Understanding and Creating Switchable Many-State Architectured Materials Through the Exploitation of Nonlinear Post-Buckling Behavior

建筑材料由两种或两种以上的构成材料和排列有序的空白空间组成。这些材料具有任何一种材料单独无法提供的特性。一类相关的材料是晶格材料，其中细长材料元素的周期性组装组成了材料的内部结构。当受到机械载荷时，这些材料可以以极其复杂和高度非线性的方式做出响应。响应通常包括微结构元件的屈曲。在这种不稳定性过程中，微观结构从一种构型变化到另一种构型。该奖项支持基础研究，以产生理解和设计具有理想类型的微级屈曲行为的建筑材料所需的知识。这些材料可以在许多不同的屈曲状态之间切换，每种状态都有自己的特性，可以为特定的应用量身定做。这类材料将有许多应用，从具有多种飞行状态的航空结构的振动控制到多功能传感器，例如，一种材料状态可以感知磁场的变化，另一种材料状态的温度变化，以及第三种机械载荷的变化。该研究项目将在新兴的建筑材料科学以及屈曲和不稳定力学方面培训研究生和本科生。它还将通过将研究成果纳入明尼苏达大学的研究生和本科课程，以及通过与K-12教职员工和学生的互动，鼓励未被充分代表的群体参与研究和工程。该项目将研究周期性建筑材料中后屈曲行为的基本问题。研究内容将包括：建筑材料微结构中屈曲和不稳定性的非线性数学建模和表征；这些复杂材料的高性能计算模拟；以及了解这些材料的组成材料和/或制造中存在的缺陷如何影响这些材料的行为。这项研究将利用分叉和对称群的数学理论来理解周期性结构材料中发生的复杂屈曲机制。它将使用这些数学工具来探索和创建计算算法，以有效和系统地绘制出与这些材料相关的丰富的状态集和屈曲行为。这项研究还将研究周期性结构材料的屈曲行为如何取决于其周期单胞属性，如尺寸、形状、晶格几何形状和组成材料的属性。

Architectured materials consist of two or more constituent materials and empty space arranged in and ordered assembly. These materials have properties not offered by any one material alone. One class of relevant materials is that of lattice materials where periodic assemblies of slender material elements make up the material's internal structure. When subjected to mechanical loads, these materials can respond in extremely complex and highly nonlinear ways. The response often includes buckling of the microstructure elements. During this instability the microstructure changes from one configuration to another. This award supports fundamental research to generate the knowledge necessary to understand and design architectured materials with desirable types of microlevel buckling behavior. These materials would be switchable between many different buckled states, and each state would have its own properties that could be tailored for specific applications. Such materials would have many applications ranging from vibration control in aerospace structures with multiple flight regimes to multi-function sensors where, for example, one material state would sense changes in magnetic field, another changes in temperature, and a third changes in mechanical load. The research project will train graduate and undergraduate students in the emerging science of architectured materials and the mechanics of buckling and instabilities. It will also encourage participation of underrepresented groups in research and engineering through the incorporation of research results in graduate and undergraduate courses at the University of Minnesota, and through interaction with K-12 faculty and students.The project will research the fundamental issue of post-buckling behavior in periodic architectured materials. Research will be conducted on the nonlinear mathematical modeling and characterization of buckling and instabilities in the microstructure of architectured materials; on the high-performance computational simulation of these complex materials; and on understanding how the behavior of these materials is affected by the presence of imperfections in their constituent materials and/or their manufacture. The research will employ the mathematical theories of bifurcation and symmetry groups to understand the complex buckling mechanisms that occur in periodic architectured materials. It will use these mathematical tools to explore and create computational algorithms for efficiently and systematically mapping out the rich set of states and buckling behavior associated with these materials. The research will also study how a periodic architectured material's buckling behavior depends on its periodic unit cell properties such as size, shape, lattice geometry, and constituent material properties.