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

基于机理的高阶连续统理论的计算方法H.高，斯坦福大学力学与计算系，加州帕洛阿尔托94305 Y。Huang，部门机械及工业工程师，伊利诺伊大学，厄巴纳，CA 61801的目标是开发新的计算方法，最近提出的虚拟内部键（VIB）的方法。VIB方法将经典连续介质力学的应用范围扩展到在小得多的长度尺度上模拟内聚弹性（例如，弹性变形中的晶格间距）。这种理论的应用的一个主要障碍是缺乏有效的数值方法，高阶或非局部连续介质理论，涉及多个不同的材料长度尺度。 在这里，我们计划开发一个强大的和可靠的数值方法来分析多尺度现象，不能解决经典连续介质理论。我们的努力将包括开发高效和可扩展的多尺度计算的数值方法。我们将比较数值结果与实验来验证理论，并使用数值方法来研究几个基本问题，不能解决的经典连续介质理论。

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.