Education - Colloquium - WPI Only
Wednesday, December 5, 2012
2:00 PM-3:00 PM
The analysis of wave propagation in solids with complex microstructures,and local heterogeneities
findsextensive applications in areas such as material characterization, structural health monitoring,
and metamaterial design. Within continuum mechanics, sources of heterogeneities are typically
associated to localized defects in structural components, or to periodic microstructures in phononic
crystals and acoustic metamaterials. It is common for the size of the microstructure to be small
compared to the dimensions of the structural component under investigation, which suggests multiscale
analysis as an effective approach to minimize computational costs while retaining predictive accuracy.
This research develops a multiscale framework for the efficient analysis of the dynamic behavior of
heterogeneous solids. The proposed method, called Geometric Multiscale Finite Element Method
(GMsFEM), is based on the formulation of multi-node elements with numerically computed shape functions.
Such shape functions are capable to explicitly model the geometry of heterogeneities at sub-elemental
length scales, and are computed to automatically satisfy compatibility of the solution across the
boundaries of adjacent elements. Numerical examples first illustrate the approach and validate it
through comparison with available analytical and numerical solutions. The developed methodology is
then applied to the analysis of periodic media, structural lattices, and phononic crystal structures.
Finally, GMsFEM is exploited to study the interaction of elastic waves and defects in plate structures.
Suggested Audiences: College
Last Modified: November 29, 2012 at 2:19 PM