Wave Propagation Prediction in Homogeneous Materials Using Hybrid Lattice Particle Modeling

1. Wave Propagation Prediction in Homogeneous Materials Using Hybrid Lattice Particle Modeling Investigators: Ge Wang, Ahmed. Al-Ostaz, Alexander H.-D. Cheng and P. Raju Mantena Civil Engineering Department University of Mississippi

2. Research Background • Dynamic deformation often involves wave propagation, i.e., stress has to travel through the material body. • Dynamic fracture and fragmentation under high strain rate loads (impact, blasting, crush, collapse, high speed puncture/penetration, comminution, .etc.) has broad civilian/military applications. Hopkinson Bar Test (by M.A. Kaiser, 1998) Spallation as a result of impact without penetration of the impacting object Shock on a sharp-nosed supersonic body (http://en.wikipedia.org/wiki)

3. Outline • Brief review of major macroscopic dynamic fracture approaches • Hybrid lattice particle modeling (HLPM) • HLPM of wave propagation and applications • Conclusions

4. Outline • Brief review of major dynamic fracture approaches • Hybrid lattice particle modeling (HLPM) • HLPM of wave propagation and applications • Conclusions

5. 1. Brief review of major dynamic fracture approaches • Continuum Mechanics Based Approaches (CMBA): • FEM • Discrete Element Based Approaches (DEBA): • PFC, SPH, PM, etc. • Combinations of CMBA-DEBA: • PFEM, MPM (material point method), etc.

6. Simulations with meshing techniques Lagrange ALE (Arbitrary Lagrange Euler) Meshless (SPH) Euler FEM (AUTODYN course materials)

7. Outline • Brief review of major dynamic fracture approaches • Hybrid lattice particle modeling (HLPM) • HLPM of wave propagation and applications • Conclusions

8. Hybrid Lattice Particle Modeling (HLPM) of Dynamic Fragmentation of Solids Ge Wang, Ahmed Al-Ostaz, Alexander H.-D. Cheng and P. Raju Mantena Department of Civil Engineering, the University of Mississippi, MS 38655, http://www.olemiss.edu/~gewang Motivations Interactions of HLPM Thermally induced fracture: Mixture of calcite and pyrite subject to a microwave Mechanical behavior of a solid material is controlled by its microstructure. Complex macroscopic behaviors, such as fracture and failure, arise from microstructure interactions. Thus, if the microstructure and the microstructural interactions within a numerical model could be correctly and accurately replicated, then that model should precisely reproduce the macroscopic behaviors. However, current computing power limits the size of the atomic ensemble to numbers of atoms that are too small to be useful for most engineering-scale systems. Hybrid Lattice Particle Modeling (HLPM) is developed to directly mimic microstructural features and can be executed in reasonable times on standard computers. Linear: Non-linear: Meshing structures (a) Temperature (b) Fracture Blasting: (a) Polynomial (b) Lennard–Jones Validations of HLPM Crack propagation: Spallation of plate impact: Model Introduction (a) Epoxy in tension (b) Indentation of polymeric materials HLPM is a dynamic simulation that uses small discrete solid physical particle (or quasi-molecular particles) as a representation of a given fluid or solid. Different particle interaction schemes and mesh structures can be adopted. It combines the knowledge of both lattice modeling and particle modeling. Applications of HLPM Wave propagation: High strain rate loading: 3-D puncture/penetration:

9. Numerical discretization scheme in PFC (particle flow code), PFEM (particle finite element method) and HLPM PFC HLPM PFEM critical time increment: critical time increment: critical time increment: k : the stiffness m: a point mass r: displacement k : the stiffness m: a point mass x: displacement k : the stiffness m: a point mass u: displacement

10. Outline • Brief review of major dynamic fracture approaches • Hybrid lattice particle modeling (HLPM) • HLPM of wave propagation and applications • Conclusions

11. HLPM simulations of Wave Propagation Prediction in Homogeneous Materials • Problem descriptions: • Material properties: • Theoretical wave propagation speeds: • 1-D: • 2-D: 1-D: L=12.7 cm 2-D: A=12.7x1.21

12. (cont.) Using dynamic BC • Dynamics BC: . Duration= Horizontal amplitude Wave propagation speed: (i) 1D: 2000.0 m/s; (ii) 2D: 2133.0 m/s

13. (cont.) Using dynamic BC Vertical amplitude

14. (cont.) Using Kinematic BC • Kinematic BC: constantly Horizontal amplitude Wave propagation speed: 2133.0 m/s

15. (cont.) Using Kinematic BC Vertical amplitude

16. Applications Spall Crack Formation (b) MD simulations (A. M. Krivtsov, 2004) (a) HLPM simulations

17. (cont.) (a) weak interface interaction (b) strong interface interaction HLPM simulations

18. (cont.) Cavity Blasting HLPM simulations

19. Outline • Brief review of major dynamic fracture approaches • Hybrid lattice particle modeling (HLPM) • HLPM of wave propagation and applications • Conclusions

20. Conclusions • Hybrid lattice particle modeling (HLPM) can be an alternative tool to explore wave propagation in materials. • HLPM is being developed ultimately for investigating shock wave related problems. • Validations are required in the coming stage.

21. Grant Acknowledgement Department of Homeland Security-through Southeast Region Research Initiative (SERRI), USA. ONR, Office of Naval Research, Solid Mechanics Program, USA. Thanks a lot for your attention! Any questions?