Modeling and Homogenization of Magneto-Mechanical Material Behaviour at Multiple Scales

这个项目的目的是为了更好地理解有限变形下复合磁力耦合材料的非线性耗散性质。磁流变弹性体(MRE)作为底层材料体系将被考虑。这些材料的特征是具有由弹性基体和铁磁性夹杂物组成的异质微结构。为了进行可靠的材料设计，必须解决关于其有效响应、可能的失稳现象以及潜在的失效机制的公开问题。因此，计划中的研究项目涉及(I)确定和优化磁力耦合复合材料的有效耦合性能，(Ii)分析不同长度尺度下的稳定性现象，包括其技术开发方法，以及(Iii)可能的断裂失效机制。总的目标是构建一个兼容的模型层次，用于描述多个长度尺度上的耦合磁力行为，并将其嵌入到尺度桥均化技术中。这将通过对耗散的、磁力耦合的连续统公式使用新的变分概念来阐述。为此，我们将系统地推广第一阶段发展的均匀化和微磁弹性域演化的几何线性公式。该研究项目的预期结果是提供理论和算法公式，以加深对源于微结构形态的大应变磁力耦合的理解。基于极小化原理和相应的凸性条件，几何非线性问题的严格变分形式将给出耦合现象的材料稳定性和结构稳定性的新定义。稳定性分析与断裂现象的结合将为极限状态下的磁力学问题的分析提供新的质量。这将为磁机耦合功能材料的建模和优化提供重要的方法学基础。

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.