Introduction .................................................... 1
Stefan Hiermaier
Part I Simulation of Automotive Crash Processes
1 Simulation of Recoverable Foams under Impact Loading ......... 9
Stefan Kolling, Andre Werner, Tobias Erhart and Paul A.
Du Bois
1.1 Introduction ........................................... 10
1.2 Current Implementation According to Fu Chang ........... 11
1.2.1 Theoretical Framework ........................... 11
1.2.2 Validation Tests ................................ 13
1.2.3 Application: Leg Impact ......................... 17
1.3 Addition of a Damage Model ............................. 19
1.3.1 Theoretical Framework ........................... 19
1.3.2 Examples ........................................ 22
References .................................................. 24
2 The Numerical Simulation of Foam - An Example of Inter-
Industrial Synergy .......................................... 27
Paul A. Du Bois
2.1 Introduction ........................................... 27
2.2 Foams - Physical Nature and Numerical Modeling ......... 28
2.3 Numerical Modeling of Foams in Automotive Crash ........ 30
2.4 Impacted Foam - The Columbia Accident .................. 35
2.5 Summary and Conclusion ................................. 41
References .................................................. 42
3 Influence of Hardening Relations on Forming Limit Curves
Predicted by the Theory of Marciniak, Kuczyński, and
Pokora ...................................................... 43
Heinrich Werner
3.1 Introduction ........................................... 43
3.2 Theoretical Model ...................................... 45
3.2.1 Constitutive Equations .......................... 47
3.2.2 Derivation of Evolution Equations for the
Onset of Instability ............................ 48
3.3 Numerical Solution Method .............................. 51
3.4 Initial Conditions ..................................... 53
3.5 Validation ............................................. 55
3.6 Convergence Properties ................................. 57
3.7 Influence of Different Hardening Relations on the
FLCs ................................................... 58
3.7.1 Effect of Various Quasi-Static Hardening
Relations on Forming Limit Curves ............... 59
3.7.2 Effect of Various Strain Rate Formulations on
the Forming Limit Curves ........................ 61
3.8 Summary ................................................ 63
References .................................................. 64
4 The Challenge to Predict Material Failure in
Crashworthiness Applications: Simulation of Producibility
to Serviceability ........................................... 67
André Haufe, Markus Feucht and Frieder Neukamm
4.1 Introduction ........................................... 68
4.2 The Process Chain of Sheet Metal Part Manufacturing .... 68
4.3 Some Ideas for Failure Modelling in Forming and
Crashworthiness Simulations ............................ 70
4.3.1 The Barlat Constitutive Model for Forming
Simulations ..................................... 71
4.3.2 Constitutive Models for Crashworthiness
Applications .................................... 72
4.3.3 A Hybrid Approach to Estimate the Void Volume
Fraction in Forming Simulations ................. 73
4.3.4 A Generalized Scalar Damage Model for Forming
and Crashworthiness Simulations ................. 75
4.4 Path-Dependent Localization ............................ 77
4.4.1 Stress and Strain Measures ...................... 77
4.4.2 Linear Accumulation of the Instability
Criterion ....................................... 79
4.4.3 Nonlinear Accumulation of the Instability
Criterion ....................................... 80
4.5 Post Critical Behaviour ................................ 81
4.5.1 Damage-Dependent Yield Stress ................... 82
4.5.2 Energy Dissipation and Fadeout .................. 83
4.6 Application of a Demonstrator Part ..................... 84
4.7 Conclusions ............................................ 85
References .................................................. 87
5 Cohesive Zone Modeling for Adhesives ........................ 89
Matthias Nossek and Stephan Marzi
5.1 Introduction ........................................... 90
5.2 Characterization Procedure ............................. 90
5.2.1 Bulk Tensile Tests .............................. 91
5.2.2 Coupon Tests .................................... 92
5.2.3 Fracture Mechanical Tests ....................... 93
5.3 Cohesive Zone Model .................................... 94
5.4 Validation ............................................. 99
5.5 Application ........................................... 101
5.6 Summary ............................................... 104
References ................................................. 104
6 Modeling the Plasticity of Various Material Classes with
a Single Quadratic Yield Function .......................... 107
Markus Wicklein
6.1 Introduction .......................................... 107
6.2 A Quadratic Yield Function ............................ 109
6.3 Parameter Identification for Foams .................... 112
6.4 Application to Honeycombs ............................. 114
6.5 Application to Carbon Fiber-Reinforced Plastics ....... 117
