5.6 Contact Deformation in Auxetic Composites |
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195 | (2) |
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5.7 Indentation of Auxetic Foams |
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197 | (4) |
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199 | (2) |
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201 | (16) |
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6.1 Stretching of Auxetic Bars |
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201 | (2) |
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6.2 Cantilever Bending of Auxetic Beams with Circular Cross Sections |
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203 | (2) |
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6.3 Cantilever Bending of Auxetic Beams with Rectangular Cross Sections |
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205 | (1) |
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6.4 Cantilever Bending of Auxetic Beams with Narrow Rectangular Cross Sections |
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206 | (1) |
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6.5 Cantilever Bending of Auxetic Beams with Wide Rectangular Cross Sections |
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206 | (1) |
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6.6 Cantilever Bending of Auxetic Beams with Regular Rectangular Cross Sections |
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207 | (3) |
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6.7 Uniformly Loaded Auxetic Beams with Narrow Rectangular Cross Sections |
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210 | (1) |
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6.8 Torsion of Auxetic Rods |
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211 | (2) |
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6.9 Remarks on Auxetic Rods with Circular Cross Sections |
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213 | (4) |
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215 | (2) |
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7 Auxetic Solids in Polar and Spherical Coordinates |
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217 | (14) |
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217 | (1) |
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7.2 Thick-Walled Auxetic Cylinders |
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218 | (3) |
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7.3 Rotating Thin Auxetic Disks |
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221 | (3) |
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7.4 Rotating Thick Auxetic Disks |
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224 | (2) |
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7.5 Thick-Walled Auxetic Spheres |
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226 | (5) |
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230 | (1) |
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8 Thin Auxetic Plates and Shells |
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231 | (62) |
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232 | (1) |
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8.2 Flexural Rigidity of Auxetic Plates |
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232 | (9) |
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8.3 Circular Auxetic Plates |
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241 | (18) |
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8.4 Rectangular Auxetic Plates |
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259 | (16) |
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8.5 Auxetic Plates on Auxetic Foundation |
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275 | (8) |
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8.6 In-Plane Compression of Constrained Auxetic Plate |
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283 | (2) |
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8.7 Spherical Auxetic Shells |
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285 | (8) |
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291 | (2) |
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9 Thermal Stresses in Auxetic Solids |
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293 | (28) |
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293 | (1) |
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9.2 General Thermoelasticity of Auxetic Solids |
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294 | (4) |
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9.3 Thermoelasticity of 3D Auxetics with Complete Geometrical Constraints |
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298 | (1) |
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9.4 Thermoelasticity of Plates with Temperature Variation Along Thickness |
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298 | (2) |
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9.5 Thermoelasticity of Beams with Temperature Variation Along the Beam Thickness |
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300 | (2) |
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9.6 Dimensionless Thermal Stresses for Auxetic Plates and Shells |
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302 | (6) |
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9.7 Thermal Stresses for Auxetic Plates and Shells |
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308 | (8) |
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9.8 Summary on Thermal Stresses in Auxetic Plates and Shells |
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316 | (2) |
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9.9 Thermal Conductivity in Multi-re-entrant Honeycomb Structures |
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318 | (3) |
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320 | (1) |
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10 Elastic Stability of Auxetic Solids |
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321 | (24) |
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321 | (1) |
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10.2 Buckling of Auxetic Columns |
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322 | (2) |
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10.3 Buckling of Rectangular Auxetic Plates |
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324 | (4) |
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10.4 Buckling of Circular Auxetic Plates |
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328 | (4) |
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10.5 Buckling of Cylindrical Auxetic Shells |
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332 | (4) |
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10.6 Buckling of Spherical Auxetic Shells |
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336 | (2) |
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10.7 Recent Advances on Instability in Relation to Auxetic Materials and Structures |
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338 | (7) |
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344 | (1) |
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11 Vibration of Auxetic Solids |
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345 | (22) |
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345 | (1) |
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11.2 Vibration of Circular Auxetic Plates |
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346 | (4) |
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11.3 Vibration of Rectangular Auxetic Plates |
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350 | (8) |
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11.4 Vibration of Cylindrical Auxetic Shells |
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358 | (3) |
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11.5 Vibration of Spherical Auxetic Shells |
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361 | (1) |
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11.6 Advanced Topics on Vibration and Acoustics of Auxetic Solids and Structures |
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362 | (5) |
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364 | (3) |
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12 Wave Propagation in Auxetic Solids |
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367 | (18) |
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367 | (2) |
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12.2 Longitudinal Waves in Prismatic Auxetic Bars |
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369 | (1) |
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12.3 Plane Waves of Dilatation in Auxetic Solids |
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370 | (1) |
