LCE: Computational Methods for Mechanism-Based Higher-Order Continuum Theories

LCE：基于机制的高阶连续体理论的计算方法

• 批准号: 9979717
• 负责人: Huajian Gao
• 金额: $ 21.11万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-10-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9979717&HistoricalAwards=false
• 关键词: LCE; Computational; Methods; Mechanism; Based

Computational Methods for Mechanism-Based Higher-Order Continuum TheoriesH. Gao, Division of Mechanics and Computation, Stanford University, Palo Alto, CA 94305Y. Huang, Dept. of Mechanical and Industrial Engr., University of Illinois, Urbana, CA 61801The objective is to develop novel computational methods for the recently proposed virtual internal bond (VIB) method. The VIB method extends the application range of classical continuum mechanics to modeling cohesive elasticity at much smaller length scales (e.g., lattice spacing in elastic deformation). A major obstacle to the application of such theory is the lack of efficient numerical methods for higher order or nonlocal continuum theories involving multiple distinct materials length scales. Here we plan to develop a robust and reliable numerical method to analyze multiscale phenomena that cannot be addressed by classical continuum theories. Our effort will include the development of efficient and scalable numerical methods for multiscale computation. We will compare the numerical results with experiments to validate the theory, and use the numerical method to investigate several fundamental problems that cannot be addressed by classical continuum theories.

基于机制的高阶连续体理论的计算方法H．高，斯坦福大学力学与计算系，帕洛阿尔托，CA 94305Y。 Huang，机械与工业工程系，伊利诺伊大学厄巴纳分校，CA 61801 目标是为最近提出的虚拟内键 (VIB) 方法开发新颖的计算方法。 VIB 方法扩展了经典连续介质力学的应用范围，可以在更小的长度尺度（例如弹性变形中的晶格间距）下模拟内聚弹性。应用这种理论的一个主要障碍是缺乏涉及多个不同材料长度尺度的高阶或非局部连续理论的有效数值方法。 在这里，我们计划开发一种稳健可靠的数值方法来分析经典连续介质理论无法解决的多尺度现象。我们的努力将包括开发用于多尺度计算的高效且可扩展的数值方法。我们将数值结果与实验进行比较来验证理论，并利用数值方法研究经典连续介质理论无法解决的几个基本问​​题。