Project P3

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Project description

Modelling and homogenization of magneto-mechanical material response on multiple scales

The goal of this project is to contribute to a better understanding of the nonlinear-dissipative nature of composite magneto-mechanically coupled materials at finite deformations. As underlying material system, magneto-rheological elastomers (MRE) will be considered. These materials are characterized by a heterogenoeus microstructure, which consists of elastomeric matrix and ferromagnetic inclusions. In order to allow for reliable material design, open problems concerning their effective response, possible instability phenomena as well as potential failure mechanisms have to be solved. Thus, the planned research project addresses (i) the determination and the optimization of effective coupling properties of magneto-machanically coupled composites, (ii) the analysis of stability phenomena at different length scales including ways of their technical exploitation, as well as (iii) possible failure mechanisms due to fracture. The overall goal is to construct a compatible hierarchy of models for the description of coupled magneto-mechanical behavior at multiple length scales, and their embedding in scale-bridging homogenization techniques. This will be elaborated by using new variational concepts for dissipative, magneto-mechanically coupled continuum formulations. To this end, we will systematically extend the geometrically linear formulations of homogenization and micromagneto-elastic domain evolution developed in the first period. The expected result of the research project is to provide theoretical and algorithmic formulations which allow for a deepened understanding of large-strain magneto-mechanical coupling rooted in microstructural morphologies. The rigorous variational formulation of geometrically nonlinear problems will yield new definitions of material and structural stability of coupled phenomena on the basis of minimization principles and associated convexity conditions. The combination of stabilityanalyses with fracture phenomena will offer a new quality in the analysis of magneto-mechanical problems for limit states. This willprovide an important methodical element for the modeling and the optimization of functional materials with magneto-mechanicalcoupling.