AUTODYN_theory_manual.pdf

【核心代码】

Table of Contents
3
VARIABLE NOTATION .......................................................................................................... 8
CHAPTER 1...........................................................................................................OVERVIEW 17
1. Introduction............................................................................................................ 17
2. Theory Overview ................................................................................................... 18
§1. Lagrange Processor .......................................................................................... 19
§2. Euler Processors ............................................................................................... 19
§3. ALE Processor................................................................................................... 20
§4. Structural Processor .......................................................................................... 20
§5. Processor Coupling ........................................................................................... 21
§6. Material Models ................................................................................................. 22
3. Summary ............................................................................................................... 22
CHAPTER 2.......................................................................................................... RESERVED 23
CHAPTER 3........................................................................LAGRANGE PROCESSOR IN 2D 25
1. Introduction............................................................................................................ 25
2. Governing Equations............................................................................................. 25
3. Lagrange Subgrids ................................................................................................ 28
§1. Centering Of Variables ...................................................................................... 30
4. Zone Volumes and Strain Rates............................................................................ 32
§1. Zone Volumes ................................................................................................... 32
§2. Strain Rates....................................................................................................... 33
5. Pressures and Stresses ........................................................................................ 36
§1. Stress Increments.............................................................................................. 36
§2. Stress Rotation Correction................................................................................. 37
6. Nodal Forces ......................................................................................................... 38
§1. Internal Forces................................................................................................... 39
§2. External Forces.................................................................................................. 41
§3. Pseudo-Viscous Forces..................................................................................... 43
§4. Hourglass Damping ........................................................................................... 43
§5. Anti-Tangle Forces ............................................................................................ 46
7. Nodal Accelerations, Velocities and Displacements.............................................. 48
§1. Static Damping (Dynamic Relaxation)............................................................... 48
8. Boundary Conditions ............................................................................................. 49
§1. Velocity Constraints........................................................................................... 49
§2. Pressure Boundaries ......................................................................................... 50
§3. Transmitting Boundaries.................................................................................... 50
9. Timestep................................................................................................................ 51
10. Conservation of Momentum and Energy ............................................................... 52
11. Rezoning ............................................................................................................... 53
CHAPTER 4........................................................................LAGRANGE PROCESSOR IN 3D 55
1. Introduction............................................................................................................ 55
2. Governing Equations............................................................................................. 56 
Table of Contents
3. Lagrange Subgrids ................................................................................................ 58
§1. Centering of Variables ....................................................................................... 60
4. Zone Volumes and Strain Rates............................................................................ 61
§1. Strain Rates....................................................................................................... 64
5. Pressures and Stresses ........................................................................................ 66
§1. Stress Increments.............................................................................................. 66
§2. Stress Rotation Correction................................................................................. 67
6. Nodal Forces ......................................................................................................... 69
§1. Internal Forces................................................................................................... 69
§2. External Forces.................................................................................................. 72
§3. Pseudo-Viscous Forces..................................................................................... 73
§4. Hourglass Damping ........................................................................................... 74
7. Nodal Accelerations, Velocities and Displacements.............................................. 76
§1. Static Damping (Dynamic Relaxation)............................................................... 77
8. Boundary Conditions ............................................................................................. 77
§1. Velocity Constraints........................................................................................... 78
§2. Pressure Boundaries ......................................................................................... 78
§3. Transmitting Boundaries.................................................................................... 79
9. Time-step............................................................................................................... 80
10. Conservation of Momentum and Energy ............................................................... 81
CHAPTER 5.......................................................................ALE PROCESSOR IN 2D AND 3D 82
1. Introduction............................................................................................................ 82
2. Governing Equations ............................................................................................. 83
3. ALE Subgrids......................................................................................................... 85
4. ALE Methodology .................................................................................................. 87
5. Grid Motion Constraints......................................................................................... 88
6. Regrid Phase in 2D ............................................................................................... 89
7. Advective phase in 2D........................................................................................... 91
§1. Mass .................................................................................................................. 91
§2. Momentum and energy...................................................................................... 91
§3. Update cell velocities......................................................................................... 93
§4. Advection of Other Variables............................................................................. 93
§5. Reevaluation of the Pressure ............................................................................ 94
