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As smart structures are becoming increasingly ubiquitous in our daily life, the need for efficient modeling electromechanical coupling devices is also rapidly advancing. Smart structures are often made of piezoelectric materials such as lead zirconate titanate (PZT), which exhibits strong nonlinear behavior known as hysteresis effect under a large applied electric field. There have been numerous modeling techniques that are able to capture such an effect; some techniques are suitable for obtaining physical insights into the micro-structure of the material, while other techniques are better-suited to practical structural analyses. In this paper, we aim to achieve the latter. We propose a simplified phenomenological macroscopic model of a nonlinear ferroelectric actuator. The assumption is based on the direct relation between the irreversible strain and irreversible electric field, and the consequently irreversible polarization. The proposed model is then implemented in a finite element framework, in which the main features such as local return mapping and the tangent moduli are derived. The outcomes of the model are compared and validated with experimental data. Therefore, the development presented in this paper can be a useful tool for the modeling of nonlinear ferroelectric actuators.

We present a high electrode density and high channel count CMOS (complementary metal-oxide-semiconductor) active neural probe containing 1344 neuron sized recording pixels (20 µm × 20 µm) and 12 reference pixels (20 µm × 80 µm), densely packed on a 50 µm thick, 100 µm wide, and 8 mm long shank. The active electrodes or pixels consist of dedicated in-situ circuits for signal source amplification, which are directly located under each electrode. The probe supports the simultaneous recording of all 1356 electrodes with sufficient signal to noise ratio for typical neuroscience applications. For enhanced performance, further noise reduction can be achieved while using half of the electrodes (678). Both of these numbers considerably surpass the state-of-the art active neural probes in both electrode count and number of recording channels. The measured input referred noise in the action potential band is 12.4 µVrms, while using 678 electrodes, with just 3 µW power dissipation per pixel and 45 µW per read-out channel (including data transmission).