LCE: Variational Multiscale Methods to Embed Macromechanical Formulations with Fine Scale Physics

LCE：将宏观力学公式与精细尺度物理相结合的变分多尺度方法

• 批准号: 0087019
• 负责人: Krishnakumar Garikipati
• 金额: $ 19万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-02-01 至 2005-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0087019&HistoricalAwards=false
• 关键词: LCE; Variational; Multiscale; Methods; Embed

Mathematical and computational methods will be developed to endow the macromechanical continuum formulation with the fine scale physics of micromechanical material models. Cases of interest are: (1) Micromechanical models that are typically applied at spatial scales of the order of a micron. (2) Theories which incorporate microscale kinematics, constitutive laws, forces and force balance coupled with macroscopic counterparts. The aim is to extend the applicability of fine scale micromechanics to macroscopic problems, which could then be analyzed with enhanced physical accuracy by the resulting multiscale model. The methods eliminate the need for computational grid refinement to the finest microscales, thereby ensuring efficiency, while preserving a tight coupling between coarse and fine scales.

将发展数学和计算方法，使宏观力学连续体公式具有微观力学材料模型的精细尺度物理。感兴趣的案例有：(1)通常应用于微米级空间尺度的微力学模型。(2)微观运动学、本构定律、力和力平衡与宏观力学相结合的理论。目的是将细尺度微观力学的适用性扩展到宏观问题，然后可以通过由此产生的多尺度模型以更高的物理精度分析宏观问题。这些方法消除了计算网格细化到最细的微尺度的需要，从而确保了效率，同时保持了粗尺度和细尺度之间的紧密耦合。