Modelling of non-linear switching effects in piezoceramics: a three-dimensional polygonal finite-element-based approach applied to oligo-crystals

A polygonal finite-element formulation is applied to solve electromechanically coupled inhomogeneous boundary value problems for polycrystalline materials. Each grain is discretised by one single polygonal finite element, which allows the efficient simulation of general boundary value problems which still resolves individual grains in space. The constitutive model proposed for switching in piezoceramics makes use of a volume-fraction-based framework, where the respective volume fractions refer to the respective crystallographic variants and take the interpretation as internal variables. Their evolution is combined with non-linear hardening-type functions which additionally account for grain-size dependencies. The computational model is shown to reproduce typical hysteresis and butterfly curves on the polycrystalline level under complex electromechanical loading conditions. The results are obtained by direct volume-averaging with respect to the discretised domain and are in good qualitative agreement with experimental data. Moreover, grain-size effects, such as an increase in the coercive electric field value with decreasing grain size, are also captured.