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Numerical simulations of Rayleigh-Taylor instability in elastic solids

Published online by Cambridge University Press:  21 September 2006

J.J. LÓPEZ CELA ,
A.R. PIRIZ ,
M.C. SERNA MORENO  and
N.A. TAHIR
J.J. LÓPEZ CELA
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Spain
A.R. PIRIZ
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Spain
M.C. SERNA MORENO
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Spain
N.A. TAHIR
Affiliation:
Gesellschaft für Schwerionenforschung, Darmstadt, Germany
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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.

Keywords

Elastic solid/elastic solidElastic solid/viscous fluidNumerical simulationsRayleigh-Taylor instability
Type
Research Article
Information
Laser and Particle Beams , Volume 24 , Issue 3 , September 2006 , pp. 427 - 435
Copyright
© 2006 Cambridge University Press

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References

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.CrossRefGoogle Scholar
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.CrossRef
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.CrossRefGoogle Scholar
Barnes, J.F., Blewet, P.J., McQueen, R.G., Meyer, K.A. & Venable, D. (1974). Taylor instability in solids. J. Appl. Phys. 45, 727.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Dienes, J.K. (1978). Method of generalized coordinates and an application to Rayleigh-Taylor instability. Phys. Fluids 21, 736.Google Scholar
Dimonte, G., Gore, R. & Schneider, M. (1998). Rayleigh-Taylor instability in elastic-plastic materials. Phys. Rev. Lett. 80, 1212CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Plohr, B.J. & Sharp, D.H. (1998). Instability of accelerated elastic metal plates. ZAMP 49, 786.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Robinson, A.C. & Swegle, J.W. (1989). Acceleration instability in elastic-plastic solids: Analytical techniques. J. Appl. Phys. 66, 2859.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Swegle, J.W. & Robinson, A.C. (1989). Acceleration instability in elastic-plastic solids: Numerical simulations of plate acceleration. J. Appl. Phys. 66, 2838.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Terrones, G. (2005). Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces. Phys. Rev. E 71, 036306.Google Scholar
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.CrossRefGoogle Scholar
Wigner, E. & Huntigton, H.B. (1935). Metallization of molecular hydrogen. J. Chem. Phys. 3, 764.CrossRefGoogle Scholar
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.Google Scholar