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A Coupled Euler-Lagrange Approach for Modeling Penetration and Blast/Structure Interaction

A Coupled Euler-Lagrange Approach for Modeling Penetration and Blast/Structure Interaction. Greg Bessette and Jason Libersky Computational Physics Research and Development (9231) Sandia National Laboratories Albuquerque NM 8 th US National Congress on Computational Mechanics Austin TX

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A Coupled Euler-Lagrange Approach for Modeling Penetration and Blast/Structure Interaction

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  1. A Coupled Euler-Lagrange Approach for Modeling Penetration and Blast/Structure Interaction Greg Bessette and Jason Libersky Computational Physics Research and Development (9231) Sandia National Laboratories Albuquerque NM 8th US National Congress on Computational Mechanics Austin TX 25 – 27 July 2005 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.

  2. Zapotec Collaborators • John Prentice (SCI-TAC LLC) • Paul Yarrington (SNL, 9902) • Courtenay Vaughan (SNL, 9224) • Ray Bell (SNL, 9231) • Sue Goudy (SNL, 9224) • Steve Attaway (SNL, 9134) • Steward Silling (SNL, 9231) • Richard Koteras (SNL, 9142) • Bob Cole (Orion International Technologies) • And others ....

  3. Motivation • Penetration and blast/structure interaction characterized by: • Transient wave propagation, large material deformations, high strain rates, multi-body contact, etc. • Materials exhibiting vastly differing strengths and degrees of deformation • Many regimes of interest cannot be modeled using traditional methods • Coupled solution approach can fill the void Earth Penetration Blast Loading on a Building

  4. Coupled Methods • Many coupled approaches available for modeling penetration and blast/structure interaction • Engineering models/FE, CEL, FE/SPH, ALE, etc. • One-way vs. loosely-coupled methods • Present discussion focused on coupled Euler-Lagrange (CEL) approach embedded in the Zapotec code

  5. What is Zapotec? • Coupled Euler-Lagrange computer code • Directly couples two production codes • CTH: Eulerian shock physics code • Pronto3D: Explicit, Lagrangian FE code • Zapotec couples interaction between Lagrangian and Eulerian materials • Only handles 3D problems

  6. Zapotec Background The Coupled Algorithm in Time • CTH and Pronto3D are run sequentially, cycle by cycle • Algorithm permits Pronto3D subcycling

  7. The Zapotec Coupling Algorithm • Coupled treatment conducted in two steps, referred to as material insertion and force application • Material insertion step updates CTH data • Force application step updates Pronto3D data

  8. Lagrangian Material The Zapotec Coupling AlgorithmMaterial Insertion Step • Remove pre-existing Lagrangian material from the CTH mesh • Get updated Lagrangian data • Insert Lagrangian material into CTH mesh • Compute volume overlaps • Map Lagrangian data – mass, momentum, sound speed, stress, internal energy tn L2 L1 CTH Mesh PL,inserted = (VO,L1 PL1 + VO,L2 PL2) / VO Voverlap = VO = VO,L1 + VO,L2

  9. Lagrangian Material The Zapotec Coupling AlgorithmForce Application Step • Remove pre-existing Lagrangian material from the CTH mesh • Get updated Lagrangian data • Insert Lagrangian material into CTH mesh • Compute volume overlaps • Map Lagrangian data • Compute external force on Lagrangian surface • Determine surface overlaps • Compute surface tractions based on Eulerian stress state • Compute normal force on element surface (element-centered force) • If friction, compute tangential force as ft = fns • Distribute forces to nodes tn CTH Mesh fn = (t · nL ) Aoverlap nL fI = NIfn

  10. Highlight of Zapotec Capabilities • Supports several Pronto3D element types for material insertion • 8-node hexahedral element • 8-node tetrahedral element • 4-node shell element • Compatible with CTH-AMR capability • Can model response of complex, thin-shell structures • Element death (a.k.a. erosion) accounted for in the force application step • Parallel implementation

  11. CTH Contact Workers Pronto3D Parallel Implementation • CTH and Pronto3D have different mesh decompositions •Data resides on different processors • Lagrangian data communicated for coupled calculations Zapotec Master processor CTH

  12. Processor Interactions Between CTH and Pronto3D Pronto3D Mesh Decomposition Processor Interactions CTH / PRONTO Total • 1 - 7, 8, 9, 10 4 • 2 - 6, 7, 8, 94 • 5 - 5, 72 • 6 - 1, 2, 3, 4, 5, 6, 77 • 10 - 0, 1, 23 10 9 8 2 0 3 1 6 7 6 4 5 3 4 5 7 1 2 • Overlapping data owned by • different processors •  Pronto3D data and CTH mesh • coordinates communicated to idle • processors to load balance work 0 11 8 9 10 13 14 12 15 CTH Mesh Decomposition

