Design and analysis of functional composites with strain induced magneto-electric coupling

磁-电耦合功能材料对于医学工程和信息技术中功能工具的增强和发展具有重要意义。但只有具有显著大的磁电耦合特性的功能材料才具有可靠的相关性。天然材料在技术上相关的温度范围内不会表现出这种行为。因此，人工制造磁电材料的设计具有很高的科学价值。在这个项目中，应该对磁电复合材料进行分析和建模，该复合材料由带有磁性夹杂物的压电矩阵表示。因此，在微观尺度上的单个成分的建模以及在宏观尺度上的材料表征是主要的兴趣。第一个资助期的重点是利用数值均匀化方法模拟磁电复合材料的宏观行为。因此，有必要对磁-机械和电-机械耦合相进行适当的本构描述。对于多尺度计算框架，在耦合问题的背景下，定义了合适的尺度转换定义。利用所建立的方法对合适的边值问题进行了仿真，分析了电相极化过程对磁电耦合系数的影响。在第二个建立阶段，我们将着重于改进已开发的模型，以预测两相复合材料的磁电耦合系数。因此，铁磁材料的行为将使用preisach模型的一种变体来描述。为了进行必要的实验比较，重建真实的三维微观结构是必不可少的。从这些重建的通常非周期离散化的边界结果，因此，弱周期边界条件的发展，为定义微观边值问题是必要的。此外，还应考虑微观相界的不连续（不完美界面）。数值结果还将与实验数据进行比较，重点讨论了各相的铁本构规律、不完善界面和耦合系数的宏观表征。

Functional materials with magneto-electric coupling are of high importance with respect to the enhancement and development of functional tools in medical engineering and information technology. But only functional materials, which are characterized by a significantly large magneto-electric coupling, own a reliable relevance. Natural materials do not exhibit this behavior in a technically relevant temperature range. Thus, the design of artificially produced magento-electric materials is of high scientific interest. Within this project magneto-electric composites, which are represented by a piezo-electric matrix with magnetic inclusions, should be analyzed and modeled. Thereby, the modeling of the individual constituents at the microscale as well as the material characterization at the macroscale is of major interest.The focus of the first funding period was the modeling of the macroscopic behavior of magneto-electric composites using numerical homogenization methods. On that account, the development of suitable constitutive descriptions of the magneto-mechanically and electro-mechanically coupled phases was necessary. For a multiscale computational framework, in the context of coupled problems, a suitable definition of the scale transition was defined. The developed methods were used for the simulation of appropriate boundary value problems to analyze the influence of the polarization process of the electric phase on the magneto-electric coupling coefficient.In the second founding period we will focus on the enhancement of the developed models with respect to the prediction of the magneto-electric coupling coefficient in two-phase composites. Therefore, the ferromagnetic material behavior will be described using a variation of the Preisach-model. For the necessary experimental comparison reconstructions of real three-dimensional microstructures are essential. From these reconstructions ordinarily non-periodic discretizations of the boundary result, consequently, the development of weak periodic boundary conditions for the definition of the microscopic boundary value problem is required. Furthermore, the discontinuities across microscopic phase boundaries (imperfect interfaces) should be considered. The numerical results will also be compared to experimental data, in detail we concentrate on the ferroic constitutive laws of the individual phases, the imperfect interfaces and the macroscopic characterization of the coupling coefficient.