Pattern-Changing Instabilities and Giant Magnetostriction in Periodic Magnetoelastic Composites

该资助的研究目的是阐明具有周期性微结构的磁弹性复合材料中某种类型的“模式改变”不稳定性的影响，以便实现比这些系统迄今为止可能实现的更大的磁致伸缩应变。在纯机械背景下，众所周知，这些模式变化的不稳定性，即复合材料中的变形突然从通常的单细胞周期模式转变为涉及细胞之间集体相互作用的新的、较低能量的变形模式，通常与“软”变形模式相关，其中施加应力的微小变化可能导致大应变。在早期工作的基础上，将设计理论工具来有效地模拟这些不稳定性的可能出现以及分叉后“软”状态下复合材料的宏观响应。然后，这些工具将用于设计磁弹性复合材料，该复合材料能够产生比迄今为止可能更大（“巨大”）的磁致伸缩应变。这项研究将产生新颖且高效的多场建模技术，该技术将广泛应用于大类活性材料系统，并将有助于在有限元代码中进行数值实现。磁弹性复合材料建模和导致大磁致伸缩应变的微结构设计的改进应该会提高这些材料在许多工业应用中的性能，从汽车悬架系统中的自适应调谐减振器到机器人行业中的人造肌肉，以及声子和光子带隙开关。该研究将与教育和外展活动协同进行。

The research objective of this grant is to elucidate the effect of a certain type of "pattern-changing" instabilities in magneto-elastic composites with periodic microstructures in order to achieve much larger magnetostrictive strains than have been possible to date in these systems. In the purely mechanical context, it is known that these pattern-changing instabilities, where the deformation in the composite abruptly changes (or bifurcates) from the usual one-cell periodic pattern to a new, lower energy deformation pattern involving collective interactions between the cells, is typically associated with a "soft" mode of deformation, where small changes in the applied stress can lead to large strains. Building on earlier work, theoretical tools will be designed for modeling efficiently the possible appearance of these instabilities and the macroscopic response of the composite in the post-bifurcation "soft" regime. These tools will then be used to design magneto-elastic composites that are capable of significantly larger ("giant") magnetostrictive strains than have been possible to date. This research will result in novel and highly efficient multi-field modeling techniques, which will be of broad application to large classes of active material systems, and will lend themselves to numerical implementation in FEM codes. Improvements in the modeling of magneto-elastic composites and in the design of microstructures leading to large magnetostrictive strains should lead to enhanced performance of these materials in many industrial applications, ranging from adaptive tuned vibration absorbers in automotive suspension systems to artificial muscles in the robotics industry, as well as phononic and photonic bandgap switches. The research will be conducted synergistically with educational and outreach activities.