Variational Methods for Material Defect Evolution

材料缺陷演化的变分方法

• 批准号: 1009653
• 负责人: Christopher Larsen
• 金额: $ 16.75万
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1009653&HistoricalAwards=false
• 关键词: Variational; Methods; Material; Defect; Evolution

LarsenDMS-1009653 The investigator studies the evolution of defects inmaterials (e.g., fracture, damage, dislocation plasticity) usinga progression of models from global minimization-basedquasi-statics to full dynamics. Global minimization models arenow well understood, but very little is understood in the morephysically realistic settings of local minimization-based anddynamic problems. Specifically, existence is open for bothcohesive and sharp-interface (Griffith) dynamic fracture, andeffective macro-scale models for local minimization-baseddislocation plasticity are unknown. The investigator seeks tomake significant progress on these and related problems. The propagation of defects in materials is of obviousfundamental importance, yet in the most physically realisticsettings mathematical foundations and analysis are lacking,leaving engineering models largely ad hoc. The investigatorworks on developing mathematical support in these areas, leadingto improved models, better understanding of solutions, andimproved (and justified) algorithms for computing simulations.

研究者使用从基于全局最小化的准静力学到全动力学的一系列模型来研究材料缺陷（例如断裂、损伤、位错塑性）的演变。全局最小化模型现在已经被很好地理解了，但是在基于局部最小化和动态问题的更现实的物理设置中却知之甚少。具体来说，内聚和锐界面（Griffith）动态断裂的存在是开放的，而有效的基于局部最小位错塑性的宏观模型是未知的。研究者寻求在这些和相关问题上取得重大进展。材料中缺陷的传播显然具有根本性的重要性，但在大多数物理现实环境中，缺乏数学基础和分析，使得工程模型在很大程度上是临时的。研究者致力于开发这些领域的数学支持，从而改进模型，更好地理解解决方案，并改进（和证明）计算模拟算法。