Mechano-Chemical Spinodal Decomposition: A Theory of Phase Transformation in Crystalline Solids, and Development of Second-Order Accurate, Unconditionally Stable Time Integration Algorithms

I will present a theory for solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals.
The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures.
The model couples the classical Cahn-Hilliard model with Toupin's theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations.