Coordinate‐invariant phase field modeling of ferro‐electrics, part II: Application to composites and poly‐crystals

Abstract

AbstractThis paper deals with the application of the model presented in the first part Schrade et al. [1] to ferroelectric composites filled with electrically conducting inclusions as well as to ferroelectric polycrystals. Composites are analyzed through the use of a computational homogenization framework for phase field methods proposed in Zäh & Miehe [2]. This will give insights into the coupled phenomena taking place on the microscale and on their relation to the overall behavior. Both will be of special interest for the development of advanced composite materials with tailored properties like, for example, particulate magneto‐electric composites, which are composed of a ferroelectric matrix and magnetic rare‐earth elements or metals. Furthermore, we analyze the behavior of ferroelectric polycrystals with a focus on size effects. This will enable us to reveal preferred microstructure configurations depending on the system and grain size. In addition to that, it will serve as basis for the extraction of the directional properties of polycrystals with respect to their switching behavior in the different grains of the polycrystal. Associated simulations could then be used to supply coarser models with the needed directional informations. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)