, Volume 25, Issue 6, pp 795-802
Date: 21 Nov 2012

Phase equilibria in isotropic solids

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Abstract

The paper determines the forms of equations of equilibrium for stable coherent phase interfaces in isotropic solids. If the first phase satisfies the Baker Ericksen inequalities strictly and the principal stretches of the second phase differ from those of the first phase, one obtains the equality of three specific generalized scalar forces and of a generalized Gibbs function. The forms of these quantities depend on the signs of the increments of the principal stretches across the interface. The proof uses the rank 1 convexity condition for isotropic materials (Šilhavý in Proc. R. Soc. Edinb 129A:1081–1105, 1999) and is available only if the two phases are not too far from each other or if one of the two phases is a fluid (liquid). The result does not follow from the representation theorems for isotropic solids.

Communicated by Andreas Öchsner.