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

基于机构的高阶连续统理论的计算方法[j]。斯坦福大学力学与计算系，加州帕洛阿尔托94305Y。黄，机械与工业工程系。目标是为最近提出的虚拟内键（VIB）方法开发新的计算方法。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上（例如弹性变形中的晶格间距）模拟内聚弹性。对于涉及多种不同材料长度尺度的高阶或非局部连续介质理论，缺乏有效的数值方法是影响该理论应用的主要障碍。在这里，我们计划开发一种鲁棒可靠的数值方法来分析经典连续统理论无法解决的多尺度现象。我们的努力将包括为多尺度计算开发高效和可扩展的数值方法。我们将数值结果与实验结果进行比较以验证理论，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。

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.