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