1. Adaptive Multiscale Modeling and Simulation for Munitions Simulations* Progress Report PIs: Jacob Fish and Mark S. Shephard Post-docs: Gal Davidi, Caglar Oskay Students: Zheng Yuan, Rong Fan *AFRL support leveraged by support from NSF, ONR and General Motors

2. Roadmap of Developments Assessment of commercial code capabilities Mesh sensitivity studies (Gal Davidi) Mesh sensitivity studies (Gal Davidi) Validation studies (Rong Fan) Validation studies (Rong Fan) Fragmentation capabilities for metals Homogenization based approach (Gal Davidi) Homogenization based approach (Gal Davidi) Integration of homogenization in ABAQUS (Zhen Yuan) Integration of homogenization in ABAQUS (Zhen Yuan) PUM based (Zhen Yuan and Rong Fan) PUM based (Zhen Yuan and Rong Fan)

3. Roadmap of Developments (cont) Fragmentation capabilities for composites Reduced order methodology (Oskay) Reduced order methodology (Oskay) Validation studies (Oskay) Validation studies (Oskay) Integration in ABAQUS Integration in ABAQUS Multiscale Enrichment based PUM Multiscale Enrichment based PUMApplications

4. Fragmentation in Metals Experimental setup Impactor in Sabot Target Assembly DH36 Steel Plate The experimental parameters considered: Steel target plate: DH36 steel; 3/16 inch thick; 6 inch diameter; Impact velocity: In the range between 920 ft/sec. Backing material: Polyurea: 0.215 inch Impactor: non-deformable

5. Experiment vs ABAQUS simulation (without backing) Mises stress (without backing) Equivalent plastic strain (without backing)

6. Experiment vs Simulation DH36

7. Drawbacks of commercial software 0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05 3.00E+05 00.000050.00010.000150.00020.000250.00030.000350.00040.00045 Fine (160) Coarse (80) Very Coarse (40) 3D models (4- 8 layers) Shell 21 layers 1.Cost of 3D simulations (4 days for 21 layer-model, r-adaptivity) 2.Mesh dependency of both 3D and shell models 3D model (21 layers)

8. Remedy: Multiscale Enrichment Global (structure) Enrichment Enrich the kinematics of the global mesh with failure characteristic (delamination, shear banding, fragmentation) characteristic computed on the local patch Enrich the kinematics of the global mesh with failure characteristic (delamination, shear banding, fragmentation) characteristic computed on the local patch For computational efficiency Local (material) Enrichment Embed discontinuities (strong or weak) into material (micromechanical) model Embed discontinuities (strong or weak) into material (micromechanical) model For regularization of failure models

9. Better Global Enrichment (MEPU) Cell problems on Failure deformation mode- shapes delamination fracture Global deformation modes (Superposition)(Domain decomposition)

10. 0 50 100 150 200 250 300 00.00010.00020.00030.0004 Time (s) Velocity of Impactor (m/s) Global Enrichment (metals) 3D simulations DH36 & ERC (3D-21 layers) MEPU DH36 & ERC (Shell)

11. Local Enrichment (metals) (in progress) Calculate discontinuity direction at each Gauss point Align the RVE local coordinate system with one of the axis normal to the localization plane Develop a 3-point RVE model as follows: 1 2 3 4 6 7 8 5 Shell RVEDiscontinuity plane Gauss point Constrained RGB Constrained periodicity master

12. Impact Fragmentation of composites Phenomenological PhenomenologicalAdvantages -Fast Disadvantages -Reliability -Experiments architecture dependent dependent Eigendeformation-based Reduced Order Homogenization Component Material Point Direct Homogenization Advantages -Reliability -Architecture independent Exp. Disadvantages -Computationally formidable Matrix point (s) Fiber point (s) Interface point (s) Engineering Accuracy Fast Architecture independent Experiments

13. Validation: Tube Crush Experiment Experiments by Oak Ridge (Starbuck et al.) Impact Velocity: 4000 mm/sec Microstructure: Woven composite

14. Model Validation (composites)