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

在SGER资助下进行的研究将进一步发展，并为研究界提供一个新的数学框架，以适应观测材料非均质性的广泛长度尺度。PI将采用新开发的基于离散正交小波的多分辨率分解理论进行研究。这种方法将通过“相空间子结构理论”应用于力学和材料科学的界面，该理论允许对跨尺度耦合的物理进行严格的研究。这是将力学应用于材料科学的核心问题。通过应用这种新方法，迄今为止无法解决的一类问题（即不同的随机过程在不同的长度尺度上起作用的那一类现象）现在可以进行严格的分析。这类问题通常是在研究中遇到的，这些研究的目标是了解材料的宏观特性如何取决于它们的微观结构。＊＊＊

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. ***