In this paper, a thermodynamically consistent minimum-type variational model for ferroelectric materials in a macroscopical continuum approach is presented. The motivation for this results from the lack of models in the literature that have on the one hand a Helmholtz free energy based variational structure and on the other hand are able to represent all important characteristic phenomena of ferroelectrics under quasi-static conditions. First of all, a unified variational theory for the material response of dissipative electro-mechanical solids in line with the framework of the generalized standard materials (GSM) is outlined. A macroscopic ferroelectric model with microscopically motivated internal state variables representing the switching processes taking place at the material microscale is adapted to the above mentioned variational structure. Additionally, a mixed variational principle for the global electro-mechanical boundary value problem is introduced in order to embed the Helmholtz free energy based local theory in a suitable finite element formulation. The solution processes for the resulting local and global variational problems is described in detail to enable easy implementation. The capability of the presented methods to reproduce the real behavior of ferroelectric systems is demonstrated by numerical examples. Here, a comparison to experimental results from the literature is a particular focus
