Mathematical Models of Materials with Multi-Stability at the Micro-Level

DMS Award AbstractAward #： 0102841 PI： Truskinovsky，Lev机构： 明尼苏达大学双城分校 应用数学项目经理：Catherine Mavriplis职务：多稳态材料的微观数学模型我们提出研究活性材料的典型离散类似物的速率敏感性。在微观层面上，活性材料可以被视为多稳定的分子尺寸器件的复杂组合;大的变形则是由于不同的局部稳定配置之间的切换。在宏观层面上的切换导致到更小的尺度和相关的耗散的能量通量。本项目主要研究多稳态材料中尺度间能量转换的优化问题，特别是考虑了在涨落相关和尺寸效应不可忽略的情况下系统的行为，研究了形状记忆、磁致伸缩和铁磁合金、相变增韧陶瓷和材料等活性材料的动力学行为，显示出可控的分布式微损伤。活性物质的生物学实例由肌肉和其他分布的蛋白质系统提供。 该项目的目标是了解这些材料中耗散和产生主动力的机制，这可能为人工分子大小马达的实际建造开辟道路。具体来说，我们感兴趣的是开发超小型物体的原型，这些物体可以承载载荷并自行推进。

DMS Award AbstractAward #: 0102841PI: Truskinovsky, Lev Institution: University of Minnesota, Twin CitiesProgram: Applied MathematicsProgram Manager: Catherine MavriplisTitle: Mathematical Models of Materials with Multi-Stability at the Micro-LevelWe propose to study rate sensitivity of the prototypical discrete analogs of active materials. At the micro-level, active materials can be viewed as complex assemblages of multi-stable, molecular size devices; large deformations are then due to the switching between different locally stable configurations. At the macro-level the switching leads to the energy flux into smaller scales and associated dissipation. In this project we focus on optimization of energy transduction between the scales in multi-stable materials and specifically consider behavior of these systems in the situations where fluctuations are relevant and the size effect can not be neglected.In this research project we study the dynamic behavior of active materials which include shape-memory, magnetostrictive and ferromagnetic alloys, transformation-toughened ceramics and materials, exhibiting controllable distributed micro-damage. Biological examples of active materials are provided by muscles and other distributed protein systems. The goal of the project is to understand the mechanics of dissipation and active force generation in these materials which may open ways to an actual construction of the artificial molecular size motors. Specifically we are interested in developing prototypes for ultra-small objects, which can carry load and be self propelled.Date: J