Acceleration instability in elastic-plastic solids. II. Analytical techniques

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 accelerating forces. We wish to investigate the extent to which the acceleration instability response of elastic-plastic solids can be approximately modeled using a modal or one-degree-of-freedom technique assuming incompressible flow. We find that neither the response equation derived assuming a linear elastic shear response nor the so-called ‘‘minimum amplitude’’ instability criterion derived from rigid plastic analyses is sufficient to describe overall stability characteristics at very large driving pressures. Several versions of the modal approximation technique for an elastic-plastic material response are derived and compared. The features which must be included in such an analysis in order to obtain qualitative agreement with instability results seen in numerical experiments are indicated. However, quantitative agreement with numerical results cannot be obtained in all cases. The sources of the disagreement and the regions of applicability of the analysis are discussed.