A Theoretical and Computational Basis for Micro-Continuum Field Theories: From Atomic Model to Continuum Theory

微观连续体场论的理论和计算基础：从原子模型到连续体理论

• 批准号: 0115868
• 负责人: James Lee
• 金额: $ 7万
• 依托单位: George Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-02-01 至 2003-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0115868&HistoricalAwards=false
• 关键词: Theoretical; Computational; Basis; Micro; Continuum

A Theoretical and Computational Basis for Micro-continuum Field Theories:From Atomic Model to Continuum TheoryJames D. LeeDepartment of Mechanical and Aerospace EngineeringThe George Washington UniversityAbstractThe objective of this proposed research is to enhance the scientific understanding of and to establish a profound theoretical foundation for mechanics of materials with micro-structure and micromotion. It includes: (1) the construction of a unified theory for micro-continuum based on statistical mechanics, molecular dynamics, nonlocal theory, polar theory and thermodynamics. It will be capable of explaining and predicting a large class of microscopic phenomena in which the ratios of the external to internal characteristic length and time approach unity; (2) the development of a computational basis, including finite element method and molecular dynamics method, for the above-mentioned theory; (3) the applications of the theory through the computer simulations to the fields where the effect of length scale is predominant to the material response.

微观连续统场论的理论和计算基础：从原子模型到连续统理论。乔治华盛顿大学机械与航空航天工程系摘要本研究的目的是加深对微结构和微运动材料力学的科学认识，并建立深厚的理论基础。它包括：（1）在统计力学、分子动力学、非定域理论、极性理论和热力学的基础上建立了微观连续统一理论。它将能够解释和预测一大类微观现象，其中外部与内部特征长度和时间的比值接近1：（2）为上述理论发展计算基础，包括有限元方法和分子动力学方法;（3）通过计算机模拟，将理论应用于长度尺度效应对材料响应起主导作用的领域。