On the modelling of rate-dependent domain switching in piezoelectric materials under superimposed stresses

To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic approach - a purely phenomenologically motivated concept. To study the overall bulk ceramics behaviour, straightforward volume-averaging techniques are applied. In addition, rate-dependent properties under cyclic electrical loading combined with mechanical loads at various frequencies are studied, whereby use of a so-called volume fraction concept is made. The proposed model provides further insights into rate-dependent behaviour as experimentally observed and reported in the literature.