Preface |
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xiii | |
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1 | (10) |
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3 | (5) |
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8 | (1) |
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8 | (1) |
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1.4 Nonlinearities and Confinement |
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9 | (1) |
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10 | (1) |
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10 | (1) |
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2 Conservation Laws And The Hugoniot Jump Conditions |
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11 | (32) |
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2.1 Conservation Laws in the Eulerian Reference Frame |
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11 | (1) |
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2.2 Tractions and the Cauchy Stress Tensor |
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12 | (2) |
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14 | (2) |
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2.4 Conservation of Momentum |
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16 | (1) |
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2.5 Conservation of Energy |
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17 | (2) |
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19 | (1) |
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2.7 The Rankine--Hugoniot Jump Conditions |
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20 | (7) |
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2.8 Differential Jump Conditions |
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27 | (1) |
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2.9 Cylindrical and Spherical Shock Fronts |
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28 | (1) |
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29 | (4) |
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2.11 Initial and Boundary Conditions |
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33 | (1) |
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2.12 Comments on Waves and Classical Continuum Mechanics |
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34 | (4) |
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38 | (1) |
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38 | (5) |
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43 | (74) |
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43 | (2) |
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3.2 Small Strain Linear Elasticity |
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45 | (2) |
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47 | (6) |
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53 | (3) |
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56 | (3) |
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3.6 Various Yield Surfaces |
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59 | (4) |
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63 | (1) |
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3.8 Energy Dissipation through Plastic Flow |
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64 | (3) |
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3.9 Energy Stored in Elastic Deformation |
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67 | (1) |
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68 | (1) |
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3.11 A Discussion of Strain |
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68 | (2) |
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3.12 Characterization of Real Materials |
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70 | (9) |
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3.13 Constitutive Models for Yield and Flow Stress |
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79 | (5) |
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3.14 Damage, Failure, and Stress State |
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84 | (11) |
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95 | (2) |
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3.16 Exact Solution for an Arbitrary Strain Increment |
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97 | (5) |
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102 | (1) |
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102 | (15) |
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4 Mechanical Waves, Shocks, And Rarefactions |
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117 | (58) |
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4.1 Linear Elastic Waves; Pushing on a Half Space |
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117 | (2) |
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119 | (14) |
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4.3 Rarefaction Fans and the Rarefaction Shock Approximation |
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133 | (10) |
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4.4 Impacting a Rigid Wall |
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143 | (2) |
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4.5 Reflection off a Free Surface |
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145 | (1) |
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4.6 Finite Impactor Striking a Rigid Wall |
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146 | (2) |
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4.7 Finite Impactor with Hysteresis Striking a Rigid Wall |
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148 | (1) |
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4.8 A Finite Projectile Impacting a Material Wall |
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149 | (7) |
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4.9 Wave Reflection and Transmission at an Internal Interface |
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156 | (2) |
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4.10 Square Pulse Reflection: Tensile Stress States and Tensile Spall |
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158 | (6) |
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4.11 Exact Solution for Viscoelastic Smooth Wave Fronts |
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164 | (3) |
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4.12 A Warning about the (υ, ·e;) Plane |
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167 | (1) |
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168 | (1) |
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168 | (7) |
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5 Elastic-Plastic Deformation And Shocks |
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175 | (82) |
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5.1 Cylindrical Impactor Striking a Rigid Wall (Taylor Anvil) |
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175 | (8) |
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5.2 The Split-Hopkinson Pressure Bar |
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183 | (7) |
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5.3 Pushing on an Elastic-Plastic Half Space: The Two-Wave Structure and Flyer Plate Impacts |
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190 | (4) |
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194 | (2) |
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5.5 The Hugoniot Elastic Limit |
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196 | (1) |
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5.6 The Hugoniot and Rarefaction of Real Materials |
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197 | (7) |
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5.7 Flyer Plate Impact Test |
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204 | (1) |
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5.8 Elastic-Plastic Shock Rise Times |
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205 | (2) |
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207 | (2) |
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5.10 Mie-Griineisen Equation of State |
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209 | (4) |
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213 | (5) |
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5.12 Reflection and Transmission |
