Magneto-electro-mechanical coupling phenomena across multiple length scales : variational framework and stability analysis

With the rapid advances in micro-electronics and data-processing, multiscale material models can be incorporated in the development process of innovative functional materials. In this work, the broad field of magneto-electro-mechanically coupled devices is in focus. Here, the interactions of electric, magnetic and mechanical fields give rise to smart materials that are used as sensors and actuators in industrial applications. This work provides the basis for multiscale investigations of magneto-electro-mechanics both in a phenomenological and micro-mechanically motivated setting. Starting from a canonical variational principle, a numerically convenient mixed formulation of finite magneto-electro-mechanics is developed. It serves as a basis for multiscale structural and material stability analyses in a phenomenological material modeling framework. In a next step, phase-field models are employed to focus on the evolution and motion of electric and magnetic domains in the micro-structure. The related interactions of particles and their influence on the overall macroscopic deformation states are investigated.Starting from a canonical variational principle, a numerically convenient mixed formulation of finite magneto-electro-mechanics is developed. It serves as a basis for multiscale structural and material stability analyses in a phenomenological material modeling framework. In a next step, phase-field models are employed to focus on the evolution and motion of electric and magnetic domains in the micro-structure. The related interactions of particles and their influence on the overall macroscopic deformation states are investigated