Mechanics of magneto-active polymers

Magneto-active polymers (MAPs) are polymer-based composites that respond to magnetic fields with large deformation or tunable mechanical properties. While a variety of these materials exist, most are composites of a soft polymer matrix with a filler of magnetic particles. The multi-physics interactions in MAPs give them two very attractive features. First, they respond to a magnetic field with variable mechanical properties (e.g. stiffness). Second, their shape and volume may be significantly changed in a magnetic field. Both features could be tuned by engineering the microstructure of the composites. Potential applications of MAPs include sensors, actuators, bio-medicine, and augmented reality. However, their potential has not been fully uncovered, partly due to the limited understanding in the mechanisms driving the coupled multi-physics behaviors, and the lack of a quantitative tool to predict their response under various loading and boundary conditions. This study aims to enhance the understanding of mechanics of MAPs, by developing theroies and models which can explain and predict several primary features of these materials. First, the viscoelastic behaviors of ferrogels, one class of MAPs, in response to different magnetic fields are studied. A ferrogel is composed of gel-like matrix and magnetic particles that randomly distribute in the matrix. Due to the viscoelasticity of the gel-matrix, ferrogels usually demonstrate rate-dependent behaviors. However, very few models with coupled magnetic field and viscoelasticity exist in the literature, and even fewer are capable of reliable predictions. Based on the underlying principles of non-equilibrium thermodynamics, a field theory is developed to describe the magneto-viscoelasticity in solids. The theory provides a guideline for experimental characterizations and structural designs of ferrogel-based devices. A specific material model is then selected, and the theory is implemented in a finite-element code. As numerical examples, the responses of a ferrogel in uniform and non-uniform magnetic fields are respectively analyzed. The dynamic response of a ferrogel to cyclic magnetic fields is also studied, and the prediction agrees with our experimental results. In the reversible limit, our theory recovers existing models for elastic ferrogels, and is capable of capturing some instability phenomena. Second, the mechanism of the stiffening effect in magneto-rheological elastomers (MREs), a class of anisotropic MAPs, is investigated. MREs tend to be mechanically stiffer under a magnetic field. Such a stiffening effect is usually referred to as the magneto-rheological (MR) effect and often attributed to the magnetic interaction among filler particles. But the well-acknowledged dipole-interaction model fails to explain the stiffening effect in tension/compression, which was observed in experiments. Other mechanisms, such as the effect of non-affine deformation, have also been proposed, but there is no conclusive evidence on the dominating mechanism for the MR effect. This study investigates various chain structures, and seeks to identify the ultimate origin of the stiffening effect in MREs. Two different methods are used for cross verification: a dipolar interaction model and a finite element simulation based on continuum field theories. Both the shear and axial deformation of the material are studied, with a magnetic field applied in the particle-chain direction. It is found that while the magnetic interaction between particles is indeed the major cause of the stiffening effect, the wavy chain structure is the key to the modulus increase. Besides, chain-chain interaction and non-affine deformation are shown to be insignificant. In addition, the dependence of the stiffening effect on filler concentration is calculated, and the results qualitatively agree with experimental observations. The models also predict some interesting results that could be easily verified by future experiments. Third, a simpler and easy-to-use homogenenous model is further developed to predict the magnetostriction and the MR effect of MAPs subjected to a uniform magnetic field. In general, the magnetic permeability of a MAP varies during a deformation due to the change of the microstructure. The strain dependence of permeability has been discussed for MAPs with various microstructures. It is shown that when the magnetostriction is primary caused by the difference in the permeability of an MAP and its surrounding media, the MR effect is due to the change of the permeability under a strain. Besides, it is found that both the magnetostriction and the MR effect are microstructure dependent. When the magnetostriction is more significant in isotropic MAPs, the MR effect only exists in anisotropic MAPs. In addition, it is shown that only the materials with wavy particle chains are possible to exhibit MR effect in tensile modulus