Variational modeling and homogenization in dissipative magneto-mechanics

摘要

The aim of this work is to present new variational-based modeling and homogenization approaches in dissipative magneto-mechanics. On the modeling side, the presented constitutive models are motivated by the underlying physical phenomena at the micro- and nano-scale that are embedded in appropriate variational-based finite element frameworks. We discuss aspects that are characteristic to magneto-mechanical problems such as the unity constraint on the magnetization, the inclusion of the surrounding free-space, the micro-mechanics of the coupled response etc. Following a hierarchical structure of scales, we present new variational principles for three model scenarios: (i) The modeling of magnetic domains at a micro-level, (ii) the modeling of magnetorheological elastomers at a macro-level and (iii) a homogenization-based scale bridging scenario. Numerical simulations are outlined in each focus area in order to demonstrate the salient features of the variational-based formulations. From the theoretical and computational standpoint, this work aims to contribute a building block to the ultimate goal of construction of a compatible hierarchy of computational models for magneto-mechanically coupled materials.