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A non-equilibrium thermodynamics framework for domain evolution: phase field models and finite element implementation

A continuum thermodynamics framework for the diffuse interface or "phase field" approach to domain evolution is presented. The theory distinguishes the fundamental balance laws which are universal (i.e. mechanical equilibrium, Gauss' law, and a new micro-force balance) from the constitutive laws, which describe the behavior of a specific material. A finite element formulation based on a virtual work statement is implemented using mechanical displacements, electrical potential, and polarization components (the vector "order parameter") as nodal degrees of freedom. The finite element code is then applied to simulate the growth of a 180° domain needle through a parent domain.