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218 | (3) |
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5.13 Additional Comments on Sound Speed and Precursors |
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221 | (3) |
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224 | (8) |
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232 | (4) |
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5.16 Detonation of Explosives |
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236 | (6) |
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242 | (1) |
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242 | (15) |
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257 | (36) |
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6.1 The One-Dimensional Cavity Expansion |
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257 | (3) |
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6.2 The Boundary Condition at the Elastic-Plastic Interface |
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260 | (1) |
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6.3 The Compressible Cylindrical Cavity Expansion |
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261 | (8) |
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6.4 The Compressible Spherical Cavity Expansion Solution |
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269 | (9) |
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6.5 Comparing the One-Dimensional, Cylindrical, and Spherical Cavity Expansions |
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278 | (2) |
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6.6 Effect of Incompressibility and Velocity Bounds for the Cylindrical Cavity Expansion |
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280 | (3) |
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6.7 Extending the Cavity Expansion to Address Nonlinear Pressure Response |
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283 | (2) |
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6.8 Numerical Implementation |
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285 | (1) |
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285 | (1) |
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286 | (7) |
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293 | (40) |
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7.1 Steel Projectiles Penetrating Aluminum Targets |
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293 | (2) |
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7.2 Tungsten Projectiles Penetrating Steel Targets |
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295 | (2) |
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297 | (3) |
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7.4 Phases of Penetration |
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300 | (1) |
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7.5 Centerline Momentum Balance and Hydrodynamic Approximation |
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300 | (2) |
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7.6 Numerical Simulations |
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302 | (1) |
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7.7 Numerical Simulations of L/D = 10 Tungsten Impacting Steel |
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303 | (10) |
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7.8 The Stress at the Projectile--Target Interface |
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313 | (2) |
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7.9 Crater Radii, Plastic and Elastic Strains, and the Energy Partition |
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315 | (4) |
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319 | (10) |
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7.11 Hypervelocity Impact |
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329 | (1) |
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330 | (1) |
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330 | (3) |
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8 The Tate-Alekseevskii Model |
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333 | (38) |
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8.1 Bernoulli's Equation for Steady Flow |
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333 | (2) |
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335 | (3) |
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8.3 Behavior of the Tate Model |
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338 | (2) |
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340 | (5) |
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8.5 Further Examples with the Tate Model |
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345 | (3) |
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8.6 Tate's Later Modifications |
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348 | (5) |
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8.7 The Link between Rt and the Cavity Expansion |
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353 | (4) |
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8.8 Target Resistance and the Rt Dilemma |
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357 | (6) |
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8.9 Sensitivity of the Tate Model to Various Parameters |
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363 | (1) |
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8.10 The Minimum Speed for Penetration |
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364 | (2) |
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366 | (1) |
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366 | (5) |
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371 | (20) |
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9.1 Axial Change in Momentum for the Target |
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371 | (1) |
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9.2 Axial Change in Momentum for the Projectile |
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371 | (1) |
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9.3 Radial Momentum and the Crater Radius |
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372 | (4) |
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9.4 Two Empirical Relations |
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376 | (2) |
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9.5 Where Does the Material Go? |
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378 | (6) |
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9.6 A Shear Band Motivated Damage Model |
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384 | (4) |
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388 | (1) |
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389 | (1) |
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389 | (2) |
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10 The Walker-Anderson Model |
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391 | (52) |
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10.1 The Centerline Momentum Balance |
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391 | (2) |
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393 | (1) |
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10.3 A Velocity Profile in the Projectile |
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394 | (1) |
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10.4 A Velocity Profile in the Target |
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395 | (4) |
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10.5 The Deceleration of the Rear of the Projectile |
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399 | (2) |
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10.6 The Stress in the Target and the Penetration Resistance |
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401 | (4) |
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10.7 The Momentum Balance Equation |
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405 | (2) |
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10.8 The Extent of the Plastically Flowing Region in the Target |
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407 | (1) |
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10.9 The Extent of the Plastically Flowing Region in the Projectile |
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408 | (1) |
