Micromechanical Modeling of Switching Effects in Piezoelectric Materials — A Robust Coupled Finite Element Approach

A micromechanically motivated model for piezoelectric materials has been developed in this work. In particular, the nonlinear behavior of poly-crystalline specimens with tetragonal perovskite-type substructure are studied, and a robust three-dimensional coupled finite element formulation is elaborated. Differently oriented grains are taken into account within the proposed model, whereby representative dipole directions attached to each grain are randomly oriented. Furthermore, an energy reduction criterion applied to individual domains is adopted as a criterion for the initiation of domain switching processes. Based on this, macroscopic bulk response can be predicted by classical volume-averaging techniques. In practice, however, domain switching might occur even below the classical critical energy barrier which mainly stems from so-called intergranular effects. These effects are incorporated into the developed framework via a phenomenologically motivated probabilistic approach by relating the actual energy level to a critical energy level. In order to compare representative coupled finite element examples with experimental data reported in the literature, macroscopically uni-axial and quasi-static loading is applied to the bulk material: first, hysteresis and butterfly curves under purely electrical loading are discussed; secondly, additional mechanical loads in axial and lateral direction are applied to the specimen.