Hiermaier Structures Under Crash and Impact

Continuum Mechanics, Discretization and Experimental Characterization
1. Auflage 2007
ISBN: 978-0-387-73863-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 416 Seiten

This book examines the testing and modeling of materials and structures under dynamic loading conditions. Readers get an in-depth analysis of the current mathematical modeling and simulation tools available for a variety of materials, alongside discussions of the benefits and limitations of these tools in industrial design. Following a logical and well organized structure, this volume uniquely combines experimental procedures with numerical simulation, and provides many examples.

Autoren/Hrsg.

Hiermaier, Stefan

Inhaltsverzeichnis

1;Introduction;12
2;Thermo-Mechanical Basics;19
2.1;Kinematic Equations;19
2.1.1;Coordinates and Displacements in Reference Systems;20
2.1.2;Deformation Gradients and Displacement Gradients;25
2.1.3;Strain Measures;28
2.1.4;Material and Spatial Time Derivatives of Deformations;36
2.1.5;Strain Rate Tensors;39
2.1.6;Compatibility Conditions;43
2.2;Stress Measures;44
2.2.1;Cauchy Stresses;44
2.2.2;Alternative Stress Measures;46
2.2.3;Rate Dependent Stress Measures;47
2.3;Descriptions of Static Equilibrium;50
2.3.1;Direct Formulation of Equilibrium;50
2.3.2;Calculus of Variations;51
2.3.3;Equilibrium Formulated as Variational Problem;57
2.4;Conservation Equations;59
2.4.1;Four Ways of Describing Conservation;59
2.4.2;Conservation of Mass;61
2.4.3;Conservation of Momentum;62
2.4.4;Conservation of Energy;64
2.4.5;Compressed Formulation of the Conservation Equations;65
2.5;Variational Solutions of the Balance Equations;66
2.5.1;What are Weak Forms?;67
2.5.2;Weak Forms of the Equation of Motion;68
2.5.3;Hamilton's Principle of Least Action;70
2.6;Thermodynamic Basics;71
2.6.1;Energy Is Conserved - The First Law;71
2.6.2;Entropy Increases - The Second Law;72
2.6.3;Thermodynamic Potentials;74
2.6.4;Formulations of the Clausius-Duhem Inequality;76
2.6.5;Consequences for Constitutive Equations;77
3;Constitutive Equations;80
3.1;Equations of State;81
3.1.1;Axiomatic Equations of State;82
3.1.2;Empirical Equations of State;84
3.2;Constitutive Equations for Total Stresses;85
3.2.1;Cauchy Elasticity;86
3.2.2;General Elastic Anisotropy;87
3.2.3;Elasticity with Symmetry Planes;88
3.2.4;Green Elasticity - Hyperelastic Behavior;92
3.2.5;Some Examples of Hyperelastic Formulations;96
3.3;Constitutive Equations for Inelastic Deformations;107
3.3.1;Basic Terminology in Plasticity Theory;108
3.3.2;Selected Yield Criteria;113
3.3.3;Flow Rules;121
3.3.4;Strain Rate Dependent Yield Criteria;123
3.3.5;Plasticity Effects at Shock Compression States;127
3.3.6;Meso-Mechanical Calculation of Yield Loci;129
3.3.7;Polymers - Nonlinear Elasticity, Initial Plastic Softening, Visco-Plastic Hardening;132
4;Shock Waves and Related Equations of State;153
4.1;Elastic Wave Propagation in Solids;153
4.1.1;Wave Equation and Sound Speeds;154
4.1.2;Solution to the One-Dimensional Wave Equation;156
4.2;Shock Wave Formation;158
4.3;Shock Wave Propagation in Solids;161
4.3.1;Conditions for Shock Waves - Phenomenological Aspects;161
4.3.2;Shock Front Dimensions;165
4.4;Thermo-Mechanics of Shock Waves;166
