Skip to main content Accessibility help
×
Home

Numerical simulations of Rayleigh-Taylor instability in elastic solids

  • J.J. LÓPEZ CELA (a1), A.R. PIRIZ (a1), M.C. SERNA MORENO (a1) and N.A. TAHIR (a2)

Abstract

Numerical simulations of the Rayleigh-Taylor instability in the interface of two semi-infinite media have been performed based on the finite element method. Two different interfaces have been considered: elastic solid/elastic solid and elastic solid/viscous fluid. The results have been compared with previously published analytical models. In particular, the asymptotic growth rate has been compared with the model by Terrones (2005) while the initial transient phase is compared with the model by Piriz et al. (2005). Finally, some examples show the importance of such an initial transient phase if more realistic material laws (for example, elastoplastic behavior) are taken into account.

Copyright

Corresponding author

Address correspondence and reprint requests to: J.J. López Cela, ETSI Industriales, Universidad de Castilla-La Mancha, Campus Universutario, 13071 Ciudad Real, Spain. E-mail: juanjose.lopez@uclm.es

References

Hide All

REFERENCES

Arnold, R., Colton, E., Fenster, S., Foss, M., Magelssen, G. & Moretti, A. (1982). Utilization of high-energy, small emittance accelerators for ICF target experiments. Nucl. Instrum. Met. Phys. Res. 199, 557.
Bakharakh, S.M., Drennov, O.B., Kovalev, N.P., Lebedev, A.I., Meshkov, E.E., Mikhailov, A.L., Nevmerzhitsky, N.V., Nizovtsev, P.N., Rayevsky, V.A., Simonov, G.P., Solovyev, V.P. & Zhidov, I.G. (1997). Hydrodinamic instability in strong media. Report No. UCRL-CR-126710. Livermore, CA: Lawrence Livermore National Laboratory.
Breil, J., Hallo, L., Maire, P.H. & Olazabal-Louma, M. (2005). Hydrodynamic instabilities in axisymmetric geometric self-similar models and numerical simulations. Laser Part. Beams 23, 47.
Barnes, J.F., Blewet, P.J., McQueen, R.G., Meyer, K.A. & Venable, D. (1974). Taylor instability in solids. J. Appl. Phys. 45, 727.
Barnes, J.F., Janney, D.H., London, R.K., Meyer, K.A. & Sharp, D.H. (1980). Further experimentation on Taylor instability in solids. J. Appl. Phys. 51, 4678.
Bowers, R.L., Brownell, J.M., Lee, H., Mclenithan, K.D., Scannapieco, A.J. & Shanhan, W.R. (1998). Design and modelling of precision solid liner experiments on Pegasus. J. Appl. Phys. 83, 4146.
Colvin, J.D., Legrand, M., Remington, B.A., Schurtz, G. & Weber, S.V. (2003). A model for instability growth in accelerated solid metals. J. Appl. Phys. 93, 5287.
Dienes, J.K. (1978). Method of generalized coordinates and an application to Rayleigh-Taylor instability. Phys. Fluids 21, 736.
Dimonte, G., Gore, R. & Schneider, M. (1998). Rayleigh-Taylor instability in elastic-plastic materials. Phys. Rev. Lett. 80, 1212
Drucker, D.C. (1980). Taylor instability of the surface of an elastic-plastic plate. In Mechanics Today (Nemmat-Nasses, S., Ed.), Vol. 5, p. 37. Oxford: Pergamon.
Henning, W.F. (2004). The future GSI facility. Nucl. Instrum. Methods Phys. Res. B 214, 155.
Hoffmann, D.H.H., Blazevic, A., Ni, P., Rosmej, O., Roth, M., Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D., Weyrich, K. & Maron, Y. (2005). Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser Part. Beams 23, 47.
Hughes, T.J.R. (1984). Numerical Implementation of Constitutive Models: Rate Independent Deviatoric Plasticity (Nemat-Nasser, S., Asaro, R.J. & Hegemier, G.A., Eds.). Boston, MA: Martinus Nujhoff Publishers.
Keinigs, R.K., Atchison, W.L., Faehl, R.J., Thomas, V.A., Maclenithan, K.D. & Trainor, R.J. (1999). One and two dimensional simulations of imploding metal shells. J. Appl. Phys. 85, 7626.
Lorenz, K.T., Edwards, M.J., Glendinning, S.G., Jankowski, A.F., McNaney, J., Pollain, S.M. & Remington, B.A. (2005). Accessing ultrahigh-pressure, quasi-isentropic states of matter. Phys. Plasmas 12, 056309.
McQueen, R.G., Marsh, S.O., Taylor, J.W., Fritz, J.N. & Carter, W.J. (1970). High-velocity impact phenomena (Kinslow, R., Ed.). New York: Academic Press.
Miles, J.W. (1966). Taylor instability of a flat plate. General Dynamics Report No. GAMD-7335, AD643161. San Diego, CA: General Dynamics.
Nizovtsev, P.N. & Raevskii, V.A. (1991). Approximate analytic solution for the problem of Rayleigh-Taylor instability in strong media. VANT Ser. Teor. I Prikl. Fiz. 3, 11.
Piriz, A.R., Lopez Cela, J.J., Cortazar, O.D., Tahir, N.A. & Hoffmann, D.H.H. (2005). Rayleigh-Taylor instability in elastic solids. Phys. Rev. E 72, 056313.
