The classical Rayleigh-Taylor (RT) instability is developed in the interface that separates a heavy fluid from a lighter one in the presence of a gravitational field. If the interface is not perfectly planar, its small perturbations will grow without bound. When a solid is submitted to a very high acceleration, for example by the application of an external pressure on one of its faces, this interface is also RT unstable. This kind of situations are found in several technological applications like explosive forming process, laser implosion of fusion targets, electromagnetic implosion of metal liners or experiments to achieve hydrogen metallization [
]. If the RT instability appears the experiment could fail. So it is important to study which are the mechanisms that produce stabilizing effects to alleviate the growth of the instability. When we are dealing with fluids the stabilizing mechanisms are, for example, gradient effects, viscosity and superficial tension. Dealing with solids, their intrinsic properties can produce such a stabilizing effect. In a very simple interpretation, the elastic forces that the solid develop can compensate the buoyancy force that leads the instability, but when the material plastifies it can again be unstable.
Analytical solutions are only available for elastic solids. The exact analytical solution describing the entire process exists only for solid-vacuum interfaces [
]. For solid/solid and viscous fluid/solid interfaces there is an exact analytical model that describes only the asymptotic phase [
] and an approximate analytical model that we have presented elsewhere [
] that describes not only the asymptotic behaviour but also the initial transient phase. The initial transient phase is of great importance because the instability could enter in the non-linear regime or in the plastic flow before the asymptotic regime is reached.
In this work we present some numerical simulations based on the Finite Element Method for a very thick solid layer. In particular we have verified that the stability criteria defined by previous models are consistent with the simulations and also we have studied the influence of the elastic material parameters.