Linking and Unifying Atomistic and Continuum Mechanics Formulation

在过去的几十年里，阻碍多尺度模拟进步的一个巨大障碍是缺乏一种允许波、热和缺陷通过原子连续介质界面的同步原子连续介质方法。为了应对这一关键挑战，经典输运过程的统计力学理论被重新表述，以便统一平衡定律的原子和连续体描述，并重新定义控制定律的数学表示，以促进不连续材料行为的粗尺度有限元模拟。预计本研究将产生一种新的连续介质力学公式，该公式在原子尺度上相当于完全原子模型，在宏观尺度上相当于经典连续介质力学，从而自然地导致原子-连续介质同步耦合的方法。新方法有望将当前基于原子模拟的预测能力从亚微米扩展到亚毫米尺寸的材料，从而实现复杂材料的多尺度分析。它不仅会对连续介质力学和多尺度模拟领域产生影响，而且会对新材料的开发产生影响。研究结果将整合到现有的力学课程中，并将在课堂上使用，以促进对多尺度材料行为的理解。开发的计算机代码将公布给公众使用和反馈。PI还将利用居里系列讲座，邀请知名女学者到校园为研究生树立榜样。

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.