6.6 Outlook ............................................... 118
References ................................................. 119
7 On the Computation of a Generalised Dynamic J-Integral
and its Application to the Durability of Steel
Structures ................................................. 121
Ingbert Mangerig and Stefan Kolling
7.1 Introduction .......................................... 121
7.2 Basic Equations ....................................... 123
7.3 Theory of Configurational Forces ...................... 124
7.4 Finite Element Formulation ............................ 126
7.5 Fatigue, Stress Intensity Factor and Crack Growth
Rate .................................................. 127
7.6 Application to Durability Analysis .................... 128
7.7 Summary ............................................... 130
References ................................................. 131
Part II Numerical Modeling of Blast and Impact Phenomena
8 The MAX-Analysis: New Computational and Post-Processing
Procedures for Vehicle Safety Analysis ..................... 135
David Vinckier
8.1 Introduction .......................................... 135
8.2 Prediction Capabilities for Vehicle Mine and IED
Blast Simulations ..................................... 136
8.3 The MAX-Analysis: Unification of the Computational
Results ............................................... 138
8.4 Summary ............................................... 140
9 10 Years RHT: A Review of Concrete Modelling and
Hydrocode Applications ..................................... 143
Werner Riedel
9.1 Introduction: Dynamic Measurements and Model
Development ........................................... 143
9.1.1 The Starting Point of the Developments ......... 143
9.1.2 Equation of State for a Large-Scale
Heterogeneous Composite ........................ 146
9.1.3 Combining Civil Engineering Knowledge and
Shock Physics .................................. 148
9.2 Applications in Impact Analysis ....................... 150
9.2.1 Extended Validation and Sensitivity Analysis ... 150
9.2.2 Deformable Projectiles and Coupling with
Explosions ..................................... 154
9.3 Protecting Critical Infrastructure against Explosion
Effects ............................................... 155
9.3.1 Comparison to Engineering Models and
Empirical Formula .............................. 158
9.3.2 From Power Plant Security to Future High-
Rise-Buildings ................................. 159
9.4 Summary and Outlook ................................... 163
References ................................................. 163
10 Numerical Simulations of the Penetration of Glass Using
Two Pressure-Dependent Constitutive Models ................. 167
Sidney Chocron and Charles E. Anderson Jr.
10.1 Introduction .......................................... 167
10.2 Materials ............................................. 168
10.3 Experimental Techniques for Material
Characterization ...................................... 168
10.3.1 'Bomb' Technique ............................... 168
10.3.2 'Sleeve' Technique ............................. 170
10.4 Constitutive Model Interpretations .................... 171
10.4.1 Drucker-Prager Model ........................... 171
10.4.2 Mohr-Coulomb Model ............................. 173
10.5 Numerical Simulation of Penetration ................... 175
10.5.1 Drucker-Prager Model ........................... 176
10.5.2 Mohr-Coulomb Model ............................. 180
10.6 Summary and Conclusions ............................... 182
Appendix ................................................... 184
References ................................................. 186
11 On the main mechanisms in ballistic perforation of steel
plates at sub-ordnance impact velocities ................... 189
Tore Børvik, Sumita Dey, Odd Sture Hopperstad and Magnus
Langseth
11.1 Introduction .......................................... 190
11.2 Experimental Studies .................................. 191
11.2.1 Experimental Set-Up ............................ 191
11.2.2 Projectiles and Targets ........................ 192
11.2.3 Experimental Programs .......................... 193
11.3 Experimental Results .................................. 194
11.3.1 Effect of Projectile Impact Velocity ........... 194
11.3.2 Effect of Target Thickness ..................... 195
11.3.3 Effect of Projectile Nose-Shape ................ 196
11.3.4 Effect of Target Strength ...................... 199
11.3.5 Effect of Target Layering ...................... 201
11.3.6 Summary of Experimental Data ................... 203
11.4 Material Modelling, Material Tests and
Identification of Material Constants .................. 206
11.4.1 Constitutive Relation and Fracture Criteria .... 206
11.4.2 Material Data and Model Calibration ............ 209
11.5 Numerical Studies ..................................... 211
11.5.1 Numerical Models ............................... 212
11.5.2 Some Numerical Results ......................... 213
11.6 Concluding Remarks .................................... 216
References ................................................. 217
12 Dimensioning of concrete walls against small calibre
impact including models for deformable penetrators and
