Multiscale modeling of ferroelectrics with stochastic grain size distribution

Macroscopic properties of ferroelectrics are controlled by processes on the microscale, in particular switching crystal unit cells and movement domain walls, respectively. Besides these microscopic levels, grains a polycrystalline material constitute mesoscopic scale. Interactions with statistically distributed orientations, as consequence mechanical electrostatic mismatch, give rise to for example, residual stress which turn affects switching. A multiscale modeling thus has incorporate at least three interacting scales. In this context, condensed method recently been elaborated an efficient tool low computational cost effort implementation. It is extended toward statistical distributions grain sizes representative volume element amended regard evolution. Each few parameters constitutive approach unique physical meaning adapted available experimental values macroscopic quantities barium titanate taken from various sources.