Linking and Unifying Atomistic and Continuum Mechanics Formulation

连接和统一原子力学和连续力学公式

• 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

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.

在过去的几十年中，一个巨大的障碍站在多尺度模拟的进步的方式是缺乏一个并发的原子连续统的方法，允许波，热，和缺陷通过原子连续统接口。为了满足这一关键的挑战，经典的统计力学理论的运输过程重新制定，以统一原子和连续描述的平衡定律和重铸的数学表示的管理法律，以促进粗尺度的有限元模拟不连续材料的行为。预计这项研究将导致一个新的配方的连续介质力学，相当于一个完全原子模型在原子尺度和经典连续介质力学在宏观尺度上，从而自然导致并发耦合原子连续介质方法。 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。它不仅将影响连续介质力学和多尺度模拟领域，而且将影响新材料的发展。研究成果将被整合到现有的力学课程，并将在课堂上使用，以促进多尺度材料行为的理解。 所编制的计算机代码将张贴供公众使用和反馈。PI还将使用居里系列讲座，将知名女学者带到校园，作为研究生的榜样。