The Theory of Phase-Space Substructuring and the Application of Mechanics to Materials Science

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9320717 McCoy The research to be performed under this SGER grant will further develop, and make known to the research community, a new mathematical framework for accommodating the wide range of length scales for observing material heterogeneity. The PI will carry out research employing the newly developed Theory of Multiresolution Decomposition, which is based on the use of discrete orthogonal wavelets. This approach will be applied at the interface of mechanics and of materials science through the "Theory of Phase- Space Substructuring" that allows for the rigorous investigation of the physics of across-scale coupling... an issue which is central to the application of mechanics to materials science. By application of this new methodology, a class of problems which, hitherto, was inaccessible (namely, that category of phenomena in which different stochastic processes are operative on different length scales) now becomes amenable to rigorous analysis. This type of problem is typically encountered in investigations which have as their goal an understanding of how the macro properties of materials depend on their microstructure. ***