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12.4 Plane Waves of Distortion in Auxetic Solids |
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371 | (2) |
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12.5 Rayleigh Waves in Auxetic Solids |
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373 | (1) |
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12.6 Non-dimensionalization of Wave Velocities |
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374 | (6) |
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12.7 Advanced Topics on Wave Motion in Auxetic Solids |
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380 | (5) |
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382 | (3) |
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13 Wave Transmission and Reflection Involving Auxetic Solids |
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385 | (20) |
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385 | (2) |
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387 | (2) |
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13.3 Longitudinal Wave (1D Stress State or 3D Strain State) |
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389 | (1) |
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13.4 Longitudinal Wave (Width-Constrained Plates) |
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390 | (1) |
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13.5 Plane Waves of Dilatation (1D Strain State or 3D Stress State) |
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390 | (1) |
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391 | (1) |
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392 | (1) |
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13.8 Non-dimensionalization of Transmitted and Reflected Stresses |
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392 | (2) |
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13.9 Dimensionless Transmitted Stress in Longitudinal Waves (1D Stress State) |
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394 | (1) |
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13.10 Dimensionless Transmitted Stress in Longitudinal Waves (Constrained-Width Plates) |
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395 | (2) |
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13.11 Dimensionless Transmitted Stress in Plane Waves of Dilatation |
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397 | (2) |
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13.12 Dimensionless Transmitted Stress in Torsional Waves |
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399 | (2) |
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13.13 Dimensionless Transmitted Stress in Rayleigh Waves |
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401 | (2) |
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13.14 Summary on Stress Wave Transmission Involving Auxetic Solids |
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403 | (2) |
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404 | (1) |
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14 Longitudinal Waves in Auxetic Solids |
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405 | (22) |
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405 | (2) |
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14.2 Review of Elementary Analysis |
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407 | (1) |
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408 | (1) |
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409 | (2) |
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14.5 Density Correction and Lateral Inertia |
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411 | (5) |
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14.6 Analogy with Plane Waves of Dilatation |
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416 | (3) |
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14.7 Lateral Inertia in Auxetic Love Rods |
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419 | (3) |
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14.8 Lateral Inertia and Density Correction in Auxetic Love Rods |
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422 | (5) |
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425 | (2) |
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15 Shear Deformation in Auxetic Solids |
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427 | (48) |
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427 | (1) |
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15.2 Laterally-Loaded Thick Auxetic Beams |
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428 | (8) |
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15.3 Shear Correction Factors for Isotropic Plates Within -1 ≤ v ≤ 0.5 |
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436 | (4) |
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15.4 Laterally-Loaded Thick Circular Auxetic Plates |
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440 | (4) |
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15.5 Laterally-Loaded Thick Polygonal Auxetic Plates |
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444 | (3) |
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15.6 Laterally-Loaded Thick Rectangular Auxetic Plates |
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447 | (6) |
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15.7 Buckling of Thick Auxetic Columns |
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453 | (6) |
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15.8 Buckling of Thick Auxetic Plates |
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459 | (8) |
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15.9 Vibration of Thick Auxetic Plates |
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467 | (8) |
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472 | (3) |
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16 Simple Semi-auxetic Solids |
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475 | (58) |
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475 | (1) |
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16.2 Elastic Properties of a Directional Semi-auxetic Solid |
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476 | (6) |
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16.3 Kinematical Studies on Rotation-Based Semi-auxetics |
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482 | (7) |
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16.4 Analysis of Semi-auxetic Yams |
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489 | (9) |
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16.5 Processing of Semi-auxetic Yams |
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498 | (5) |
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16.6 Functionally-Graded Semi-auxetic Beams |
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503 | (5) |
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508 | (7) |
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16.8 Semi-auxetic Sandwich Plates |
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515 | (6) |
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16.9 Mixed Auxeticity of Semi-auxetic Sandwich Structures |
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521 | (12) |
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531 | (2) |
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17 Semi-auxetic Laminates and Auxetic Composites |
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533 | (48) |
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533 | (1) |
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17.2 Semi-auxetic Unidirectional Fiber Composites |
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534 | (2) |
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17.3 Out-of-Plane Modulus of Semi-auxetic Laminates |
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536 | (8) |
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17.4 In-plane Modulus of Semi-auxetic Laminates |
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544 | (6) |
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17.5 Further Counter-Intuitive Modulus from Semi-auxetic Laminates |
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550 | (7) |
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17.6 Comparison Between In-Plane and Out-of-Plane Modulus of Semi-auxetic Laminates |
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557 | (1) |
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17.7 Semi-auxetic and Alternating Positive and Negative Thermal Expansion Laminates |
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558 | (11) |
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569 | (12) |
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579 | (2) |
Index |
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581 | |