| Magnetoelastic material is a remarkable material system in which several interactions compete at a wide range of length scales, rendering it a rich variety of microstructural configurations and macroscopic properties. The micromagnetic studies of ferromagnetic microstructures were traditionally pursued through the large-scale computations, where the non-convexity and non-locality of the energy functional make the simulations extremely expensive computationally. In magnetoelastic materials, these simulations have to resolve the intrinsic magnetoelastic coupling phenomena, making the situation even worse. In response to these difficulties, in this dissertation, we studied the microstructure and effective behavior of heterogeneous magnetoelastic materials through the combination of numerical implementation of continuum theory of micromagnetics, as well as the mathematical analysis based on the nonlinear homogenization theory of heterogeneous materials. The multi-scale micromagenetic approach developed is proved to be a very efficient tool for studying the microstructure formation and macroscopic properties of the magnetoelastic material systems. |
