Piezoelectric PDE Modelling
Skills Used: FlexPDE, Python, Maple
Overall Summary:
Informed by the expertise of our professors and teaching assistants, our approach integrates material science to effectively model a polymer cantilever with a piezoelectric layer.
The model, which operates using linear algebra and differential calculus principles, allows us to test different material parameters and find polymer compositions that are optimal for the system of interest. This model has applications in sensors and actuators in microelectrochemical systems (MEMS) including, but not limited to, vibration sensing/damping, or precision actuators. In these sensor systems, the partial differential equation model allows us to accurately tune the sensitivity of the detecting elements for its intended purpose.
“The validation process helped us gain confidence in our script. The results from our FlexPDE model matched all of our predictions of how the cantilever should react under various conditions like no voltage, or no temperature change.”
Motivation
Piezoelectric materials have seen an increase of use in technology due to their ability to turn mechanical strain into electrical charge. They’ve quickly become essential for applications such as microelectrochemical systems (MEMS), healthcare, robotics, and power generation. The global market for piezoelectric applications peaked at $39.5 billion in 2022, with a projected annual growth rate (PAGR) of 7.4% to $68.3 billion in 2030. This rise can be attributed by an rising demand for smaller and more efficient sensors, actuators, and a need for sustainable energy solutions, especially in the Internet of Things industry, where self-powering systems are vital. The IoT market is projected to grow from $379.5 billion in 2023, to $1.56 trillion by 2032.
Modern piezoelectric ceramics, however, have limitations in flexibility and biocompatibility, thus restricting their use in wearable technology, robotics, and biomedical implants. This has increased the interest in polymer-based piezoelectric materials, which can increase flexibility while lowering manufacturing costs. In using only polymers, however, sacrifices the piezoelectric capabilities of ceramics.
A promising pathway that benefits from both materials involves the combination of polymers with piezoelectric ceramic layers to enhance performance in flexible sensors and actuators.
The goal of the project was to model a piezoelectric polymer cantilever to optimize its mechanical and electrical properties for next-generation sensors, actuators, and energy harvesting systems with the hopes of addressing issues of sensitivity, flexibility, and sustainability.
Project Presentation:
Using FlexPDE, Maple, and Python, the a model for a piezoelectric polymer cantilever was built. The model is capable of modelling a wide range of materials with its modifiable properties such as physical dimensions. material proportions, stiffness matrices, thermal strain coefficients, young’s modulus, densities, piezoelectric coupling matrices, and applied electric field.
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How the model works?
The model works by considering all properties, and solving the net force, Hooke’s Law, and strain equations for a system in static equilibrium. We also incorporated an optimization script to run iterations of the model to find an optimal property measurement for a desired outcome. In the documentation, the piezoelectric layer thickness was optimized to maximize the curvature of the model given a set of properties.
Prototype Design and Fabrication
The fabrication process can be explored in the document here. Generally, the creation of the model involved a modular process in which the properties were incorporated piece by piece until all properties were appropriately operating in the system. To verify the system, several test cases were run, and the curvature of the cantilever was compared to Maple calculations of the system. The Python optimization script was developed in three steps: grid search, curve fitting, and parabolic interpolation.