Linking and Unifying Atomistic and Continuum Mechanics Formulation

在过去的几十年里，阻碍多尺度模拟取得进展的一个巨大障碍是缺乏一种并行的原子-连续介质方法，允许波、热和缺陷通过原子-连续介质界面。为了迎接这一严峻挑战，对经典的输运过程统计力学理论进行了重新表述，以统一平衡定律的原子描述和连续介质描述，并重塑了支配定律的数学表示，以便于对不连续材料行为进行粗略的有限元模拟。预计这项研究将产生一种新的连续介质力学公式，它在原子尺度上等价于完全原子论模型，在宏观尺度上等价于经典连续介质力学，从而自然地导致同时耦合的原子-连续介质方法。新的方法有望将目前基于原子模拟的预测能力从亚微米级扩展到亚毫米级，从而使复杂材料的多尺度分析成为可能。它不仅会对连续介质力学和多尺度模拟领域产生影响，而且会对新材料的发展产生影响。研究成果将被整合到现有的力学课程中，并将用于课堂，以促进对多尺度材料行为的理解。编写的计算机代码将张贴供公众使用和反馈。PI还将使用居里夫人系列讲座，将知名女学者引入校园，作为研究生的榜样。

One formidable obstacle standing in the way of progress in multiscale simulation over the past decades is the lack of a concurrent atomistic-continuum methodology that allows waves, heat, and defects to pass through the atomistic-continuum interface. To meet this critical challenge, the classical statistical mechanical theory of transport processes is reformulated so as to unify atomistic and continuum descriptions of balance laws and to recast the mathematical representation of the governing laws to facilitate coarse-scale finite element simulation of discontinuous material behavior. It is anticipated that this research will lead to a new formulation of continuum mechanics that is equivalent to a fully atomistic model at the atomic scale and to classical continuum mechanics at the macroscopic scale, thus naturally leading to a concurrently-coupled atomistic-continuum methodology. The new methodology promises to expand current atomistic simulation-based predictive capability from sub-micron- to sub-millimeter-sized materials, thereby enabling multiscale analysis of complex materials. It will not only impact the areas of continuum mechanics and multiscale simulation, but also new materials development. The research results will be integrated into existing mechanics courses, and will be used in the classrooms to facilitate understanding of multiscale materials behavior. Computer codes developed will be posted for public use and feedback. The PI will also use a Curie Lecture Series that brings in well-established female scholars to campus as role models for graduate students.