Structures Under Crash and Impact (eBook)

Introduction 12
Thermo-Mechanical Basics 19
Kinematic Equations 19
Coordinates and Displacements in Reference Systems 20
Deformation Gradients and Displacement Gradients 25
Strain Measures 28
Material and Spatial Time Derivatives of Deformations 36
Strain Rate Tensors 39
Compatibility Conditions 43
Stress Measures 44
Cauchy Stresses 44
Alternative Stress Measures 46
Rate Dependent Stress Measures 47
Descriptions of Static Equilibrium 50
Direct Formulation of Equilibrium 50
Calculus of Variations 51
Equilibrium Formulated as Variational Problem 57
Conservation Equations 59
Four Ways of Describing Conservation 59
Conservation of Mass 61
Conservation of Momentum 62
Conservation of Energy 64
Compressed Formulation of the Conservation Equations 65
Variational Solutions of the Balance Equations 66
What are Weak Forms? 67
Weak Forms of the Equation of Motion 68
Hamilton's Principle of Least Action 70
Thermodynamic Basics 71
Energy Is Conserved - The First Law 71
Entropy Increases - The Second Law 72
Thermodynamic Potentials 74
Formulations of the Clausius-Duhem Inequality 76
Consequences for Constitutive Equations 77
Constitutive Equations 80
Equations of State 81
Axiomatic Equations of State 82
Empirical Equations of State 84
Constitutive Equations for Total Stresses 85
Cauchy Elasticity 86
General Elastic Anisotropy 87
Elasticity with Symmetry Planes 88
Green Elasticity - Hyperelastic Behavior 92
Some Examples of Hyperelastic Formulations 96
Constitutive Equations for Inelastic Deformations 107
Basic Terminology in Plasticity Theory 108
Selected Yield Criteria 113
Flow Rules 121
Strain Rate Dependent Yield Criteria 123
Plasticity Effects at Shock Compression States 127
Meso-Mechanical Calculation of Yield Loci 129
Polymers - Nonlinear Elasticity, Initial Plastic Softening, Visco-Plastic Hardening 132
Shock Waves and Related Equations of State 153
Elastic Wave Propagation in Solids 153
Wave Equation and Sound Speeds 154
Solution to the One-Dimensional Wave Equation 156
Shock Wave Formation 158
Shock Wave Propagation in Solids 161
Conditions for Shock Waves - Phenomenological Aspects 161
Shock Front Dimensions 165
Thermo-Mechanics of Shock Waves 166
Dispersion - Precondition for Shock Wave Evolution and Stability 166
Thermodynamic Conditions upon Shock Wave Transit 168
Riemann Problem and Rankine-Hugoniot Equations 169
Hugoniot Curves and vS-v1 Relations 173
Energy Dissipation upon Shock Wave Transition 177
Nonlinear Equations of State for Shock Waves 179
Grüneisen Theory for Crystalline Oscillators 180
Equations of State for High-Pressure and High-Energy Regimes 181
Nonlinear Equations of State for Anisotropic Materials 199
Discussion of Nonlinear Equations of State for Shock Waves 211
Summary of Shock Thermodynamics 211
Influence of Nonlinear EOS Formulations on the Calculated Sound Speed 215
Hydrocodes 222
Modelling of Dynamic Deformation Processes 222
Components of a Hydrocode 224
Marching Solutions in Time Steps 225
Classification of Partial Differential Equations 225
Discretization - The Basic Idea 234
Finite Difference Methods 236
Time Integration with Finite Difference Schemes 239
Explicit or Implicit Time Integration Schemes? 244
Finite Volume Method 246
Basic Concept of Finite Volume Methods 246
Finite Element Method 250
Solutions of the Euler-Lagrange Equation 251
Ritz Version of Finite Elements 253
Finite Elements for Dynamic Problems 256
Shape Functions 258
Stiffness Matrices, Mass Matrices and Numerical Solution 267
Shell Elements 270
Finite Element Methodologies for Discontinuities 274
Meshfree Methods 278
Motivation to Develop Meshfree Methods 278
Evolution and Maturing of Meshfree Methods 281
Smoothed Particle Hydrodynamics 282
Coupling and Adaptive Change of Discretizations 302
Meshfree - Finite Element Coupling 302
Coupling of Static and Dynamic Solvers 310
Shock Wave Simulation with Hydrocodes 310
Artificial Viscosity 312
Air Blast Effects on Structures 317
Failure Models for Dynamic Loading Conditions 322
Continuum Damage Mechanics 324
Effective Stress and Strain Equivalence Concepts 324
Degradation and Damage Accumulation Functions 327
Isotropic Failure Models 329
Maximum Stress or Strain Criteria 329
Gurson Micro-mechanical Model for Ductile Fracture 331
Phenomenological Stress Triaxiality Dependent Failure Models 332
Brittle Failure 336
Spallation Modelling 339
Failure Models for Composites 342
Analytical Models for Intra-Laminar Failure 344
Continuum Damage Based Intra-Laminar Failure Models 351
Delamination models 355
Discretization Aspects of Composite Failure 357
Aspects of Advanced Dynamic Material Testing 360
Objectivity of Material Parameter Derivation 360
Material Characterization in the Low Dynamic Regime 361
Uniaxial Tension to Failure with Optical Strain Measurement 362
Shear Failure Characterization 363
Material Tests at Moderate Dynamic Strain Rates 367
Hopkinson-Bar Facilities 367
Direct-Impact Test for Low-Impedance Materials 369
Material Characterization at Extreme Strain Rates 372
Taylor Anvil-Test 372
Flyer-Plate Experiments 376
Edge-On Impact Test 384
References 387
Index 411