PMID: 11308719Apr 20, 2001Paper

Phase-field modeling of stress-induced instabilities

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Klaus KassnerP Kohlert

Abstract

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. Using a formulation that is independent of the state of reference chosen for the displacement field, we write down the elastic energy in an unambiguous fashion, thus obtaining an entire class of models. According to the choice of reference state, the particular model emerging from this class will become equivalent to one of the two independently constructed models on which brief accounts have been given recently [J. Müller and M. Grant, Phys. Rev. Lett. 82, 1736 (1999); K. Kassner and C. Misbah, Europhys. Lett. 46, 217 (1999)]. We show that our phase-field approach recovers the sharp-interface limit corresponding to the continuum model equations describing the Asaro-Tiller-Grinfeld instability. Moreover, we use our model 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 reproducing some known results and by comparison with a sharp-interface simulation. We then proceed to investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding...Continue Reading

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Citations

Jul 3, 2015·The Journal of Chemical Physics·Rabia LaghmachThierry Biben
Apr 23, 2004·The European Physical Journal. E, Soft Matter·K SekimotoA Bernheim-Grosswasser
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K R Elder, Martin Grant
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V I Marconi, E A Jagla
Nov 18, 2009·Journal of Physics. Condensed Matter : an Institute of Physics Journal·E A BrenerD E Temkin
Feb 21, 2006·Physical Review Letters·Robert SpatschekKlaus Kassner
May 24, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M FleckE A Brener
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Fabien ClosaElie Raphaël
Sep 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Clemens GugenbergerKlaus Kassner
Oct 4, 2020·The European Physical Journal. E, Soft Matter·Robert ChojowskiFalko Ziebert
Aug 31, 2016·Physical Review. E·Maria E StournaraBrian W Sheldon
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Badrinarayan P AthreyaNikolas Provatas
Jun 6, 2003·Physical Review Letters·Patrick BergerChaouqi Misbah
Dec 17, 2004·Physical Review Letters·J SchmittbuhlR Toussaint
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N WangA Karma
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jérôme Paret
Apr 12, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Biben, C Misbah
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Klaus Kassner, Chaouqi Misbah
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zhi-Feng Huang
Nov 13, 2008·Physical Review Letters·Zhi-Feng Huang, K R Elder
Mar 16, 2007·Physical Review Letters·D PilipenkoH Müller-Krumbhaar
Mar 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Champika G Gamage, Zhi-Feng Huang
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Efim A BrenerR Spatschek
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R SpatschekB Nestler
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L O EastgateC R Myers

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