1. 1 BROOKHAVEN SCIENCE ASSOCIATES Nick Simos Brookhaven National Laboratory EXPERIENCE WITH IMPLICIT AND EXPLICIT CODES IN ANALYZING BEAM-INDUCED RAPID THERMO-MECHANICAL TRANSIENTS

2. 2 BROOKHAVEN SCIENCE ASSOCIATES OBJECTIVE Discuss similarities and differences between implicit and explicit numerical formulations applicable to the thermo- mechanical shock problem Overview experience from the benchmarking of numerical schemes against experimental results Collectively identify a path that will serve the needs of beam- induced shock and damage to collimator elements

3. 3 BROOKHAVEN SCIENCE ASSOCIATES FE Numerical Schemes IMPLICIT FORMULATION dependent variable(s) defined through set of coupled DE variable(s) solved using formation and inversion of matrix EXPLICIT FORMULATION performs direct computation of dependent variable in terms of known quantities

4. 4 BROOKHAVEN SCIENCE ASSOCIATES Solving Time-Dependent Problems Total Soln = transient + steady-state We are particularly interested in the transient component IMPLICIT FORMULATION Most appropriate scheme for steady-state cases –It affords large time steps (even in an iterative solution) EXPLICIT FORMULATION Obtains steady-state conditions asymptotically (not good) BUT, in the transient phase, it produces greater accuracy with less computational effort

5. 5 BROOKHAVEN SCIENCE ASSOCIATES Time-Dependent Problems (cont.) IMPLICIT FORMULATION Couples all the elements in the grid together allowing communication for any step (iterative or time marching) between all To maintain numerical stability it introduces either large numerical damping OR iterative solution steps smaller than the physical time step EXPLICIT FORMULATION Advances solution based on speed of sound and the size of the smallest FE element Only info from neighboring cells is shared (no matrix inversion) Therefore: When time accuracy in solution is key  Explicit Formulation

6. 6 BROOKHAVEN SCIENCE ASSOCIATES Solving/benchmarking transient problems with IMPLICIT formulation

7. 7 BROOKHAVEN SCIENCE ASSOCIATES BNL Target Test

8. 8 BROOKHAVEN SCIENCE ASSOCIATES BNL Target Test

9. 9 BROOKHAVEN SCIENCE ASSOCIATES Beam-window interaction test experiment prediction

10. 10 BROOKHAVEN SCIENCE ASSOCIATES Solving/benchmarking transient problems with EXPLICIT formulation

11. 11 BROOKHAVEN SCIENCE ASSOCIATES Projectile Impact Study

12. 12 BROOKHAVEN SCIENCE ASSOCIATES M289 Impact Test – LS-DYNA Simulations

13. 13 BROOKHAVEN SCIENCE ASSOCIATES M289 Impact Test – Simulation Results

14. 14 BROOKHAVEN SCIENCE ASSOCIATES M289 Impact Test – Comparison with Analysis According to test results, missile-induced dent on upstream face of wall = 20 mm Analysis prediction matched the experimental data precisely !

15. 15 BROOKHAVEN SCIENCE ASSOCIATES M289 Impact Test – Comparison of observed damage Damage observed in the downstream face of the impacted wall

16. 16 BROOKHAVEN SCIENCE ASSOCIATES Exploring Eulerian-Lagrangian Formulation Capabilities of LS-DYNA Proton Beam - Hg Jet Interaction Experiment High velocity projectiles emanating from Hg target

17. 17 BROOKHAVEN SCIENCE ASSOCIATES Explicit Formulation Results

18. 18 BROOKHAVEN SCIENCE ASSOCIATES Explicit Formulation Results

19. 19 BROOKHAVEN SCIENCE ASSOCIATES Missile Impact Studies – Large Structures

20. 20 BROOKHAVEN SCIENCE ASSOCIATES Basic Relations behind thermo-mechanical shock  (or ΔP) = Γ ρ ΔE m Γ = [E/(1-2ν)] α/(ρ c v ) ; Γ = Gruneisen parameter Above based on extrapolation from “slow” thermalization During SHOCK (temp spike/high strain rate) materials exhibit anomalous behavior that may lead to enhanced strength !!!!) + Density discontinuity (reduction behind advancing front)

21. 21 BROOKHAVEN SCIENCE ASSOCIATES Overcoming Phase Transformation

22. 22 BROOKHAVEN SCIENCE ASSOCIATES What can be done? explicit codes such as LS-DYNA are capable of capturing the final state in its highly distorted state (if the imposed loads push it past its yield) allowing equations of state to be described enabling ALE formulation However, when it comes to phase transformation, it is the user that is responsible to numerically implement the path within the phases That poses a challenge: It is one thing to write a subroutine, it is another to understand the process

23. 23 BROOKHAVEN SCIENCE ASSOCIATES STEPS forward Analyze the accident LHC collimator condition using the explicit formulation provided by LS-DYNA Base damage and material ablation on basic principles of pressure-temperature state Open a discussion between people on the computational and the theoretical sides to figure out the best possible way to describe phase transformations under intense beam action (laser community can also help) Use beam-based “ damage ” tests using SPS for benchmarking