Foreword |
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vii | |
About the book... |
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ix | |
Acknowledgments |
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xvii | |
Introduction to Inelasticity |
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Simple Structural Elements |
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1 | (2) |
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Introduction to Inelasticity |
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3 | (24) |
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5 | (1) |
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Why should one study inelasticity? |
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5 | (1) |
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6 | (2) |
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Observation, experimentation and modeling of material response |
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8 | (1) |
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Experimental observations and model development |
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9 | (4) |
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Plastic deformations and the friction block analogy |
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13 | (6) |
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Creep and time dependent behavior |
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19 | (7) |
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26 | (1) |
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Thermodynamics of Inelastic Materials: A lumped parameter approach |
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27 | (62) |
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Notion of a lumped parameter model |
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31 | (5) |
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The role of lumped parameter models |
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31 | (1) |
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Elements of lumped parameter systems: Extending the results of Chapter 1 |
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32 | (1) |
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33 | (3) |
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General considerations of springs and dashpots |
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36 | (11) |
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Linear and nonlinear springs |
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36 | (3) |
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39 | (1) |
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40 | (3) |
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Springs and dashpots in 2 dimensions |
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43 | (4) |
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Energy formulation of the equations of motion |
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47 | (1) |
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48 | (17) |
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Frequently asked questions and clarifications |
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52 | (13) |
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Thermal considerations: The Helmholtz and Gibbs potentials |
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65 | (20) |
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Extension of the power theorem |
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69 | (7) |
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Finding the Helmholtz and Gibbs potentials for a system |
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76 | (2) |
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Determination of the equations of motion and the temperature of the system |
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78 | (7) |
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Solving the thermo-mechanical evolution equations for an inertialess system |
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85 | (1) |
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Lumped parameter models: Gibbs potential approach |
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86 | (2) |
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88 | (1) |
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Inelastic Response of Truss Elements |
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89 | (36) |
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91 | (2) |
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Inelastic bars under axial loading |
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93 | (17) |
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Make a preliminary list of the variables of interest |
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93 | (1) |
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Make simplifying assumptions about the response |
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93 | (2) |
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Modeling of the response of the truss |
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95 | (15) |
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110 | (2) |
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112 | (4) |
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Modeling the Bauschinger effect |
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114 | (2) |
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An example cyclic loading problem |
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116 | (3) |
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116 | (1) |
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117 | (2) |
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General loading conditions |
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119 | (3) |
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122 | (3) |
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Elastoplastic Beams: An Introduction to a Boundary Value Problem |
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125 | (26) |
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127 | (1) |
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Modeling of a thermoelastoplastic beam |
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127 | (3) |
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130 | (19) |
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Make a preliminary list of variables of interest |
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130 | (1) |
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Make simplifying assumptions on the response |
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131 | (1) |
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Modeling the response of the beam |
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132 | (7) |
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Formulate the solution strategy |
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139 | (1) |
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140 | (4) |
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Beam with axial confinement |
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144 | (1) |
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Statically indeterminate problems / general beam problems |
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145 | (4) |
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149 | (1) |
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149 | (2) |
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151 | (28) |
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Rehabilitation of a crane girder |
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153 | (5) |
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Passive Damping of a frame structure using superelastic shape memory alloys (SMA) bracings |
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158 | (21) |
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Modeling the material response |
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160 | (4) |
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Modeling the SMA braced frame |
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164 | (6) |
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Dynamic analysis of the SMA braced system |
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170 | (1) |
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171 | (6) |
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177 | (2) |
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Introduction to Small Deformation Plasticity |
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179 | (34) |
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181 | (1) |
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The J2 rigid-plasticity model |
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182 | (8) |
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182 | (1) |
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183 | (1) |
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Constitutive laws: The J2 rigid plasticity equations |
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183 | (4) |
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Standard form for rigid plastic (Kuhn-Tucker form) |
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187 | (1) |
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188 | (2) |
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The J2 elasto-plasticity model |
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190 | (11) |
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The value of Ø and the ``tangent modulus'' |
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194 | (6) |
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200 | (1) |
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Hardening and the plastic are length |
