| Introduction | p. 1 |
| Thermo-Mechanical Basics | p. 9 |
| Kinematic Equations | p. 9 |
| Coordinates and Displacements in Reference Systems | p. 10 |
| Deformation Gradients and Displacement Gradients | p. 15 |
| Strain Measures | p. 18 |
| Material and Spatial Time Derivatives of Deformations | p. 26 |
| Strain Rate Tensors | p. 29 |
| Compatibility Conditions | p. 33 |
| Stress Measures | p. 34 |
| Cauchy Stresses | p. 34 |
| Alternative Stress Measures | p. 36 |
| Rate Dependent Stress Measures | p. 37 |
| Descriptions of Static Equilibrium | p. 40 |
| Direct Formulation of Equilibrium | p. 40 |
| Calculus of Variations | p. 41 |
| Equilibrium Formulated as Variational Problem | p. 47 |
| Conservation Equations | p. 49 |
| Four Ways of Describing Conservation | p. 49 |
| Conservation of Mass | p. 51 |
| Conservation of Momentum | p. 52 |
| Conservation of Energy | p. 54 |
| Compressed Formulation of the Conservation Equations | p. 55 |
| Variational Solutions of the Balance Equations | p. 56 |
| What are Weak Forms? | p. 57 |
| Weak Forms of the Equation of Motion | p. 58 |
| Hamilton's Principle of Least Action | p. 60 |
| Thermodynamic Basics | p. 61 |
| Energy Is Conserved - The First Law | p. 61 |
| Entropy Increases - The Second Law | p. 62 |
| Thermodynamic Potentials | p. 64 |
| Formulations of the Clausius-Duhem Inequality | p. 66 |
| Consequences for Constitutive Equations | p. 67 |
| Constitutive Equations | p. 71 |
| Equations of State | p. 72 |
| Axiomatic Equations of State | p. 73 |
| Empirical Equations of State | p. 75 |
| Constitutive Equations for Total Stresses | p. 76 |
| Cauchy Elasticity | p. 77 |
| General Elastic Anisotropy | p. 78 |
| Elasticity with Symmetry Planes | p. 79 |
| Green Elasticity - Hyperelastic Behavior | p. 83 |
| Some Examples of Hyperelastic Formulations | p. 87 |
| Constitutive Equations for Inelastic Deformations | p. 98 |
| Basic Terminology in Plasticity Theory | p. 99 |
| Selected Yield Criteria | p. 104 |
| Flow Rules | p. 112 |
| Strain Rate Dependent Yield Criteria | p. 114 |
| Plasticity Effects at Shock Compression States | p. 118 |
| Meso-Mechanical Calculation of Yield Loci | p. 120 |
| Polymers - Nonlinear Elasticity, Initial Plastic Softening, Visco-Plastic Hardening | p. 123 |
| Shock Waves and Related Equations of State | p. 145 |
| Elastic Wave Propagation in Solids | p. 145 |
| Wave Equation and Sound Speeds | p. 146 |
| Solution to the One-Dimensional Wave Equation | p. 148 |
| Shock Wave Formation | p. 150 |
| Shock Wave Propagation in Solids | p. 153 |
| Conditions for Shock Waves - Phenomenological Aspects | p. 153 |
| Shock Front Dimensions | p. 157 |
| Thermo-Mechanics of Shock Waves | p. 158 |
| Dispersion - Precondition for Shock Wave Evolution and Stability | p. 158 |
| Thermodynamic Conditions upon Shock Wave Transit | p. 160 |
| Riemann Problem and Rankine-Hugoniot Equations | p. 161 |
| Hugoniot Curves and v[subscript S]-v[subscript 1] Relations | p. 165 |
| Energy Dissipation upon Shock Wave Transition | p. 169 |
| Nonlinear Equations of State for Shock Waves | p. 171 |
| Gruneisen Theory for Crystalline Oscillators | p. 172 |
| Equations of State for High-Pressure and High-Energy Regimes | p. 173 |
| Nonlinear Equations of State for Anisotropic Materials | p. 191 |
| Discussion of Nonlinear Equations of State for Shock Waves | p. 203 |
| Summary of Shock Thermodynamics | p. 203 |
| Influence of Nonlinear EOS Formulations on the Calculated Sound Speed | p. 207 |
| Hydrocodes | p. 215 |
| Modelling of Dynamic Deformation Processes | p. 215 |
| Components of a Hydrocode | p. 217 |
| Marching Solutions in Time Steps | p. 218 |
| Classification of Partial Differential Equations | p. 218 |
| Discretization - The Basic Idea | p. 227 |
| Finite Difference Methods | p. 229 |
| Time Integration with Finite Difference Schemes | p. 232 |
| Explicit or Implicit Time Integration Schemes? | p. 237 |
| Finite Volume Method | p. 239 |
| Basic Concept of Finite Volume Methods | p. 239 |
| Finite Element Method | p. 243 |
| Solutions of the Euler-Lagrange Equation | p. 244 |
| Ritz Version of Finite Elements | p. 246 |
| Finite Elements for Dynamic Problems | p. 249 |
| Shape Functions | p. 251 |
| Stiffness Matrices, Mass Matrices and Numerical Solution | p. 260 |
| Shell Elements | p. 263 |
| Finite Element Methodologies for Discontinuities | p. 267 |
| Meshfree Methods | p. 271 |
| Motivation to Develop Meshfree Methods | p. 271 |
| Evolution and Maturing of Meshfree Methods | p. 274 |
| Smoothed Particle Hydrodynamics | p. 275 |
| Coupling and Adaptive Change of Discretizations | p. 295 |
| Meshfree - Finite Element Coupling | p. 295 |
| Coupling of Static and Dynamic Solvers | p. 303 |
| Shock Wave Simulation with Hydrocodes | p. 303 |
| Artificial Viscosity | p. 305 |
| Air Blast Effects on Structures | p. 310 |
| Failure Models for Dynamic Loading Conditions | p. 315 |
| Continuum Damage Mechanics | p. 317 |
| Effective Stress and Strain Equivalence Concepts | p. 317 |
| Degradation and Damage Accumulation Functions | p. 320 |
| Isotropic Failure Models | p. 322 |
| Maximum Stress or Strain Criteria | p. 322 |
| Gurson Micro-mechanical Model for Ductile Fracture | p. 324 |
| Phenomenological Stress Triaxiality Dependent Failure Models | p. 325 |
| Brittle Failure | p. 329 |
| Spallation Modelling | p. 332 |
| Failure Models for Composites | p. 335 |
| Analytical Models for Intra-Laminar Failure | p. 337 |
| Continuum Damage Based Intra-Laminar Failure Models | p. 344 |
| Delamination models | p. 348 |
| Discretization Aspects of Composite Failure | p. 350 |
| Aspects of Advanced Dynamic Material Testing | p. 353 |
| Objectivity of Material Parameter Derivation | p. 353 |
| Material Characterization in the Low Dynamic Regime | p. 354 |
| Uniaxial Tension to Failure with Optical Strain Measurement | p. 355 |
| Shear Failure Characterization | p. 356 |
| Material Tests at Moderate Dynamic Strain Rates | p. 360 |
| Hopkinson-Bar Facilities | p. 360 |
| Direct-Impact Test for Low-Impedance Materials | p. 362 |
| Material Characterization at Extreme Strain Rates | p. 365 |
| Taylor Anvil-Test | p. 365 |
| Flyer-Plate Experiments | p. 369 |
| Edge-On Impact Test | p. 377 |
| References | p. 381 |
| Index | p. 405 |
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