Existence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage

摘要: A typical phase field approach for describing separation and coarsening phenomena in alloys is the Cahn-Hilliard model. This model has been generalized to so-called Cahn-Larche system by combining it with elasticity capture non-neglecting deformation phenomena, which occur during and coarsening processes material. In order account damage effects, we extend existing framework of systems by incorporating an internal variable local character. damage allows model effect that a material point influenced its surrounding. The process described unidirectional rate-dependent evolution inclusion for variable. For introduced systems coupled rate-dependent damage processes, we establish suitable notion weak solutions prove existence solutions.