8:30 AM-9:15 PM
Chair: Randolph E. Bank, University of California, San Diego
The speaker focuses here on a classical problem of resolving the effects of data of multiple scales in modeling problems of heterogeneous media. Homogenization theories applied to heterogeneous materials are aimed at capturing properties of materials that reflect averaged effects of microstructural constituents. But when these averaged properties are used in the analysis of the behavior of structural or machine components, the results can be in significant error compared with the fine-scale solutions corresponding to the heterogeneous media. In this lecture, a theory and methodology are presented for adaptive hierarchical modeling of heterogeneous structures based on a posteriori error estimates of the modeling error due to homogenization. A parallel adaptive procedure is described which is designed to account for only sufficient microstructure to deliver an approximation of the fine scale solution of a prescribed accuracy. Some preliminary results on application to composite materials are presented.
J. Tinsley Oden
University of Texas, Austin
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