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Superseismic Loading

Superseismic Loading. Marco Arienti, Joseph E. Shepherd CIT ASCI-ASAP FY01 Research Review October 22-23, 2001 [Also presented at the 2001 APS Conference on Shock Compression of Condensed Matter]. Motivations.

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Superseismic Loading

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  1. Superseismic Loading Marco Arienti, Joseph E. Shepherd CIT ASCI-ASAP FY01 Research Review October 22-23, 2001 [Also presented at the 2001 APS Conference on Shock Compression of Condensed Matter]

  2. Motivations • Find a solution of a fully coupled fluid-solid problem to verify the Eulerian/Lagrangian coupling algorithm • Gain understanding on curvature of shock fronts due to deformable boundaries

  3. Simplest formulation: single deflection, linear elastic • Isotropic medium (0-1-2)density rLamé coefficients m, lPlane strain / small strains • Perfect gas g = 1.4 (3-4) • Dilatational front p: • Distortional front s: elastic solid compressible gas: single deflection

  4. Simplest formulation: solution • Use particle velocities (in the solid material): • flow deflection (in the solid, for a frame traveling with Us): • shock polar (in the gas, given Ms= Us /cgas): to obtain a relation between the shock angle b, the deflection d=q of the boundary and the strength of the shock Ms.

  5. Validation: Ms-b curve and convergence study • Finite Elements mesh: 164,000 triangles (L1)16,000 triangles (L2) • Cartesian grid:201x201 nodes (E1)101x101 nodes (E2) • Superseismic limit for Us® cP (Ms )limit = cP/cgas @ 2.23 • Range of initial Mach numbers: Ms=2.4 to Ms=9. • rfluid=1000. kg/m3 Pfluid= 2.6x109 Pa

  6. Validation: detail of self-similar solution close to contact point • Initial conditions:Ms=4.5rfluid=1000. kg/m3Pfluid= 2.6x109 Pa • FE Material:r =8970. kg/m3n =0.33E=110x109 Pa • Examine simulation when a steady state is developed in the reference of the moving shock • Steady state:Ms=4.399b =87.23ºd =10.21º

  7. Validation: p- and s- fronts in the solid half-plane • Vertical sectionat x=0.1 m • Origin of the front at x=0.306 • Stress fronts are according to theory and well resolved by the FE solver

  8. Generalization: Shock Diffraction at a Deformable Boundary • Modify transition diagram for shock diffraction at a rigid boundary. RR DMR CMR SMR Perfect Gas g=1.4 channel vNR

  9. Elastic-plastic material + Irregular Mach Reflection • Von Mises criterion for yielding: • Dilatational front p: • Plastic front: • Distortional front s: • Large compression (4): Von Mises solid: 0-5-6-7 compressible gas: 1-2-3-4

  10. Solution via Shock Polars • Example: Regular Reflection with copper and high-density gas (g=3).

  11. Solution via Shock Polars • Example: Mach Reflection with copper and high-density gas (g=3).

  12. Result: transition boundaries for copper and high density gas (g=3, P/k>>1) Use to validate coupling The single deflection (sd) boundary in the subsonic regime is of interest in the study of detonations

  13. Applications: strong confinement of HE • Subsonic single deflection can be used to study the interaction HE-confinement in a cylinder test experiment.

  14. Conclusions • Found a self-similar solution in the frame of the shock loading a linear elastic material. • In the case of elastic single deflection, it was verified that the coupling algorithm makes the transient converge to the correct steady solution. • The problem was extended to consider Irregular Mach Reflection and Von Mises materials subject to large compression. • Found new transition boundaries for shock diffraction at a deformable wedge.

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