Phase field under stress
摘要
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the Grinfeld instability. Moreover, we use our approach to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by comparison with a sharp-interface simulation. We then investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wavenumbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion.
引用
@article{arxiv.cond-mat/0005476,
title = {Phase field under stress},
author = {Klaus Kassner and Chaouqi Misbah and Judith Mueller and Jens Kappey and Peter Kohlert},
journal= {arXiv preprint arXiv:cond-mat/0005476},
year = {2007}
}
备注
40 pages, 12 figures, submitted to Phys. Rev. E