Energy-Based Constitutive Modeling and Finite Element Analysis of Magnetostrictive Energy Harvesters

This thesis validates the suitability of a thermodynamic magneto-mechanical constitutive model based on Helmholtz free energy density and an equivalent stress model to analyze galfenol-based magnetostrictive energy harvesters. The models are validated against measurement results obtained from prototype harvester devices. The choice of using galfenol as an active material was made after comparing the magnetic and mechanical properties of giant magnetostrictive materials. Rod-type and cantilever-beam-type energy harvester geometries have been utilized for the development of prototype energy harvesters. The choice of such geometries was based on a survey of state-of-the-art energy harvesters.

The aim of the thesis is to present a modeling approach that can be utilized to analyze different geometric configurations of the magnetostrictive energy harvesters. The magneto-mechanical constitutive models are implemented in 2D axisymmetric and 3D finite element (FE) models to investigate the coupled magneto-mechanical behavior of the galfenol material. The 2D axisymmetric model is implemented in MATLAB using in-house coding, whereas COMSOL Multiphysics is utilized for 3D finite element simulations. The measured and simulated results were compared, keeping in mind the sensitivity and repeatability of the measurements and limitations of the models. The leading principle of this thesis is the validation of the proposed modeling approaches to analyze both rodtype and cantilever-beam-type energy harvesters.

The research involved studying the influence of change in the operating conditions and the design parameters on the performance of magnetostrictive energy harvesters. The thermodynamic magneto-mechanical model is able to successfully predict the magneto-mechanical behavior of a rod-type energy harvester under different mechanical loadings and magnetic bias conditions. The model is also able to determine the influence of the mechanical preload, dynamic load, magnetic bias, and load resistance on the output power under forced dynamic mechanical excitations. The model also confirms that the optimal preload value changes as a function of the magnetic bias. For a cantilever beamtype energy harvester, the model is able to accurately predict the influence of magnetostriction upon resonant frequency. In addition, the model can also successfully determine the resonant frequency and open circuit voltage under different amplitudes of mechanical vibrations.

The equivalent stress model can transform any arbitrary stress tensor into a uniaxial stress. The model is able to determine the correct permeability of the material for a combination of flux density vector and stress tensor. It allows a simplified approach to predict the permeability change from measurements to analyze the magnetostrictive energy harvesters and to determine the influence of mechanical loading over magnetic bias. The results validate that both models are able to reproduce the measurement results with reasonable accuracy and are therefore suitable to be utilized as a tool to analyze magnetostrictive energy harvesters.