Linear analysis of the cylindrical and spherical interface instability in elastic solids

A Lagrangian method is presented for solving linear perturbations of elastic solids in cylindrical and spherical geometry. The model consists of one-dimensional base equations and linearly perturbed modal component equations, and the elasticity constitutive equations and its linearized form are considered. The component equations based on perturbation expansions are described uniformly under different geometries and perturbation assumptions. In the numerical format of a linearly perturbed system, the radial and transverse numerical fluxes based on the Godunov discretization format use the same Riemann solver to ensure the consistency of the numerical scheme, and the time-step constraint scheme is empirical. Based on this method, this paper investigates the Rayleigh–Taylor instability at the interface of elastic solids in cylindrical and spherical geometries, analyzes the differences between the initial and asymptotic phases of perturbation development, and compares it with the two-dimensional theory. Furthermore, we point out the effects of pseudo-three-dimensional perturbations and finite thickness, which cannot be ignored.