Richtmyer-Meshkov instability in elastic-plastic media

Richtmyer-Meshkov instability in elastic-plastic media*
A. R. Piriz1,#,J. J. López Cela1, N. A. Tahir2, and D. H. H. Hoffmann2,3
1Univ. de Castilla-La Mancha, Spain;2GSI, Darmstadt, Germany, 2Technische Universität of Darmstadt, Germany
A sort of Richtmyer-Meshkov (RM) instability occurs when a shock wave is launched into the bulk of continu-ous medium from its boundary surface. Such is the situa-tion in the LAPLAS (Laboratory of Planetary Sciences) experiment planned at GSI to be performed on the future FAIR facility for the study of high energy density states of matter. It happens when the absorber region expands driv-ing the implosion of the pusher layers. Since the pusher remains in solid state during the implosion, it retains elas-tic-plastic properties that will affect the evolution of the hydrodynamic instabilities. We have studied the RM dy-namics of a vacuum/solid interface by means of an ana-lytical model and by two-dimensional numerical simula-tions with the code ABAQUS [1-3]. The typical behav-iour of the perturbation amplitude is shown in Fig.1 for different values of the yield strength Y (5, 10, 20, 40, ∞MPa) and for a shear modulus G = 13 GPa. For reference we also show the classical growth rate (G = 0, Y = ∞).
Figure 1: Amplitude evolution for different values of the yield strength and for the classical case.
As we can see, the perturbation grows up to a maxi-mum value ξm determined by the yield strength and then it oscillates elastically with an amplitude that is much less than ξm (ξ0 = 20 µm is the initial perturbation amplitude of the interface).
In Fig.2 we have represented the results of extensive numerical simulations for the relative amplitude ξm−ξp, where ξp is taken as the amplitude at the time when the interface is free of stresses (the inflexion point in Fig.1). We find that this magnitude is only a function of the pa-rameters combination kY
p
/2ξρ&, where k is the pertur-bation wavenumber, ρis the density of the shocked phase and it is determined by the Mie-Grüneisen equation
of state, and
p
p
u
k
ξ
ξ=
& is the classical growth rate (u
p is the fluid velocity behind the shock).
Figure 2: Relative maximum amplitude for different
cases.
The previous results suggest a new method to measure the yield strength under dynamic conditions as alternative to the experiments that use the Rayleigh-Taylor (RT) insta-bility [4]. In fact, using RM instability would require de-termine the perturbation amplitude at any time
]
)
(
[
m
m
m
t
t
tξ
ξ=
≥. This one measurement experiment would be advantageous in comparison with the RT based experiments that require the experimental determination of the growth rate.
References
[1] A. R. Piriz et al. Phys. Rev. E 72, 056313 (2005).
[2] A. R. Piriz et al. Am. J. Phys. 74, 1095 (2006).
[3] A. R. Piriz et al. Phys. Rev. E. 74, 037301 (2006).
[4] K. T. Ruden et al. Phys. Plasmas 12, 056309 (2005).
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