We study the electromechanical behavior of Lead Zirconate Titanate ferroelectric ceramics (PZT), by means of a three-dimensional continuum model for deformable ferroelectric bodies in their polar phase characterized by spontaneous polarization and strain. Spontaneous polarization and strain organize into a domain structure which minimizes electrostatic and elastic energies and which can be modified by the application of electromechanical loads. Such process, which is called "domain switching", is associated with electrical and mechanical hysteresis and can be studied as a minimization problem for a functional which reminds the micromagnetic energy of deformable ferromagnetics. In this paper, which is the first of two, we deal with the electromechanical model and related constitutive assumptions, as well as with the analysis of domain structure in PZT. In particular, following the discover of a new monoclinic phase in PZT carried by Noheda and co-workers, we analyze twinning between spontaneous strain at the various phase boundaries and show that both non-generic, non-conventional twins and finely-twinned laminates are possible, and also that the presence of a monoclinic phase may explain PZT exceptional properties.
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