A TEXT-BOOK ON ROOFS AND BRIDGES: HIGHER STRUCTURES
1 Introduction 1 11 High-Temperature Inelasticity in Structural Materials 2 111 Uni-axial Stress State 2 112 Multi-axial Effects 22 12 High-Temperature Inelasticity in Structures 30 121 Examples for Creep in Structures 30 122 Examples for Thermo-mechanical Cycling 39 13 Microstructural Features and Length Scale Effects 52 14 Temporal Scale Effects 59 15 Modeling Approaches and Objectives 60 151 Modeling Approaches 60 152 Objectives, Modeling Requirements, and Steps for Structural Analysis 66 References 68 2 Continuum Mechanics in One Dimension 79 21 Motion, Derivatives, and Deformation 80 22 Conservation of Mass 83 23 Balance of Momentum 83 24 Balance of Energy 85 25 Entropy Inequality 87 26 Dissipation Inequality, Free Energy, and Stress 88 References 90 3 Elementary Uni-axial Constitutive Models 91 31 Heat Transfer 91 32 Thermo-elasticity 94 33 Non-linear Viscosity, Viscoplasticity, and Rigid Plasticity 96 34 Elasto-plasticity 99 35 Hardening, Softening, and Ageing 106 351 Strain Hardening 106 352 Kinematic Hardening 110 353 Phase Mixture Models for Hardening and Softening 115 354 Ageing 120 36 Damage 123 361 Kachanov-Rabotnov Model 124 362 Continuum Damage Mechanics 131 References 136 4 Three-Dimensional Continuum Mechanics 141 41 Motion, Derivatives and Deformation 142 411 Motion and Derivatives 142 412 Deformation Gradient and Strain Tensors 144 413 Velocity Gradient, Deformation Rate, and Spin Tensors 150 42 Conservation of Mass 159 43 Balance of Momentum 159 431 Stress Vector 159 432 Integral Form 160 433 Stress Tensor and Cauchy Formula 161 434 Local Forms 164 44 Balance of Angular Momentum 165 45 Balance of Energy 166 46 Entropy and Dissipation Inequalities 168 References 170 5 Constitutive Models 173 51 Heat Transfer 174 52 Material and Physical Symmetries 176 53 Thermo-elasticity 179 531 Preliminary Remarks 179 532 Isotropic Materials 182 533 Anisotropic Materials 184 534 Linear Elasticity 187 54 Non-linear Viscosity, Viscoplasticity, and Rigid Plasticity 190 541 Preliminary Remarks 190 542 Isotropic Materials 198 543 Initially Anisotropic Materials 205 544 Functions of Stress and Temperature 223 55 Elasto-plasticity 227 551 Multiplicative Decomposition of Deformation Gradient 228 552 Small Strains 236 56 Hardening and Softening Rules 238 561 Time and Strain Hardening 240 562 Kinematic Hardening 242 563 Phase Mixture Models for Hardening and Softening 250 57 Damage Processes and Damage Mechanics 254 571 Scalar-Valued Damage Variables 254 572 Damage-Induced Anisotropy 266 References 272 6 Examples of Constitutive Equations for Various Materials 283 61 Basic Approaches of Identification 283 62 Isotropic Materials 285 621 Type 316 Steel 285 622 Steel 13CrMo4-5 286 623 Steel X20CrMoV12-1 287 624 Aluminium Alloy BS 1472 299 63 Initially Anisotropic Materials 302 631 Forged Al-Cu-Mg-Si Alloy 303 632 Multi-pass Weld Metal 308 References 318