Computational and Experimental Multiscale Analysis of Heterogeneous Solids and Metamaterials

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

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.