the scattering of experimental results ..................... 221
Norbert Gebbeken, Tobias Linse, Thomas Hartmann, Martien
Teich and Achim Pietzsch
12.1 Introduction .......................................... 221
12.2 Penetration and perforation of concrete walls with
non-deformable penetrators ............................ 223
12.3 Deformable projectiles ................................ 226
12.3.1 Jacketed projectiles ........................... 226
12.3.2 Homogenous deformable projectiles .............. 229
12.4 Scattering of experimental data ....................... 232
12.5 The new software-tool PenSim .......................... 235
References ................................................. 236
13 Numerical Analysis of Fluiddynamic Instabilities and
Pressure Fluctuations in the Near Field of a Detonation .... 239
Arno Klomfass
13.1 Introduction .......................................... 239
13.2 Physical Models ....................................... 243
13.3 Numerical Methods ..................................... 245
13.4 Computational Methodology ............................. 247
13.5 Results ID, 2D and 3D Free Field ...................... 248
13.6 Results 2D Above-Ground Detonation .................... 250
13.7 Conclusions ........................................... 251
References ................................................. 251
14 Numerical Simulation of Muzzle Exit and Separation
Process for Sabot-Guided Projectiles at M > 1 .............. 261
Jorn van Keuk and Arno Klomfass
14.1 Introduction .......................................... 261
14.2 Technical Specifications / Experimental Setup ......... 262
14.3 Numerical Solution Method ............................. 263
14.4 Simulation Results / Comparison with Experiments ...... 264
14.5 Conclusions / Future Work ............................. 268
References ................................................. 269
15 Numerical Analysis of the Supercavitating Flow about
blunt Bodies .............................................. 271
Arno Klomfass and Manfred Salk
15.1 Introduction .......................................... 271
15.2 Physical Models ....................................... 273
15.2.1 Conservation Equations ......................... 273
15.2.2 Equation of State .............................. 273
15.3 Numerical Method ...................................... 275
15.4 Steady State Row Fields ............................... 276
15.5 Summary ............................................... 277
References ................................................. 278
16 Numerical Analysis Method for the RC Structures
Subjected to Aircraft Impact and HE Detonation ............. 281
Masahide Katayama and Masaharu Itoh
16.1 Introduction .......................................... 281
16.2 Analytical Method ..................................... 282
16.2.1 Analysis Code .................................. 282
16.2.2 Material Models ................................ 283
16.3 Numerical Analyses .................................... 287
16.3.1 Missile Impact on RC Structure (2D) ............ 287
16.3.2 HE Detonations On and Near the RC Slab (2D &
3D) ............................................ 290
16.3.3 F-4 Phantom Crashing on a RC Wall (3D) ......... 296
16.3.4 Boeing 747 Jet Impacting on Thick Concrete
Walls (3D) ..................................... 302
16.3.5 HE Detonation in Tunnel Structure with Inner
Steel Liner (3D) ............................... 307
16.4 Conclusions ........................................... 311
References ................................................. 311
17 Groundshock Displacements - Experiment and Simulation ...... 315
Eliahu Racah
17.1 Introduction .......................................... 316
17.2 Experiment ............................................ 316
17.2.1 Experimental Setup ............................. 316
17.2.2 Experimental results ........................... 317
17.3 MSC.DYTRAN DYMMAT14 Material Model .................... 319
17.3.1 Deviatoric Behavior ............................ 319
17.3.2 Hydrostatic Behavior ........................... 321
17.4 Soil Data ............................................. 321
17.4.1 Density ........................................ 322
17.4.2 Refraction Survey and Elastic Moduli ........... 323
17.4.3 Pressiometer Tests and Volumetric Crush ........ 324
17.4.4 Direct Shear Tests and Yield Surface ........... 325
17.5 Simulation ............................................ 326
17.5.1 Simulation Setup ............................... 326
17.5.2 Simulation Results and Discussion .............. 327
17.6 Conclusion ............................................ 330
References ................................................. 330
Part III Numerical Simulation of Hypervelocity Impact
Effects
18 Hypervelocity Impact Induced Shock Waves and Related
Equations of State ......................................... 333
Stefan Hiermaier
18.1 Introduction .......................................... 333
18.2 Shock Wave Formation and the Necessity of Adequate
Equations of State .................................... 334
18.2.1 Wave Dispersion due to Nonlinear Compressive
Material Characteristics ....................... 334