8. Regrid Phase in 3D ............................................................................................... 94
9. Advective Phase in 3D .......................................................................................... 95
§1. Mass .................................................................................................................. 96
§2. Momentum and Energy ..................................................................................... 96
§3. Update cell velocities......................................................................................... 98
§4. Advection of Other Variables............................................................................. 99
§5. Reevaluation of the Pressure ............................................................................ 99
10. Conclusion of ALE Phase...................................................................................... 99
11. Time-step............................................................................................................... 99
CHAPTER 6.......................................................................THIN SHELL PROCESSOR IN 2D 103
1. Introduction.......................................................................................................... 103
2. Governing Equations ........................................................................................... 104
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Table of Contents
5
§1. Strain - Displacement Relations ...................................................................... 106
§2. Equations of Motion......................................................................................... 107
3. Shell Subgrids ..................................................................................................... 110
§1. Interaction With Other Subgrids....................................................................... 110
§2. Centering of Variables ..................................................................................... 111
§3. Segment Masses and Volumes....................................................................... 112
4. Strains and Curvatures........................................................................................ 112
§1. Curvatures at an End Node ............................................................................. 114
5. Stresses............................................................................................................... 115
6. Stress Resultants and Bending Moments ........................................................... 116
7. Nodal Forces ....................................................................................................... 117
§1. Planar Symmetry ............................................................................................. 118
§2. Axial Symmetry................................................................................................ 121
8. Boundary Conditions ........................................................................................... 123
§1. Velocity Constraints......................................................................................... 124
§2. Pressure Boundaries ....................................................................................... 124
9. Time Step ............................................................................................................ 124
CHAPTER 7.......................................................................THIN SHELL PROCESSOR IN 3D 126
1. Introduction.......................................................................................................... 126
2. Elements of Mindlin plate theory ......................................................................... 126
3. Finite element formulations ................................................................................. 129
§1. Corotational Coordinate System...................................................................... 129
§2. Interpolation Function And Isoparametric Formulation.................................... 130
§3. Strain Rates And B Matrix ............................................................................... 131
4. Curvature terms for warped elements ................................................................. 134
§1. Resultant Membrane Forces And Moments .................................................... 134
§2. Nodal Forces ................................................................................................... 135
CHAPTER 8.......................................................................................................... RESERVED 138
CHAPTER 9.......................................................................................................... RESERVED 138
CHAPTER 10........................................................................................................ RESERVED 138
CHAPTER 11..................................................................................... MATERIAL MODELING 140
1. Introduction.......................................................................................................... 140
§1. Thermodynamic Equilibrium ............................................................................ 140
§2. Phase Diagrams .............................................................................................. 142
§3. Material Strength Effects ................................................................................. 144
§4. Complex Materials........................................................................................... 144
§5. High Explosives ............................................................................................... 144
§6. Calculation of Temperature ............................................................................. 145
2. Forms of Hydrodynamic Equations of State ........................................................ 145
§1. Solution of The Energy Equation And Equation of State.................................. 146
§2. Materials In Tension And Expansion ............................................................... 147 
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§3. Ideal Gas Form of Equation of State ............................................................... 147
§4. Linear Equation of State .................................................................................. 148
§5. Mie-Gruneisen Form of Equation of State ....................................................... 149
§6. Polynomial Equation of State........................................................................... 150
§7. The “Shock” Equation of State......................................................................... 151
§8. Expansion Equations of State.......................................................................... 154
§9. Tillotson Equation of State............................................................................... 155
§10. Regions of Interest........................................................................................... 156
§11. Regional Formulations..................................................................................... 157
§12. Puff Equation of State...................................................................................... 158
§13. Regional Formulations..................................................................................... 159
§14. Two-Phase Equation of State.......................................................................... 159
§15. Single Phase Region ....................................................................................... 160
§16. Two-Phase Region .......................................................................................... 161
3. Modeling of strength effects ................................................................................ 162
§1. Numerical Methodology................................................................................... 162
§2. Elastic Flow Region ......................................................................................... 163
§3. Plastic Flow Region ......................................................................................... 165
§4. Calculation Of Effective/Geometric Strains...................................................... 171
§5. Strength Models .............................................................................................. 173
§6. Mohr-Coulomb Model ...................................................................................... 173
§7. Johnson-Cook Model....................................................................................... 174
