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Material Point Method Simulations of Fragmenting Cylinders
Biswajit BanerjeeDepartment of Mechanical Engineering
University of Utah
17th ASCE Engineering Mechanics Conference, 2004
Outline
• Scenario
• Material Point Method (MPM)
• Approach
• Validation
• Simulations of fragmentation
Scenario
What happens to the container ?
Simulation Requirements
• Fire-container interaction
• Large deformations
• Strain-rate/temperature dependence
• Failure due to void growth/shear bands
The Material Point Method (MPM)(Sulsky et al.,1994)
Why MPM ?
• Tightly-coupled fluid-structure interaction.
• No mesh entanglement.• Convenient contact
framework.• Mesh generation trivial.• Easily parallelized.• No tensile instabilities.
• First-order accuracy.• High particle density for
tension dominated problems.
• Computationally more expensive than FEM.
Advantages Disadvantages
Stress update
• Hypoelastic-plastic material• Corotational formulation (Maudlin & Schiferl,1996)
• Semi-implicit (Nemat-Nasser & Chung, 1992)
• Stress tensor split into isotropic/deviatoric
• Radial return plasticity
• State dependent elastic moduli, melting temperature
Plasticity modeling
• Isotropic stress using Mie-Gruneisen Equation of State.
• Deviatoric stress :• Flow stress : Johnson-Cook, Mechanical Threshold
Stress, Steinberg-Cochran-Guinan• Yield function : von Mises, Gurson-Tvergaard-
Needleman, Rousselier
• Temperature rise due to plastic dissipation• Associated flow rule
Damage/Failure modeling
• Damage models:• Void nucleation/growth (strain-based)• Porosity evolution (strain-based)• Scalar damage evolution: Johnson-Cook/Hancock-
MacKenzie
• Failure• Melt temperature exceeded• Modified TEPLA model (Addessio and Johnson, 1988)
• Drucker stability postulate• Loss of hyperbolicity (Acoustic tensor)
Fracture Simulation
• Particle mass is removed.
• Particle stress is set to zero.
• Particle converted into a new material that interacts with the rest of the body via contact.
Validation: Plasticity Models
6061-T6 Aluminum EFC Copper
JC MTS SCG JC MTS SCG
635 K 194 m/s
655 K 354 m/s
718 K 188 m/s
727 K 211 m/s
Validation: Mesh dependence
OFHC Copper298 K 177 m/sMTS
6061-T6 Al655 K 354 m/sJC
1,200,000 cells151,000 cells18,900 cells
735,000 cells91,800 cells11,500 cells
Validation: Penetration/Failure
Validation: Penetration/Failure
160,000 cells 1,280,000 cells
Validation: Erosion Algorithm
Validation: Impact
Validation: Impact Results
Validation: 2D Fragmentation
Validation: 2D Fragmentation
Gurson-Tvergaard-Needleman yield, Drucker stability, Acoustic tensor, Gaussian porosity, fragments match Grady equation, gases with ICE-CFD code.
JC (steel), ViscoScram (PBX 9501)
MTS (steel), ViscoScram (PBX 9501)
Simulations: 3D Fragmentation
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Simulation: Container in Fire
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Questions ?