Acceleration instability in elastic-plastic solids. I. Numerical simulations of plate acceleration

Abstract

Acceleration instability occurs when a body is accelerated by surface tractions. This situation resembles classic Rayleigh–Taylor instability, but differs due to the temporal and spatial variation of the stress field in the accelerated body caused by wave propagation and the time dependence of the accelerating forces. These factors produce phenomena in acceleration instability which are without precedent in classical Rayleigh–Taylor analyses. An extensive numerical study of acceleration instability using a Lagrangian finite-difference wavecode has determined the influence of various parameters including amplitude and wavelength of initial surface perturbations, material yield strength, and time dependence of the driving force. The nature of the criteria determining stability or instability is established, and the fundamental physical quantity controlling perturbation growth at an interface is shown to be the local stress gradient.