Damage and Fracture Evolution

损伤和断裂演变

• 批准号: 0807825
• 负责人: Christopher Larsen
• 金额: $ 16.22万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-08-15 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0807825&HistoricalAwards=false
• 关键词: Damage; Fracture; Evolution

LarsenDMS-0807825 The investigator develops and studies models for theevolution of elastic damage (i.e., regions of weakened elasticproperties) and fracture. Difficulties come from, among otherthings, the irreversibility of these phenomena, and the fact thatexisting models are essentially variational (static). Thegeneral strategy is to first develop quasi-static models that areconsistent with these variational principles, and prove existenceand approximation results. Next, the goal is to extend theseresults to the fully dynamic setting. The first step has beenessentially completed for damage and brittle fracture, and theinvestigator works on developing corresponding methods forcohesive fracture. Dynamic models and their analysis are majoropen problems for all these phenomena, and are the main focus ofthis project. Material damage and fracture prediction are of fundamentalimportance in the areas of materials and manufacturing, civilinfrastructure, etc., yet in the most physically realisticsetting (dynamics) there is no sound mathematical footing, makingengineering models largely ad hoc. The investigator works ondeveloping this mathematical support, as well as creating andrigorously justifying algorithms for computing approximatesolutions. The project includes training mathematics Ph.D.students through work on important interdisciplinary problems.

LARSENDMS-0807825研究者开发了弹性损伤进化（即，弹性杂质的区域）和断裂的研究模型。困难来自这些现象的不可逆性，而事实的模型本质上是变异的（静态）。 The General策略首先要开发具有这些变化原则的准静态模型，并证明存在近似结果​​。 接下来，目的是将这些信息扩展到完全动态的设置。 对于损伤和脆性断裂的第一步，第一个步骤已完成，而该评估器正在开发相应的方法锻造裂缝。 动态模型及其分析是所有这些现象的主要问题问题，并且是此项目的主要重点。 材料损害和断裂预测在材料和制造，文明基础设施等领域具有基本影响力，但是在最逼真的（动态）中，没有合理的数学基础，使工程模型在很大程度上进行了临时。 研究者正在为这种数学支持而进行构建，并创建了用于计算近似色的算法的合理算法。 该项目包括通过有关重要跨学科问题的工作培训数学博士学位。