D. A. Crawford, Sandia National Laboratories

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Application of Adaptive Mesh Refinement to the
Simulation of Impacts in Complex Geometries and
Heterogeneous Materials

• D. A. Crawford, Sandia National Laboratories
• O. S. Barnouin-Jha, Johns Hopkins University
  Applied Physics Laboratory

Sandia is a multiprogram laboratory operated by
Sandia Corporation, a Lockheed Martin
Company,for the United States Department of
Energy under contract DE-AC04-94AL85000.
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3-D Problem Scaling
Oblique Al-Al impact, 5 km/s
Resolution equivalent to 160 zones across
projectile diameter
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3-D Problem Scaling
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Application of AMR to impacts on Eros

• Eros Shape obtained by NEAR Laser Rangefinder
  (shape model no. 393)
• Interior properties
• simulated with thousands of random dunite spheres
  and tets (r03.32 g/cc, Cs6.65 km/s)
• tuff matrix, surface regolith (r01.83 g/cc,
  Cs1.6 km/s)
• bulk density 2.7 g/cc
• dunite is strong, matrix is weak
• Two impactors of solid dunite, 5 km/s
• 500 m diameter
• 2 km diameter
• AMR used to keep high resolution on the impactor
  and high density gradients (0.5 g/cc/cell width)

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2-km asteroid strikes Eros
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2-km asteroid strikes Eros
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500-m asteroid strikes Eros
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Application of AMR to heterogeneous materials

• Planar impact Monte-Carlo mesoscale studies
• Construct heterogeneous material by mixing two
  simple Mie-Gruneisen (linear Us-up) materials
• Matrix r0 1.0 g/cc, Cs 1 km/s, S1.0
• Grains r0 2.0 g/cc, Cs 2 km/s, S1.5
• 500 randomly oriented 2 mm cubes (actually 2 mm x
  2mm x infinite rectangular parallelepipeds)
• Volume fraction0.298, Mass fraction0.459
• Impactor same EOS as grains
• Impact velocities 1, 2, 4 km/s
• Measured shock velocity, particle velocity and
  pressure in target and impactor
• AMR used to track shock and material interfaces

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Planar Impact2 km/s, impactor-matrix only
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Planar Impact2 km/s, impactor-matrix grains
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Planar Impact2 km/s, impactor-matrix grains
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Planar Impact2 km/s, impactor-matrix grains
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Heterogeneous Mixture EOS
Projectile/Grains Cs2 km/s, S1.5 Measured
Mixture Cs1.1 km/s, S1.16 Matrix Cs1
km/s, S1
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Additive Mixture EOS (Grady, 1993)

• Partition specific volume by mass fraction (l)
• ?(p) ?1 ?1(p) (1- ? 1) ?2(p)
• For linear shock velocity vs. particle velocity

where
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Additive Mixture EOS
Theory
CTH Monte-Carlo
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Pressure variance behind the shock front
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Particle velocity variance behind shock front
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Conclusions/Future Work

• We are establishing a methodology using AMR with
  Monte-Carlo techniques to study material
  heterogeneity
• Even simple material systems can exhibit
  interesting properties when spatial heterogeneity
  added to the mix
• Next steps
• automate generation of Monte Carlo runs and (some
  of the) analysis
• widen the variance of the heterogeneity (vary
  grain size, for example)
• 3) look at means to add variance at continuum
  level based on Monte Carlo studies at the
  mesoscale
• 4) Look at more complex material models involving
  shear and fracture strength
• 5) Compare with experiments and observations!