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