Shape instabilities of plate-like structures—II. Analysis

Abstract

In this paper, a companion to the previous one, a susceptibility analysis which delineates the primary instability mode of a terminated plate as it depends on plate width to thickness (aspect) ratio and the energy of internal boundaries of plates is presented. The analysis is based on a simple averaging of Fick's first law, and thus is based on geometrical, yet physically plausible, approximations. The analysis is carried out for both volume diffusion and surface diffusion control of the instability process. Direct cylinderization of plates is favored when the plate aspect ratio is small and the energy of internal boundaries that may be present is low. Boundary induced splitting of plates is favored when the boundary energy is high, whereas edge spheroidization is the dominant instability mode for plates with large aspect ratios containing low energy internal boundaries. The results of the analysis can be succintly represented in terms of plate instability diagrams which define the dominant instability mode in terms of plate aspect ratio and internal boundary energy. Lines of constant instability times can be superimposed on the diagrams, thereby increasing their utility.