  13. Example Problems • Ballistic penetration • Air blast loading on a thin plate • Blast loading on a buried structure

  14. Ballistic Penetration • Normal impact of 4340 steel penetrator into 6061-T651 aluminum plate • Piekutowski, Forrestal, Poorman, and Warren, “Penetration of Aluminum Plates with Ogive-nose Steel Rods at Normal and Oblique Impacts”, Int.J. Impact Engng, Vol. 18, pp. 877-887 (1996) • Penetrator characteristics • Ogive nose (3CRH), 88.9 mm long, 12.9 mm diameter • Impact velocities range from 282 to 863 m/s • Pitch/yaw generally less than one degree • Plate dimensions: 304 x 304 x 26.3 mm • Drivers for coupled modeling • Disparity in material response • Relatively low impact velocities

  15. Ballistic Penetration • Penetrator is Lagrangian, plate is Eulerian • AOA modeled in some instances • Model friction with a velocity-dependent friction model where friction coefficient is specified as a function of sliding velocity • No data available for steel-aluminum contact, but data is available for steel-steel contact • Bowden and Persson, “Deformation, heating, and melting of solids in high-speed friction”, Proc. Royal Society, Vol. 160, pp. 433-458 (1961) • Friction coefficients range from 5 to 18 percent at sliding velocities of 600 and 20 m/s, respectively • Zapotec utilizes a piecewise linear fit to the data • Comparisons with measured residual velocity (Courtesy: Bowden and Persson)

  16. Ballistic Penetration • Plate response modeled using EP and Johnson-Cook constitutive models with Mie-Gruneisen EOS • AOA (combined pitch and yaw) also considered

  17. Air Blast Loading on a Thin Plate • Air blast on 5-mm-thick flat steel plate • Boyd, “Acceleration of a Plate Subject to Explosive Blast Loading – Trial Results”, DSTO-TN-0270 (2000) • Charge suspended over plate • Plate bolted into support structure • Drivers for coupled modeling • Disparity in material response • Varying length scales • Varying time scales

  18. Air Blast Loading on a Thin Plate Air • Charge and air are Eulerian • Plate and support are Lagrangian • Plate modeled with 4-node shell elements • Block modeled with 8-node hex elements • Joint modeled as clamped BC • CTH calculation cutoff after 400 sec • Pronto3D calculation run to 100 msec • Run with and without CTH-AMR • Phenomenological-based indicators • Charge: Volume fraction > 0 • Shock: Pressure difference histogram • Plate: Vmag > 10 cm/s • Comparisons for centerline displacements Charge

  19. CTH Cell Size (cm) Peak Permanent Centerline Displacement (mm) Test 35 9 2.0 24.2 9.8 0.5 25.1 12.0 8.0 (LOR=4) 25.3 12.5 Air Blast Loading on a Thin Plate

  20. Air Blast Loading on a Thin Plate

  21. Blast Loading on a Buried Structure • Conventional Weapon Effects Backfill (CONWEB) Test 1 • Hayes, “Backfill Effects on Response of Buried Reinforced Concrete Slabs”, TR-SL-89-19 • 15.4-lb cased C-4 charge at 5-ft standoff in clay backfill • Test Structure • Reinforced concrete (RC) slab bolted to reusable reaction structure • Slab thickness: 4.3 inches • Reaction Structure: 15 ft long, 65 inches high, 4 ft deep • Structure and soil instrumented • Drivers for coupled modeling • Disparity in material response • Load duration

  22. Free Surface Plane of Symmetry Plane of Symmetry CTH Mesh Boundaries Blast Loading on a Buried Structure • Soil and charge are Eulerian • Charge: JWL Library EOS for C-4 • Steel case: Elastic-plastic • Soil: P-alpha EOS with Geologic (GEO) strength model • Structure is Lagrangian • Reinforcement and bolted connections explicitly modeled • Concrete: K&C model • Reinforcement: Rebar model • Displacement-based death criterion used to model breach (d/CS > 0.3) • Comparisons • Free-field soil stress and velocity • Structure velocities • Interface pressures

  23. Blast Loading on a Buried Structure AHS-0: Center of RC Slab RC Slab: Thickness: 4.3 inches Strength (fc’): 6095 psi Reinforcement: 1.0 % Backfill: Clay AHS-10: Base of Reaction Structure

  24. Blast Loading on a Buried Structure

  25. Concluding Remarks • CEL approach well suited for modeling penetration and blast/structure interaction • Open issues for coupling algorithm • Consistent material modeling for insertion step • Overfilled cells • Cost of volume/area overlap calculations

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