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10.10 Initial Impact Conditions |
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409 | (2) |
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411 | (5) |
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10.12 Comparison of Velocities and Projectile Residual Length |
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416 | (2) |
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10.13 Comparison to the Hohler-Stilp Data from Chapter 8 |
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418 | (1) |
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10.14 Comparison to Hypervelocity Penetration vs. Time Data |
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419 | (3) |
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10.15 Tungsten into Aluminum: Rigid and Secondary Penetration |
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422 | (4) |
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10.16 Plastic Strain in the Target |
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426 | (3) |
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10.17 Finding a using the Dynamic Plasticity Approach |
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429 | (5) |
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434 | (1) |
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434 | (9) |
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443 | (38) |
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11.1 A Velocity Field for Back Surface Bulging |
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445 | (9) |
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11.2 Model Bulge and Breakout and Experimental Comparisons |
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454 | (5) |
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459 | (2) |
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11.4 Ductility vs. Strength Influences on Vy and Vr |
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461 | (10) |
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11.5 Fragmentation and Behind Armor Debris |
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471 | (5) |
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476 | (1) |
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476 | (5) |
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12 Nondeforming (Rigid) Impactors |
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481 | (26) |
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12.1 Thin Plate Perforation by Blunt Rigid Projectiles |
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481 | (3) |
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12.2 Flow Fields for Pointed Projectiles |
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484 | (6) |
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12.3 Examples with the Walker-Anderson Model |
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490 | (7) |
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12.4 Direct Use of the Cavity Expansion |
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497 | (5) |
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12.5 Projectile Eroding-Noneroding Transition Velocity |
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502 | (1) |
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502 | (1) |
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503 | (4) |
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13 Yarns, Fabrics, And Fiber-Based Composites |
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507 | (46) |
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13.1 Deformation, Strain, and the First Piola-Kirchhoff Stress |
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508 | (7) |
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13.2 The Behavior of a Single Yarn under Impact |
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515 | (10) |
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13.3 Static Deflection of a Fabric Sheet Composed of 0/90 Yarns |
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525 | (9) |
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13.4 The Ballistic Limit of a Fabric |
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534 | (5) |
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13.5 Fiber-Based Composites |
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539 | (2) |
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13.6 Behavior of Other Fibers |
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541 | (2) |
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543 | (1) |
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544 | (4) |
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548 | (1) |
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548 | (5) |
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14 Rotation, Stretch, And Finite Elasticity |
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553 | (46) |
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14.1 The Deformation Gradient |
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553 | (2) |
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14.2 Deformation: Rotation and Stretch in Two Dimensions |
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555 | (5) |
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14.3 Deformation: Stretch and Rotation in Three Dimensions |
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560 | (4) |
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14.4 Stress and Strain in Original and Current Configurations |
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564 | (3) |
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14.5 Rate of Deformation and Rotation Rate |
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567 | (2) |
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14.6 Finite Strain Elasticity |
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569 | (3) |
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14.7 Blatz-Ko and Mooney-Rivlin Constitutive Models |
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572 | (7) |
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14.8 Incremental Constitutive Models and Corotational Stress Rates |
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579 | (7) |
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586 | (1) |
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586 | (13) |
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Appendix A Conservation Laws and Curvilinear Coordinates |
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599 | (54) |
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599 | (1) |
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A.2 The Three Conservation Laws |
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600 | (5) |
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A.3 Curvilinear Geometry and Differential Operators |
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605 | (14) |
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A.4 Cartesian Coordinates |
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619 | (3) |
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A.5 Cylindrical Coordinates |
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622 | (3) |
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A.6 Spherical Coordinates |
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625 | (4) |
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629 | (18) |
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647 | (1) |
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647 | (4) |
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Appendix B Units, Conversions, And Constants |
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651 | (2) |
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651 | (1) |
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652 | (1) |
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B.3 Constants of Interest |
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652 | (1) |
Appendix C Elastic, Shock, and Strength Properties of Materials |
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653 | (10) |
Appendix D Figure Acknowledgments |
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663 | (1) |
Exercises |
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664 | (1) |
Bibliography |
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665 | (10) |
Index |
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675 | |