Instabilities in elastic accelerated solids

When a solid plate is accelerated by an external pressure 0 p an instability similar to the Rayleigh-Taylor one appears if the plate is not perfectly flat. Due to the elastoplastic properties of the material the growth of the instability is lower than in a pure fluid case. In a very simple interpretation, the pressure difference across the irregular surface provokes the instability that can be stabilized by the elastic force of the body. Then, if the elastic regime is exceeded, the material begins to flow plastically and becomes unstable but the development of the instability is smoother than in the ideal situation. So it is important to determine which values of the elastic properties can produce this stabilizing mechanism. One of the most accepted approaches to treat the instability of accelerated elastic solids is to make a correspondence between the viscosity μ and the elastic shear modulus G, through n G / = μ assuming a factor nt e for all quantities [1]. Other approach assumes an isothermal, isotropic and hyperelastic material [2]. According to the later one, the growth rate n depends on the value of G p0 , which is not reflected by the first approach. However, in the limit of small wavelengths compared to the thickness of the plate ∞ → kh , both approaches predict the same critical wavelength given by: