Non-linear material modelling and control of piezoelectric actuators and sensors

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Piezoelectric materials (PEM) have a coupled electro-mechanical behaviour, by which a mechanical stress produces an electric polarisation, and an electric field produces a mechanical strain. For this reason, PEM have had immense success in the design of precision actuators (devices that perform movement) and sensors (devices that detect movement). However, PEM exhibit a coupling between mechanical creep (time-dependent deformation at a constant load) and electrical hysteresis (history-dependence of the polarisation on the electric field). These non-linear effects are not properly captured by the standard models, and in the case of actuators, they cause uncertainty in position over long time intervals, whereas in the case of sensors, they severely limit the range in which the sensor behaves linearly.We discovered a flaw in the widely adopted practice of obtaining non-linear constitutive laws by adding terms to the linear ones. In this project, we propose a more radical approach. Rather than extending the classical linear equations by adding extra terms, we directly study the non-linear regime and linearise where necessary. Taking inspiration from the early models of elastoplasticity, we obtained a preliminary proof-of-concept model of an idealised rigid ferroelectric material, which was able to correctly represent the hysteretic (polarisation / electric field) behaviour. The goal of this project is to establish the fully non-linear model, with coupled elastoplasticity and ferroelectricity, and to deliver a non-linear model-based control algorithm for ultraprecise devices built around PEM.The potential outcome is the application of this model and control algorithm in advanced materials and manufacturing (AMM) applications, where actuators and sensors are critical to precise and controlled movement. AMM drives key sectors such as nanotechnology, clean technology, biomedical materials, and digital industries. These are all areas deemed as having high growth potential in Alberta and Canada.