Fractional derivative operators for modeling piezoceramic polarization behaviors under dynamic mechanical stress excitation

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Polarization variations in ferroelectric materials are frequency-dependent. Measurements and simulations using the fractional derivative of polarization behaviors versus frequency and mechanical stress amplitude are discussed in this article. A dynamic dielectric hysteresis fractional model has previously been developed, and a large number of comparisons between simulations and measurements under varying electric field excitation amplitudes on a frequency bandwidth over 4 decades were performed. Good results were obtained regardless of the type of excitation waveform. Equivalent comparisons under varying mechanical stress excitations were related and a specific measuring equipment was developed in order to test piezoceramic materials under mechanical stresses up to 100MPa within a frequency bandwidth of 1mHz<f<1Hz. As previously noticed under electrical excitation, the fractional time model provided very accurate results of the dynamic ceramic behavior under mechanical stress. The fractional order was set to 0.5 under electrical conditions and the same order rendered it possible to obtain the best results under mechanical conditions. This observation was particularly interesting; the same physical origins could be attributed all the dynamical behaviors (under both mechanical and electrical excitation sources).