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Phenomenological model for coupled multi-axial piezoelectricity

A quantitative calibration of an existing phenomenological model for polycrystalline ferroelectric ceramics is presented. The model relies on remnant strain and polarization as independent variables. Innovative experimental and numerical model identification procedures are developed for the characterization of the coupled electro-mechanical, multi-axial nonlinear constitutive law. Experiments were conducted on thin PZT-5A4E plates subjected to cross-thickness electric field. Unimorph structures with different thickness ratios between PZT-5A4E plate and substrate were tested, to subject the piezo plates to coupled electro-mechanical fields. Material state histories in electric field-strain-polarization space and stress-strain-polarization space were recorded. An optimization procedure is employed for the determination of the model parameters, and the calibrated constitutive law predicts both the uncoupled and coupled experimental observations accurately.