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- W2026992224 abstract "A flat surface of stressed solid is unstable to small perturbations. This morphological instability is called Asaro–Tiller–Grinfield instability. Nonlinear evolution of this instability will result in the formation of cusp singularities. This instability can be described by a continuum model with surface diffusion driven by a stress-dependent chemical potential. The stress and strain in the solid are coupled with surface morphology and an elasticity problem must be solved numerically. We derive a nonlinear approximation equation governing the evolution of this instability in which the stress-dependent chemical potential is expressed explicitly as a function of the surface morphology. Linear instability analysis using our equation shows the same results as the well-known Asaro–Tiller–Grinfeld instability result. Compared with the exact solution of the elasticity problem for cycloid surface obtained by Chiu and Gao, our nonlinear approximation has a much wider range of applicability than linear approximation. Numerical simulation using our nonlinear evolution equation shows that the surface evolves towards a cusplike morphology from small perturbations, which agrees very well with results obtained by solving the full elasticity problem." @default.
- W2026992224 created "2016-06-24" @default.
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- W2026992224 date "2002-05-20" @default.
- W2026992224 modified "2023-10-18" @default.
- W2026992224 title "Nonlinear evolution equation for the stress-driven morphological instability" @default.
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- W2026992224 doi "https://doi.org/10.1063/1.1477259" @default.
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