# Phase field modelling of large deformations

During simulation of phase transformations large lattice parameter changes (i.e. eigenstrains) might occur. The standard linear elasticity which is typically used in phase field simulations proved to be a reliable tool in the case of small deformations. Not so in the case of the large deformations. The problem arises from the nature of the phase field numerical solution algorithm which is grid based and requires the constant grid size parameter for the correct differential operator handling. This makes it difficult to directly apply geometrically nonlinear elastic solvers as it naturally done in the FE methods where the deformation is directly applied to the finite elements.

In order to allow large deformations handling to the typical phase field simulation a special care should be taken as to correctly apply the deformation of the system while keeping the constant grid spacing. In our approach the alternating Lagrangian-Eulerian steps will be employed.