Multiscale finite element modeling of nonlinear behavior of polycrystalline piezoceramics with account of tetragonal and rhombohedral phases

The nonlinear behavior of a polycrystalline piezoceramic materials based on the two-level finite element homogenization method was investigated. Numerical experiments were carried out for rhombohedral and mixed (tetragonal-rhombohedral) variants within a single crystal using a micromechanical model of the material. Based on the results of numerical experiments, the remanent part of the free energy accounting dependence of the saturation strain on the type of the multiaxial deformed state was constructed.