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.

过去几十年来，阻碍多尺度模拟进展的一个巨大障碍是缺乏一种允许波、热和缺陷穿过原子连续介质界面的并行原子连续介质方法。为了应对这一严峻挑战，重新表述了传输过程的经典统计力学理论，以统一平衡定律的原子描述和连续描述，并重新构建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。预计这项研究将带来连续介质力学的新表述，相当于原子尺度上的完全原子模型和宏观尺度上的经典连续介质力学，从而自然地导致同时耦合的原子连续介质方法论。新方法有望将当前基于原子模拟的预测能力从亚微米尺寸的材料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。它不仅会影响连续介质力学和多尺度模拟领域，还会影响新材料的开发。研究成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发布以供公众使用和反馈。 PI 还将利用居里讲座系列，将知名女学者引入校园，作为研究生的榜样。