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201 | (5) |
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Definition of hardening, softening and perfectly plastic behavior |
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201 | (5) |
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Finding the response of the material |
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206 | (3) |
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Finding the tangent modulus |
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207 | (2) |
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209 | (2) |
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211 | (1) |
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211 | (2) |
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The Boundary Value Problem for J2 Elastoplasticity |
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213 | (24) |
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215 | (3) |
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215 | (2) |
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217 | (1) |
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218 | (8) |
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218 | (3) |
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221 | (5) |
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The stress function and the equations of compatibility |
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226 | (1) |
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Boundary conditions for the stress function |
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227 | (4) |
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231 | (2) |
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Modifying the MATLAB PDE toolbox to solve elastoplasticity problems |
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232 | (1) |
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Concluding remarks and summary |
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233 | (1) |
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233 | (4) |
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Examples of Other Yield Surfaces: Associative and Non-associative Plasticity |
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237 | (28) |
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The general, small strain elastoplastic model |
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239 | (3) |
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General characteristics of yield surfaces |
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239 | (3) |
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Examples of general yield surfaces |
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242 | (7) |
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Pressure dependent yielding and the strength-differential or S-D effect |
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242 | (1) |
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Three-invariant or isotropic yield functions |
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242 | (5) |
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Anisotropic yield functions |
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247 | (2) |
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Examples of plastic potentials and non-associative flow rules |
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249 | (3) |
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Changes in the size, location and shape of yield surfaces and methods to quantify them |
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252 | (10) |
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256 | (1) |
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The Bauschinger effect, the back stress α and certain predictable characteristics of cyclic loading |
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257 | (1) |
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Quadratic yield surface plasticity with kinematic hardening |
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258 | (3) |
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Homogeneous motions and governing differential equations |
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261 | (1) |
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262 | (1) |
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263 | (1) |
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264 | (1) |
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Thermodynamics of Elasto-plastic Materials: The Central Role of Dissipation |
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265 | (54) |
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Generalization of J2 plasticity: the rationale |
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267 | (3) |
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Foundations of the thermodynamics of continua |
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270 | (6) |
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Governing balance laws for small deformation |
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270 | (2) |
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The macroscopic state variables |
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272 | (4) |
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The entropy and the equation of state |
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276 | (5) |
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277 | (2) |
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279 | (2) |
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Equivalent forms of the equation of state: Legendre transformations |
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281 | (5) |
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282 | (3) |
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Further transformations: The Gibbs potential |
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285 | (1) |
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The ``heat'' or entropy equation and dissipative processes |
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286 | (8) |
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Results in terms of the Helmholtz potential |
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288 | (2) |
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Generalization of the state variables and obtaining small-strain, continuum versions of spring-dashpot models |
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290 | (4) |
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Constitutive Laws for εp and the satisfaction of the second law |
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294 | (3) |
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Viscoelastic and viscoplastic models |
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295 | (1) |
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Rate independent models without yield criteria |
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296 | (1) |
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The maximum rate of dissipation criterion |
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297 | (8) |
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Graphical understanding of the MRDH |
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304 | (1) |
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Rate-independent plasticity: How to get the yield function and the flow rule by using MRDH |
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305 | (4) |
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306 | (3) |
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The Bauschinger effect and history dependence |
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309 | (7) |
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A simple model for the Bauschinger effect |
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312 | (4) |
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316 | (2) |
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318 | (1) |
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Numerical Solutions of Boundary Value Problems |
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319 | (36) |
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321 | (1) |
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322 | (4) |
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326 | (13) |
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Moving least squares approximation |
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327 | (7) |
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Weak form of the balance law |
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334 | (3) |
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Generating and solving the nonlinear algebraic equations |
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337 | (2) |
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Integration of the plastic flow equations |
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339 | (7) |
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Non-dimensionalization and its importance |
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339 | (3) |
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The convex cutting plane algorithm |
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342 | (3) |
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Homogeneous deformation examples |
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345 | (1) |
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Numerical examples of boundary value problems |
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346 | (9) |
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Rod with varying cross-section |
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346 | (1) |
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Plate with a hole subjected to tension |
