Mechanics of magneto-active elastomers and applications to magnetically-tunable metamaterials

Pierce, Connor Daniel

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https://hdl.handle.net/2142/124486 Copy

Description

Title

Mechanics of magneto-active elastomers and applications to magnetically-tunable metamaterials

Author(s)

Pierce, Connor Daniel

Issue Date

2024-02-16

Director of Research (if dissertation) or Advisor (if thesis)

Matlack, Kathryn H

Doctoral Committee Chair(s)

Ewoldt, Randy S

Committee Member(s)

• Lopez-Pamies, Oscar
• Zhang, Xiaojia

Department of Study

Mechanical Science and Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• magneto-rheological elastomers
• phononic crystals
• tunable architected materials
• wave propagation
• viscoelasticity
• homogenization
• vibrations
• fuzzy band gaps

Abstract

Phononic crystals (PCs) provide advanced control of elastic wave propagation, including band gaps, due to their periodic geometry. In recent years, tunable PCs which can dynamically control the band gap frequency ranges have received much research interest. Simultaneously, the class of soft composite materials known as magneto-active elastomers (MAEs) has rapidly developed. MAEs exhibit magneto-mechanical coupling, including magnetostriction and the magneto-rheological effect. This thesis advances the state-of-the-art in tunable PCs by introducing a magneto-active elastomer phononic crystal (MAE-PC) which exhibits magnetically tunable band gaps, and by developing analysis tools for MAE-PCs through fundamental studies of the dynamics of damped PCs and the magneto-mechanics of MAEs. First, a proof-of-concept MAE-PC is developed and characterized. Two design variations are proposed and fabricated using direct-ink write additive manufacturing. The band gaps are characterized using vibration transmission measurements in the absence and presence of magnetic fields and shown to be tunable by up to 11\%. Coupled magneto-mechanical finite element simulations demonstrate that the band gap shift is due to the magneto-rheological effect, and that tunability up to 25\% can be achieved for other magnetic field configurations. The band gap tunability depends on both the strength of the applied magnetic field and on the interaction of the magnetic field and the metastructure geometry. Interpreting the band structure of MAE-PCs is nontrivial due to the inherent viscoelasticity of the MAE. In fact, the notion of a band gap is not clear in dissipative PCs, as all wave modes exhibit attenuation. This thesis proposes an ``evanescence indicator'' for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. This indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed ``fuzzy band gaps'' due to the smooth (rather than abrupt) transition between zones of evanescent and propagating wave behavior. The indicator can identify polarized fuzzy band gaps, including hybrid polarizations which consist of multiple simultaneous polarizations, and is validated using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals. Accurately predicting band gap tunability in MAE-PCs requires accurate characterization of the effective magneto-mechanical properties of MAEs. This thesis makes two contributions to this area. First, it introduces a computational periodic homogenization approach to compute the effective magnetostrictive properties of anisotropic MAEs in which the microstructure comprises chains of magnetic particles. Specifically, the effective stiffness, permeability, and magneto-mechanical coupling tensors are numerically computed using the finite element method, and the effect of various microstructural parameters on these effective tensors is investigated. Of the parameters studied, the overall magnetostriction of anisotropic MAEs is most sensitive to the gap between particles and the waviness of the particle chains. The effective tensors can be used, e.g., to compute the deformation of an MAE-PC in a magnetic field, and the effect on band gaps determined by computing the band structure of the deformed unit cell. Second, the magneto-rheological effect in anisotropic MAEs is experimentally measured using a custom-built compression-mode dynamic mechanical analysis setup which can apply a magnetic field to the specimen. The change in the longitudinal and transverse complex Young's moduli is measured under different magnetic field orientations. The relative change in the magnitude of the Young's moduli is largest when the magnetic field is applied parallel to the particle chains, while the change in the loss factor is found to be small in most cases. The measured complex moduli can be employed in simulations to predict the damped band structure of MAE-PCs or the vibration transmission through truncated MAE-PCs.

Graduation Semester

2024-05

Type of Resource

Thesis

Copyright and License Information

Copyright (c) 2024 Connor D. Pierce

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