One of the advantages of the phase-field method (PFM) is its ability to incorporate elastic interactions that dominate solid-state processes including phase transformations and plastic deformation. As mechanical equilibrium is attained much faster than chemical equilibrium, the former should be used as a constraint in deriving the governing equations of time-evolution of order parameters in PFM. Current models for elastically anisotropic and inhomogeneous media in the literature do not impose such a constraint in their governing equations, in particular, when evaluating the variational derivative of the elastic energy. In this work, we present a rigorous and physically transparent formulation of PFM governing equations for elastically anisotropic and inhomogeneous media in which the mechanical equilibrium is used as a constraint.
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