We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The
focus is placed on recent applications of phase-field simulations of solid-state microstructure …

The phase-field method is reviewed against its historical and theoretical background.
Starting from Van der Waals considerations on the structure of interfaces in materials the …

Unlike the description of cracks as sharp surfaces which requires different criteria to predict
the onset of crack propagation, the direction of crack growth, possible crack branching, and …

In this paper we present a phase-field model to describe isothermal phase transitions
between ideal binary-alloy liquid and solid phases. Governing equations are developed for …

The phase-field method has become an important and extremely versatile technique for
simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface …

A phase-field formulation is introduced to simulate quantitatively microstructural pattern
formation in alloys. The thin-interface limit of this formulation yields a much less stringent …

A continuum field theory approach is presented for modeling elastic and plastic deformation,
free surfaces, and multiple crystal orientations in nonequilibrium processing phenomena …

We introduce a phenomenological continuum model for the mode III dynamic fracture that is
based on the phase-field methodology used extensively to model interfacial pattern …

This is the first account of the history of our understanding of, and ability to model,
solidification microstructures. Its objective is to retrace the scientific steps made, from the …

In an effort to unify the various phase-field models that have been used to study
solidification, we have developed a class of phase-field models for crystallization of a pure …