Damage and Fracture Evolution

研究者开发和研究弹性损伤（即弹性性能减弱的区域）和断裂的演化模型。困难来自于这些现象的不可逆性，以及现有模型本质上是可变的（静态的）这一事实。一般策略是首先开发与这些变分原理相一致的准静态模型，并证明存在性和近似结果。接下来，我们的目标是将这些结果扩展到全动态环境。损伤和脆性断裂的第一步已经基本完成，研究者正在开发相应的粘性断裂方法。动态模型及其分析是所有这些现象的主要开放问题，也是本项目的主要重点。材料损伤和断裂预测在材料和制造、民用基础设施等领域具有重要意义，但在最现实的物理环境（动力学）中，没有可靠的数学基础，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种数学支持，以及创建和严格证明计算近似解的算法。该项目包括通过研究重要的跨学科问题来培养数学博士生。

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.