Mathematical Modeling and Simulation of Microstructured Magnetic-Shape-Memory Devices

磁性形状记忆(MSM)器件的宏观行为是由源于原子尺度的相变与介观结构(如多晶中的晶格缺陷、杂质和晶界)的相互作用决定的。此外，材料的性能可以通过复合材料、层状薄膜器件和多晶体织构的技术生产进行调整。我们的目标是定量地了解这些影响，并为指导材料生产提供标准。因此，我们将在中尺度上模拟这些微结构，并对它们进行解析和数值研究。在弹性力学和微磁学的基础上建立了连续介质模型，采用均匀化方法有效地解决了微观结构问题，并采用变分离散方法进行了数值模拟。在第一个应用阶段，我们打算专注于以下特定情况：-根据晶体的织构和缺陷对晶体宏观行为的影响来阻止MSM效应；-通过在软聚合物基质中嵌入许多小的MSM颗粒来避免阻塞；-MSM薄膜中的微结构和层状配置。

The macroscopic behavior of magnetic shape memory (MSM) devices is determined by the interplayof phase transformations originating from the atomic scale with mesoscopic structuressuch as lattice defects, impurities, and grain boundaries in polycrystals. Furthermore, materialbehavior can be tuned by technical production of composite materials, layered thin filmdevices, and textures in polycrystals. We aim to understand these effects quantitatively andprovide criteria to guide material production. Therefore, we will model these microstructureson the mesoscale and study them analytically and numerically. A continuum model will beformulated on the basis of elasticity and micromagnetism, homogenization will be applied toeffectively resolve the microstructures, and variational discretization methods will be used forthe numerical simulation. In the first application period we intend to focus on the followingspecific cases:- blocking of the MSM effect in polycrystals, in dependence of the texture, and the impactof defects on the macroscopic behavior of crystals;- avoiding blocking by embedding many small MSM particles in a soft polymer matrix;- microstructures and layered configurations in thin MSM films.