Linking and Unifying Atomistic and Continuum Mechanics Formulation

连接和统一原子力学和连续力学公式

基本信息

批准号：
1129976
负责人：
Youping Chen
金额：
$ 26万
依托单位：
University of Florida
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2012
资助国家：
美国
起止时间：
2012-01-01 至 2015-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1129976&HistoricalAwards=false
关键词：
Linking Unifying Atomistic Continuum Mechanics

项目摘要

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.

在过去几十年中，多尺度模拟中的一个强大的障碍物是缺乏同时发生的原子 - 孔子方法，该方法允许波浪，热和缺陷通过原子 - 孔孔素界面。为了应对这一关键挑战，对运输过程的经典统计机械理论进行了重新制定，以统一原子和连续的平衡法则的描述，并重塑执政诉讼的数学表示，以促进对不连续物质行为的粗略尺度有限元模拟。可以预料，这项研究将导致连续力学的新表述，等同于原子量表的完全原子模型和宏观尺度上的经典连续性力学，因此自然而然地导致了一种同时耦合的原子化方法。新方法有望扩大当前原子模拟的预测能力从亚微米 - 毫米大小的材料，从而实现对复杂材料的多尺度分析。它不仅会影响连续机械和多尺度模拟的领域，还会影响新的材料开发。研究结果将集成到现有的力学课程中，并将在教室中用于促进对多尺度材料行为的理解。开发的计算机代码将发布供公众使用和反馈。 PI还将使用Curie讲座系列，将良好的女学者带到校园，作为研究生的榜样。