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347 | (6) |
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353 | (2) |
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Summary of Continuum Thermodynamics |
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355 | (44) |
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Overview of kinematics for finite deformation |
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357 | (16) |
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Temporal and spatial gradients of the motion |
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359 | (1) |
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Local motion: Deformation of line, area and volume elements |
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360 | (4) |
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Sequential versus simultaneous action |
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364 | (2) |
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366 | (7) |
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373 | (4) |
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Dynamics and thermodynamics of motion |
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377 | (1) |
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Dynamics and thermodynamics of motion |
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377 | (12) |
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Thermodynamics or how to avoid creating perpetual motion machines |
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380 | (3) |
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Constitutive equations for thermoelasticity |
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383 | (3) |
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Isotropic elastic materials: Large strain |
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386 | (3) |
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Invariant and objective tensors |
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389 | (10) |
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When is a tensor objective? |
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393 | (3) |
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396 | (1) |
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Why do we not need to worry about objective rates? |
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396 | (3) |
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Finite Deformation Plasticity |
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399 | (56) |
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Introduction to finite deformation inelasticity |
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401 | (4) |
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The objective of a finite inelasticity constitutive model |
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403 | (2) |
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Classification of different macroscopic inelasticity models |
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405 | (2) |
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Recapitulation of small deformation inelasticity results |
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407 | (1) |
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How to develop a minimalist model for isotropic inelastic materials subject to finite deformation |
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408 | (9) |
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410 | (7) |
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Dissipative behavior of inelastic materials |
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417 | (15) |
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Isotropic hardening in finite plasticity |
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430 | (2) |
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Loading/unloading criteria and the value of Ø The advantages of strain space yield functions |
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432 | (7) |
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Results in terms of eigenvalues |
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437 | (2) |
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Numerical implementation of the plastic flow equations using the Convex Cutting Plane Algorithm |
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439 | (3) |
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442 | (1) |
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Moving natural states, aka multiplicative decompositions |
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442 | (6) |
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Geometrical significance of Dp |
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448 | (1) |
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The model can be extended to viscoplasticity and other dissipative responses |
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449 | (4) |
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Homework projects and exercises |
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453 | (2) |
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Inelasticity of Single Crystals |
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455 | (40) |
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Why is the study of the plasticity of single crystals important? |
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457 | (2) |
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Crystals and lattice vectors |
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459 | (3) |
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A word regarding our approach |
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459 | (1) |
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Introduction to crystal lattices |
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460 | (2) |
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Lattice deformation and crystallographic slip |
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462 | (4) |
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Deformation and slip of single crystals |
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466 | (4) |
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The Helmholtz potential and equation of state for a crystal |
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470 | (2) |
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Thermomechanical equation of state |
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472 | (1) |
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The dissipation function and constitutive equations for slip |
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472 | (11) |
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Independence of slip systems and other equations for the rate of slip |
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475 | (1) |
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Explicit expressions for the resolved shear stress in terms of the lattice vectors |
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476 | (1) |
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The evolution equation for ai |
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477 | (6) |
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483 | (9) |
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Phenomenological model of hardening: Single slip |
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485 | (1) |
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Hardening with multiple slip |
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486 | (6) |
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492 | (1) |
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493 | (2) |
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495 | (20) |
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Shot Peening - A Process for Creating Wear Resistant Surfaces |
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497 | (4) |
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Background and problem statement |
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497 | (1) |
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Simplifications and assumptions on modeling the system |
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498 | (2) |
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Sample results of the analysis |
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500 | (1) |
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Equal Channel Angular Extrusion - A Materials Processing Route |
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501 | (8) |
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Background and problem statement |
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501 | (2) |
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Need analysis and specification of the system |
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503 | (2) |
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505 | (3) |
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508 | (1) |
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Modeling of an Aging Face - An Application in Biomechanics |
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509 | (6) |
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Background and problem statement |
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509 | (1) |
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Need analysis and specification of the system |
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510 | (1) |
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511 | (2) |
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513 | (2) |
Bibliography |
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515 | (16) |
Index |
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531 | |