On finitely strained magnetoelastic solids.

Magnetorheological elastomers (MREs) are a class of magnetoelastic solids whose mechanical properties can be altered by the application of magnetic fields. MREs, which are particle filled elastomers, have been developed and proposed as unique solutions for a number of engineering applications, such as tunable engine and chassis mounts in automobiles. In this dissertation we present a study of the magnetoelastic coupling in finitely deformable MREs. Two different continuum formulations for these solids are presented: an Eulerian based direct approach using the second law of thermodynamics plus the conservation laws of mechanics and a new, Lagrangian type formulation based on the unconstrained minimization of a potential energy functional. It is shown that both approaches yield the same governing equations and boundary conditions. Following a discussion of general properties of the free energy function of MREs, a particular such function is used to illustrate the magnetoelastic coupling phenomena in a cylinder subjected to traction or torsion under the presence of external magnetic fields. Motivated by the classical magnetoelastic buckling problem, the general theory is then applied to the solution of the stability of a rectangular block subjected to a uniform magnetic field perpendicular to its longitudinal axis. The variational approach employed utilizes an unconstrained energy minimization. The analytical solution for the critical buckling fields for both the anti-symmetric and symmetric modes are obtained for three different constitutive laws. The corresponding result for beams is extracted asymptotically for a special material and the solution is compared to previously published results. The last part of this work delves into the constitutive modeling of MBEs. Uniaxial experiments are conducted to study the effect of particle chain orientation on the magnetostriction and magnetization responses of an MRE for different levels of compressive and tensile prestresses. Additionally, the simple shear response of an MRE in the presence of a magnetic field is experimentally investigated. The magnetoelastic coupling in MBEs seems to be strongest when the directions of the particle chain orientations, imposed tractions and applied magnetic field are all parallel. A form of the free energy for an MRE is proposed and its parameters are fitted using the experimental results.PhDAerospace engineeringApplied SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126732/2/3276199.pd