§8. Zerilli-Armstrong Model................................................................................... 175
§9. Steinberg-Guinan Model.................................................................................. 176
§10. Piecewise Model.............................................................................................. 177
§11. Johnson-Holmquist Brittle Damage Model ...................................................... 177
§12. Thermomechanical Material Model.................................................................. 178
§13. User Defined Strength Model .......................................................................... 181
§14. Modeling of Porous Solids............................................................................... 181
§15. Piecewise-Linear Porous Model ...................................................................... 182
§16. P-α Model ....................................................................................................... 185
4. Orthotropic Materials ........................................................................................... 187
§1. Orthotropic Elastic Model ................................................................................ 188
§2. Orthotropic Strength Models............................................................................ 190
§3. Orthotropic Failure Models .............................................................................. 191
5. Modeling of material failure ................................................................................. 191
§1. Failure Models ................................................................................................. 191
§2. Bulk (Isotropic) Models .................................................................................... 192
§3. Hydrodynamic Tensile Failure (Pmin).............................................................. 192
§4. Bulk Strain / Ultimate Strain / Effective Plastic Strain...................................... 193
§5. Directional Failure Models ............................................................................... 193
§6. Principal Stress Failure.................................................................................... 193
§7. Principal Strain Failure..................................................................................... 193
§8. Principal Stress / Strain Failure ....................................................................... 194
§9. Material Stress Failure..................................................................................... 194
§10. Material Strain Failure...................................................................................... 195
§11. Material Stress/Strain Failure .......................................................................... 195
§12. Failure In Orthotropic Materials ....................................................................... 196
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§13. Cumulative Damage Model ............................................................................. 197
§14. Johnson-Holmquist Damage Failure Model..................................................... 199
§15. Crack Softening ............................................................................................... 200
§16. Crack Plotting .................................................................................................. 203
§17. User Defined Failure Model............................................................................. 203
§18. User Defined Crack Softening ......................................................................... 204
6. Erosion criteria..................................................................................................... 204
§1. User Defined Erosion Criteria.......................................................................... 206
§2. Eroded Node Plotting....................................................................................... 206
7. High explosives ................................................................................................... 206
§1. Forms of Equations of State ............................................................................ 209
§2. Ideal Gas Form................................................................................................ 210
§3. Constant Beta Form ........................................................................................ 211
§4. Wilkins’ Form ................................................................................................... 212
§5. Jones - Wilkins - Lee Form.............................................................................. 213
§6. Initiation of Detonation..................................................................................... 214
§7. Burn on Time ................................................................................................... 215
§8. Burn on Compression...................................................................................... 219
§9. Constant Volume Burn .................................................................................... 219
§10. Initiation and Growth........................................................................................ 220
§11. Lee-Tarver Model ............................................................................................ 221
REFERENCES.................................................................................................................... 223
INDEX ................................................................................................................................. 229
A.....................................................................................................................................229
B.....................................................................................................................................229
C ....................................................................................................................................229
D ....................................................................................................................................229
E.....................................................................................................................................229
F.....................................................................................................................................230
G ....................................................................................................................................230
H ....................................................................................................................................230
I ......................................................................................................................................230
J .....................................................................................................................................230
L.....................................................................................................................................231
M....................................................................................................................................231
N ....................................................................................................................................231
O ....................................................................................................................................231
P.....................................................................................................................................231
R ....................................................................................................................................231
S.....................................................................................................................................232
T.....................................................................................................................................232
U ....................................................................................................................................233
V.....................................................................................................................................233
W....................................................................................................................................233
Z.....................................................................................................................................233
TABLE OF FIGURES ......................................................................................................... 234