4.4.1;Dispersion - Precondition for Shock Wave Evolution and Stability;166
4.4.2;Thermodynamic Conditions upon Shock Wave Transit;168
4.4.3;Riemann Problem and Rankine-Hugoniot Equations;169
4.4.4;Hugoniot Curves and vS-v1 Relations;173
4.4.5;Energy Dissipation upon Shock Wave Transition;177
4.5;Nonlinear Equations of State for Shock Waves;179
4.5.1;Grüneisen Theory for Crystalline Oscillators;180
4.5.2;Equations of State for High-Pressure and High-Energy Regimes;181
4.5.3;Nonlinear Equations of State for Anisotropic Materials;199
4.6;Discussion of Nonlinear Equations of State for Shock Waves;211
4.6.1;Summary of Shock Thermodynamics;211
4.6.2;Influence of Nonlinear EOS Formulations on the Calculated Sound Speed;215
5;Hydrocodes;222
5.1;Modelling of Dynamic Deformation Processes;222
5.2;Components of a Hydrocode;224
5.2.1;Marching Solutions in Time Steps;225
5.3;Classification of Partial Differential Equations;225
5.4;Discretization - The Basic Idea;234
5.5;Finite Difference Methods;236
5.5.1;Time Integration with Finite Difference Schemes;239
5.5.2;Explicit or Implicit Time Integration Schemes?;244
5.6;Finite Volume Method;246
5.6.1;Basic Concept of Finite Volume Methods;246
5.7;Finite Element Method;250
5.7.1;Solutions of the Euler-Lagrange Equation;251
5.7.2;Ritz Version of Finite Elements;253
5.7.3;Finite Elements for Dynamic Problems;256
5.7.4;Shape Functions;258
5.7.5;Stiffness Matrices, Mass Matrices and Numerical Solution;267
5.7.6;Shell Elements;270
5.7.7;Finite Element Methodologies for Discontinuities;274
5.8;Meshfree Methods;278
5.8.1;Motivation to Develop Meshfree Methods;278
5.8.2;Evolution and Maturing of Meshfree Methods;281
5.8.3;Smoothed Particle Hydrodynamics;282
5.9;Coupling and Adaptive Change of Discretizations;302
5.9.1;Meshfree - Finite Element Coupling;302
5.9.2;Coupling of Static and Dynamic Solvers;310
5.10;Shock Wave Simulation with Hydrocodes;310
5.10.1;Artificial Viscosity;312
5.10.2;Air Blast Effects on Structures;317
6;Failure Models for Dynamic Loading Conditions;322
6.1;Continuum Damage Mechanics;324
6.1.1;Effective Stress and Strain Equivalence Concepts;324
6.1.2;Degradation and Damage Accumulation Functions;327
6.2;Isotropic Failure Models;329
6.2.1;Maximum Stress or Strain Criteria;329
6.2.2;Gurson Micro-mechanical Model for Ductile Fracture;331
6.2.3;Phenomenological Stress Triaxiality Dependent Failure Models;332
6.2.4;Brittle Failure;336
6.2.5;Spallation Modelling;339
6.3;Failure Models for Composites;342
6.3.1;Analytical Models for Intra-Laminar Failure;344
6.3.2;Continuum Damage Based Intra-Laminar Failure Models;351
6.3.3;Delamination models;355
6.3.4;Discretization Aspects of Composite Failure;357
7;Aspects of Advanced Dynamic Material Testing;360
7.1;Objectivity of Material Parameter Derivation;360
7.2;Material Characterization in the Low Dynamic Regime;361
7.2.1;Uniaxial Tension to Failure with Optical Strain Measurement;362
7.2.2;Shear Failure Characterization;363
7.3;Material Tests at Moderate Dynamic Strain Rates;367
7.3.1;Hopkinson-Bar Facilities;367
7.3.2;Direct-Impact Test for Low-Impedance Materials;369
7.4;Material Characterization at Extreme Strain Rates;372
7.4.1;Taylor Anvil-Test;372
7.4.2;Flyer-Plate Experiments;376
7.4.3;Edge-On Impact Test;384
8;References;387
9;Index;411