Thermodynamically consistent Cahn-Hilliard and Allen-Cahn models in elastic solids

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November 2006, 15(4): 1169-1191. doi: 10.3934/dcds.2006.15.1169

Thermodynamically consistent Cahn-Hilliard and Allen-Cahn models in elastic solids

1.	System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland

Received May 2005 Revised December 2005 Published May 2006

Abstract
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The goal of this paper is to derive again the generalized Cahn-Hilliard and Allen-Cahn models in deformable continua introduced previously by E. Fried and M. E. Gurtin on the basis of a microforce balance. We use a~different approach based on the second law in the form of the entropy principle according to I. Müller and I. S. Liu which leads to the evaluation of the entropy inequality with multipliers.
Both approaches provide the same systems of field equations. In particular, our differential equation for the multiplier associated with the balance law for the order parameter turns out to be identical with the Fried-Gurtin microforce balance.

Keywords: Allen-Cahn models, Cahn-Hilliard, phase transitions, elastic solids..

Mathematics Subject Classification: Primary: 74A30, 35K25; Secondary: 35Q72, 35L2.

Citation: Irena Pawłow. Thermodynamically consistent Cahn-Hilliard and Allen-Cahn models in elastic solids. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1169-1191. doi: 10.3934/dcds.2006.15.1169

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