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原子尺度的相变与多晶体中的晶格缺陷、杂质和晶界等介观结构的相互作用决定的。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结构的技术生产来调整。我们的目标是定量地了解这些影响，并提供指导材料生产的标准。因此，我们将在中尺度上模拟这些微观结构，并对其进行分析和数值研究。基于弹性力学和微磁学建立了连续介质模型，采用均匀化方法有效地求解微结构，采用变分离散方法进行数值模拟。在第一个应用阶段，我们打算专注于以下具体情况：-阻塞的MSM效应在多晶体中，依赖于纹理，和impactof缺陷的宏观行为的晶体;-避免阻塞嵌入许多小MSM颗粒在软聚合物基质;-微观结构和分层配置薄MSM膜。

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.