Piriz, A.R., Portugues, R.F., Tahir, N.A. & Hoffmann, D.H.H. (2002a). Analytic model for studying heavy-ion-imploded cylindrical targets. Laser Part. Beams 20, 427.
Piriz, A.R., Portugues, R.F., Tahir, N.A. & Hoffmann, D.H.H. (2002b). Implosion of multilayered cylindrical targets driven by intense ion beams. Phys. Rev. E 66, 056403.
Piriz, A.R., Tahir, N.A., Hoffmann, D.H.H. & Temporal, M. (2003a). Generation of a hollow ion beam: Calculation of the rotation frequency required to accommodate symmetry constraint. Phys. Rev. E 67, 017501.
Piriz, A.R., Temporal, M., Lopez Cela, J.J., Tahir, N.A. & Hoffmann, D.H.H. (2003b). Symmetry analysis of cylindrical implosions driven by high-frequency rotating ion beams. Plasma Phys. Contr. Fusion 45, 1733.
Plohr, B.J. & Sharp, D.H. (1998). Instability of accelerated elastic metal plates. ZAMP 49, 786.
Reinovsky, R.E., Anderson, W.E., Atchison, W.L., Ekdahl, C.E., Faehl, R.J., Lindemuth, I.R., Morgan, D.V., Murillo, M., Stokes, J.L. & Shlachter, J.S. (2002). Instability growth in magnetically imploded high-conductivity cylindrical liners with material strength. IEEE Trans. Plasma Sci. 30, 1764.
Robinson, A.C. & Swegle, J.W. (1989). Acceleration instability in elastic-plastic solids: Analytical techniques. J. Appl. Phys. 66, 2859.
Steinberg, D.J., Cochran, S.G. & Guinan, M.W. (1980). A constitutive model for metals applicable at high-strain rate. J. Appl. Phys. 51, 1498.
Swegle, J.W. & Robinson, A.C. (1989). Acceleration instability in elastic-plastic solids: Numerical simulations of plate acceleration. J. Appl. Phys. 66, 2838.
Tahir, N.A., Adonin, A., Deutsch, C., Fortvo, V.E., Grandjouan, N., Geil, B., Grayaznov, V., Hoffmann, D.H.H., Kulish, M., Lomonosov, I.V., Mintsev, V., Ni, P., Nikolaev, D., Piriz, A.R., Shilkin, N., Spiller, P., Shutov, A., Temporal, M., Ternovoi, V., Udrea, S. & Varentsov, D. (2005). Studies of heavy ion-induced high-energy density states in matter at the GSI Darmstadt SIS-18 and future FAIR facility. Nucl. Instrum. Methods Phys. Res. A 544, 16.
Tahir, N.A., Hoffmann, D.H.H., Kozyreva, A., Tauschwitz, A., Shutov, A., Maruhn, J.A., Spiller, P., Neuner, U. & Bock, R. (2001). Designing future heavy-ion-matter interaction experiments for the GSI Darmstadt heavy ion synchrotron. Nucl. Instrum. Meth. Phys. Res. A 464, 211.
Tahir, N.A., Juranek, H., Shutov, A., Redmer, R., Piriz, A.R., Temporal, M., Varentsov, D., Udrea, S., Hoffmann, D.H.H., Deutsch, C., Lomonosov, I. & Fortov, V.E. (2003). Influence of the equation of state on the compression and heating hydrogen. Phys. Rev. B 67, 184101.
Tahir, N.A., Udrea, S., Deutsch, C., Fortov, V.E., Grandjouan, G., Gryaznov, V., Hoffmann, D.H.H., Hulsmann, P., Kirk, M., Lomonosov, I.V., Piriz, A.R., Shutov, A., Spiller, P., Temporal, M. & Varentsov, D. (2004). Target heating in high-energy-density matter experiments at the proposed GSI FAIR facility: Non-linear bunch rotation in SIS 100 and optimization of spot size and pulse length. Laser Part. Beams 22, 485.
Temporal, M., Lopez Cela, J.J., Piriz, A.R., Grandjouan, N., Tahir, N.A. & Hofmann, D.H.H. (2005). Compression of acylindrical hydrogen sample driven by an intense co-axial heavy ion beam. Laser Part. Beams 23, 137.
Temporal, M., Piriz, A.R., Grandjouan, N., Tahir, N.A. & Hoffmann, D.H.H. (2003). Numerical analysis of a multilayered cylindrical target compression driven by a rotating intense heavy ion beam. Laser Part. Beams 21, 609.
Terrones, G. (2005). Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces. Phys. Rev. E 71, 036306.
Weir, S.T., Mitchell, A.C. & Nellis, W.J. (1996). Metallization of fluid molecular hydrogen at 140 GPa (1.4 Mbar). Phys. Rev. Lett. 76, 1860.
Wigner, E. & Huntigton, H.B. (1935). Metallization of molecular hydrogen. J. Chem. Phys. 3, 764.
White, G.N. (1973). A one-degree-of-freedom model for the Taylor instability of an ideally plastic metal plate. Los Alamos National Laboratory Report LA-5225-MS. Los Alamos, NM: Los Alamos National Laboratory.
Wouchuk, J.G. (2001). Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected. Phys. Rev. E 63, 056303.

Keywords

Related content

Powered by UNSILO

Numerical simulations of Rayleigh-Taylor instability in elastic solids

  • J.J. LÓPEZ CELA (a1), A.R. PIRIZ (a1), M.C. SERNA MORENO (a1) and N.A. TAHIR (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.