18.2.2 Requirements to an EoS with Respect to Shock
Formation ...................................... 336
18.3 Equations of State for the Simulations of Shock
Processes ............................................. 337
18.3.1 Complete versus Incomplete Equations of
State .......................................... 337
18.3.2 Mie-Griineisen Shock EoS ....................... 339
18.3.3 Equations of State for Porous Materials ........ 340
References ................................................. 347
19 Artificial Viscosity Methods for Modelling Shock Wave
Propagation ................................................ 349
James Campbell and Rade Vignjevic
19.1 Introduction .......................................... 349
19.2 The Von Neumann - Richtmyer viscosity ................. 350
19.2.1 Demonstration .................................. 352
19.2.2 Wall Heating ................................... 356
19.3 Test problems for shock viscosity formulations ........ 356
19.3.1 Sod shock tube ................................. 356
19.3.2 Noh generic constant velocity shock ............ 358
19.3.3 Saltzman piston ................................ 359
19.4 Alternative forms of artificial viscosity ............. 361
19.4.1 Edge centred viscosity ......................... 362
19.4.2 Tensor viscosity ............................... 363
19.5 Summary ............................................... 364
References ................................................. 364
20 Review of Development of the Smooth Particle
Hydrodynamics (SPH) Method ................................. 367
Rade Vignjevic and James Campbell
20.1 Introduction .......................................... 367
20.2 Basic Formulation ..................................... 372
20.3 Conservation Equations ................................ 373
20.4 Kernel Function ....................................... 377
20.5 Variable Smoothing Length ............................. 378
20.6 Neighbour Search ...................................... 379
20.7 SPH Shortcomings ...................................... 380
20.7.1 Consistency ................................... 380
20.7.2 Tensile Instability ............................ 384
20.7.3 Zero-Energy Modes .............................. 389
20.8 Summary ............................................... 391
References ................................................. 392
21 Assessing the Resiliency of Composite Structural Systems
and Materials Used in Earth-Orbiting Spacecraft to
Hypervelocity Projectile Impact ............................ 397
William P. Schonberg
21.1 Introduction .......................................... 397
21.2 Historical Overview ................................... 400
21.3 Composite Material Panels ............................. 401
21.3.1 HVI Response Characterization .................. 401
21.3.2 Use in MOD Protection Systems .................. 403
21.4 Honeycomb Sandwich Panels ............................. 406
21.4.1 Early Work - The 1960s and 70s ................. 406
21.4.2 The 1980s and 90s .............................. 407
21.4.3 Recent Work .................................... 409
21.5 Conclusions ........................................... 410
References ................................................. 411
22 Numerical Simulation in Micrometeoroid and Orbital Debris
Risk Assessment ............................................ 417
Shannon Ryan
22.1 Introduction .......................................... 417
22.2 Ballistic Limit Simulation of a Representative
Satellite Structure Wall .............................. 423
22.2.1 Target Definition .............................. 424
22.2.2 Experimental Validation of the Numerical
Simulation ..................................... 424
22.2.3 Simulation Results ............................. 426
22.3 Simulation of Hypervelocity Impact on
a Representative Satellite Structure Wall Causing
Penetration and Fragment Ejection ..................... 428
22.3.1 Target Definition .............................. 430
22.3.2 Experimental Validation of the Numerical
Simulation ..................................... 430
22.3.3 Simulation Results ............................. 434
22.4 Numerical Simulation of Impact Induced Disturbances
in Satellite Structures ............................... 435
22.4.1 Target Definition .............................. 436
22.4.2 Experimental Validation of the Numerical
Simulation ..................................... 436
22.4.3 Simulation Results ............................. 439
22.5 Discussion and Summary ................................ 444
References ................................................. 445
23 Numerical Modeling of Crater Formation by Meteorite
Impact and Nuclear Explosion ............................... 447
Charles L. Mader
23.1 The NOBEL Code ........................................ 447
23.2 Modeling the Arizona Meteor Crater .................... 449
23.3 Modeling the SEDAN Crater Created by a Nuclear
Explosion ............................................. 452
23.4 Conclusions ........................................... 455
References ................................................. 457
Index ......................................................... 459
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