Computational and Experimental Multiscale Analysis of Heterogeneous Solids and Metamaterials

本基金的研究目的是研究多尺度分析在非均质和微结构材料固体中波传播的应用。提出了一种新的分析技术，以解释在分析域的几何离散化水平上出现的多个尺度。该方法依赖于多节点元素的公式，称为多尺度元素，能够在亚元素长度尺度上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局部定制的多尺度插值函数结合在一起。这些形状函数从有限数量的节点值近似未知的位移和应力场，并在小尺度上作为控制问题的微分算子的局部解得到。所开发的方法将应用于周期性和梯度超材料的设计，用于导波、转向和聚焦应用。研究成果将提高对损伤结构中波浪运动的认识，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的学术课程和本科生的研究机会广泛传播。通过结合佐治亚理工学院正在进行的项目，专门与代表性不足的学生合作，扩大参与范围。此外，佐治亚理工学院通过GIFT项目开发的教育实验室活动和课堂模块，将使代表性不足的高中和初中学生接触到研究的基本结果和潜在的波动力学原理。

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.