Inhomogeneity and material configurational forces in three dimensional ferroelectric polycrystals

Ferroelectrics are polycrystalline materials consisting of multi-grains with their individual orientations. Polarization switching under an applied electric field is predicted by a micromechanical nonlinear constitutive model for ferroelectric polycrystals proposed by Huber et al. [J. Mech. Phys. Solids 47 (1999) 1663]. A three dimensional finite element method is used to simulate the macroscopic mechanical and electrical response over the whole multi-grains body. Moreover, the microscopic behavior inside each separate grain is studied. Due to the heterogeneity highly fluctuating inhomogeneous stresses and strains are observed to be distributed in ferroelectric polycrystal body. High stresses are developed especially around the grain boundaries. This phenomenon is attributed to different lattice orientations of grains as well as grain-to-grain interactions in polycrystalline ceramic. Furthermore, a consistent thermodynamical framework is outlined to develop the theory of material configurational forces which takes into account the contribution of remanent polarization and strain due to domain switching. The conservation laws of configurational forces are concluded, i.e. the summation of three components of configurational forces on all nodes over the whole ferroelectric body is always conserved.