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

微连续介质场论的理论与计算基础：从原子模型到连续介质理论乔治华盛顿大学机械与航天工程系摘要本研究的目的是提高对具有微观结构和微运动的材料力学的科学认识，并建立深刻的理论基础。它包括：(1)建立基于统计力学、分子动力学、非局域理论、极性理论和热力学的微观连续统统一理论。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趋于一致；(2)为上述理论建立计算基础，包括有限元法和分子动力学方法；(3)通过计算机模拟将该理论应用于长度尺度对材料响应的影响占主导地位的领域。

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.