Phase Field methods (PFM) are extensively used for modeling microstructures. The reason for this success is that, using simple symmetry arguments and the conserved or non-conserved characters of the fields needed to describe the situation, it is easy to develop free energy functionals and kinetic equations for complex situations where different phenomena are coupled. However, as the fields are supposed to be continuous, the numerical implementation requires the grid spacing to be much smaller than the smallest internal length scale, i.e. the interfaces widths. This «diffuse interface» constraint limits drastically the overall accessible linear dimensions or, conversely, increases dramatically the required computational time.
We propose a new PFM formulation, in which interface widths may be as small as the grid spacing, without any pinning on the grid when the interfaces move, allowing to multiply the accessible linear dimensions by an order of magnitude or, conversely, to reduce the computational time by almost three orders of magnitude. Also, to couple this «sharp interface» PFM to elastic fields, we propose a new elastic solver that efficiently treats strong elastic heterogeneities and that is mathematically stable.