Exponentially rapid coarsening and buckling in coherently self-stressed thin plates

Abstract

The nonlinear equations that couple diffusion and stress are solved by computation for one-dimensional spinodal decomposition and coarsening in a thin plate. The vicinity of two critical values of the stress parameter are explored. At small values of elastic self-stresses, coarsening changes to exponentially fast from the exponentially slow dynamics expected for one-dimensions in the absence of stress. Coarsening is by rapid thickening of a single layer of a different phase from each of the two plate surfaces, leading to bending of the plate. Even though the diffusion equation is the same for bulk and thin plate and changes type at the coherent spinodal transition, in a thin plate the changes near this transition are gradual; the difference in behavior is due to the boundary conditions. Furthermore elasto-chemical equilibria through this transition are completely continuous. If the elastic term is large compared to the wetting term, surface wetting layers of phase of lower energy are found to disappear late in the coarsening.