On isothermal phase field models incorporating geometrically linear elasticity

A new class of phase field models is derived and studied where the elastic energy, being quasiconvex, incorporates microstructure formation on smaller length scales. After a review of the used elasticity theory, global existence of weak solutions in certain microstructural regimes is proved with two different methods.

First numerical computations illustrate the characteristic properties of the solutions and allow a comparison to the existing models with linear elasticity.