A first-order FE² homogenization of phase-field theory, with micro–macro links for both the order parameter and its gradient, matches DNS evolution of averaged fields on notched and holed specimens.
Cahn-Hilliard Phase Field Theory Coupled to Mechanics: Fundamentals, Numerical Implementation and Application to Topol- ogy Optimization
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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization
A first-order FE² homogenization of phase-field theory, with micro–macro links for both the order parameter and its gradient, matches DNS evolution of averaged fields on notched and holed specimens.