Computational and Experimental Multiscale Analysis of Heterogeneous Solids and Metamaterials

该基金的研究目标是研究多尺度分析在具有非均匀性和微结构材料的固体中波传播的应用。提出了一种新的分析技术，以占多尺度的分析域的几何离散化的水平上出现。该方法依赖于多节点元素（称为多尺度元素）的公式化，能够以子元素长度尺度明确地建模材料的实际几何形状。在每个元素中，几何和材料的异质性，通过本地定制的多尺度插值函数。这些形状函数近似未知的位移和应力场从有限数量的节点值，并获得作为局部解的微分算子在小尺度上的问题。所开发的方法将应用于波导、转向和聚焦应用的周期性和梯度超材料的设计。研究结果将提高对受损结构中波动的理解，并将使关键结构部件的结构损伤的详细表征和量化成为可能。研究课题的进展将通过波动力学学术课程和本科生研究机会广泛传播。参与的扩大将通过具体的工作与代表性不足的学生在格鲁吉亚理工学院正在进行的计划结合起来实现。此外，教育实验室活动和课堂模块，通过在格鲁吉亚理工学院的GIFT计划开发，将暴露高中和初中代表性不足的学生的研究的基本结果和基本的波动力学原理。

The research objective of this grant is to investigate the application of multiscale analysis for wave propagation in solids with heterogeneities and microstructured materials. A novel analysis technique to account for the multiple scales that appear at the level of the geometric discretization of the analysis domain is proposed. This method relies on the formulation of multi-node elements, called multiscale elements, capable of explicitly modeling the actual geometry of the material at sub-elemental length scales. Within each element, geometric and material heterogeneities are incorporated through locally tailored multiscale interpolation functions. These shape functions approximate the unknown displacement and stress fields from a finite number of nodal values and are obtained as local solutions of the differential operator governing the problem at the small scales. The developed methodology will be applied to the design of periodic and graded metamaterials for wave guiding, steering and focusing applications.Research findings will improve the understanding of wave motion in damaged structures, and will enable the detailed characterization and quantification of structural damage in critical structural components. Advances from the research topics will be disseminated widely through academic courses on wave mechanics and in undergraduate research opportunities. Broadening of participation will be achieved by specifically working with underrepresented students in conjunction with ongoing programs available at Georgia Tech. In addition, educational laboratory activities and classroom modules, developed through the GIFT program at Georgia Tech, will expose high school and middle school underrepresented students to basic results of the research and to underlying wave mechanics principles.