A model order reduced Finite Element approach to multiscale simulation of polycrystalline ferroelectrics

The computational investigation of ferroelectric constitutive behavior is a demanding task that requires a comprehensive multiscale model, accounting for microphysical processes and adequate interaction of the length scales involved. Without the need for spatial discretization, the condensed method (CM) as semi-analytical approach turns out to be very efficient in this regard. Representing the constitutive behavior at a single material point, however, the CM is unable to handle arbitrary boundary value problems. For structural analyses of ferroelectrics in technical devices a spatial discretization scheme is inevitable. The finite element method is a commonly used tool for that purpose, where drawbacks may be attributed to high computational cost, especially in case of multiscale spatial resolution, and integration point based constitutive evolution. The latter aspect also results in an unphysical correlation between discretization and microstructure. In the work at hand, an efficient and energetically consistent hybrid approach for macroscopic ferroelectric boundary value problems is elaborated by integrating the CM into a finite element (FE) framework. Introducing an independent material grid fully decouples the microstructure from FE discretization, and moreover provides a basis of model order reduction, considerably saving computational cost.