Variational Methods for Material Damage: Fracture, Fatigue, and Debonding

材料损坏的变分方法：断裂、疲劳和脱粘

• 批准号: 0505660
• 负责人: Christopher Larsen
• 金额: --
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505660&HistoricalAwards=false
• 关键词: Variational; Methods; Material; Damage; Fracture

The investigator uses variational methods to study materialdamage, with an emphasis on properties of damaged regions andtheir time evolution. Examples of damage include brittle cracks,cracking due to fatigue, and debonding of thin films. Somediscrete-time models for damage evolution exist in the engineeringcommunity, but these are generally ad hoc and not known tocorrespond to limiting continuous-time models. The investigatorstudies the existence of the limiting models, basic properties ofthe damage regions, and the justification for extending numericalmethods for static problems to methods for the quasi-static,continuous-time problems. Damage to materials is of great technological importance notonly because it results in material failure, but also because itplays an important role in building certain nanostructures, forexample by selectively debonding thin films. The project seeks togreatly improve our understanding of these materials by improvingthe mathematical models and studying basic properties of theirsolutions, as well as by developing and justifying numericalmethods. Mathematics Ph.D. students are included in the project,and are trained in the mathematical modeling and analysis ofimportant interdisciplinary problems.

研究者使用各种方法来研究材料，并着重于受损区域的特性和它们的时间演变。 损害的例子包括脆弱的裂缝，由于疲劳而裂纹以及薄膜的剥离。 工程社区中存在某些损害演化的某些时间模型，但这些模型通常是临时的，并且不知道与限制连续时模型相对应。 研究人员研究了限制模型的存在，损伤区域的基本特性以及扩展静态问题的数值方法的理由到准静态，连续时间问题的方法。 材料的损害毫无疑问是因为它导致材料失败，而且由于ITPLE在构建某些纳米结构中起着重要作用，因此可以选择性地剥离薄膜，因此具有巨大的技术重要性。 该项目通过改善数学模型并研究其溶剂的基本特性，以及开发和证明数值方法来寻求我们对这些材料的理解。 数学博士学生被包括在项目中，并接受了重要的跨学科问题的数学建模和分析。