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

2. 3-D Problem Scaling Resolution equivalent to 160 zones across projectile diameter Oblique Al-Al impact, 5 km/s

3. AMR Non-AMR 3-D Problem Scaling

4. 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 (  0 =3.32 g/cc, C s =6.65 km/s) –tuff matrix, surface regolith (  0 =1.83 g/cc, C s =1.6 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)

5. 2-km asteroid strikes Eros

7. 500-m asteroid strikes Eros

8. Application of AMR to heterogeneous materials Planar impact Monte-Carlo mesoscale studies Construct heterogeneous material by mixing two simple Mie-Gruneisen (linear U s -u p ) materials Matrix:  0 = 1.0 g/cc, C s = 1 km/s, S=1.0 Grains:  0 = 2.0 g/cc, C s = 2 km/s, S=1.5 –500 randomly oriented 2 mm cubes (actually 2 mm x 2mm x infinite rectangular parallelepipeds) –Volume fraction=0.298, Mass fraction=0.459 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

9. Planar Impact 2 km/s, impactor->matrix only

10. Planar Impact 2 km/s, impactor->matrix + grains

13. Heterogeneous Mixture EOS Projectile/Grains: C s =2 km/s, S=1.5 Measured Mixture: C s =1.1 km/s, S=1.16 Matrix: C s =1 km/s, S=1

14. Additive Mixture EOS (Grady, 1993) Partition specific volume by mass fraction ( ): (p) = 1 1 (p) + (1- 1 ) 2 (p) For linear shock velocity vs. particle velocity: where

15. Additive Mixture EOS Theory CTH Monte-Carlo

16. Pressure variance behind the shock front

17. Particle velocity variance behind shock front

18. 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: 1)automate generation of Monte Carlo runs and (some of the) analysis 2)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!