Damage and Fracture Evolution

LarsenDMS-0807825 研究人员开发和研究弹性损伤演化模型（即，弹性减弱的区域）和断裂。困难来自，除其他外，这些现象的不可逆性，以及现有模型基本上是可变的（静态的）。 一般的策略是首先建立与这些变分原理一致的准静态模型，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完全动态的设置。 对于损伤和脆性断裂的研究已经基本完成了第一步，对于内聚断裂的研究也在发展相应的方法。 动力学模型及其分析是所有这些现象的主要开放问题，也是本项目的主要焦点。 材料损伤和断裂预测在材料与制造、民用基础设施等领域具有重要意义，然而，在最现实的物理设置（动力学），没有健全的数学基础，makingengineering模型主要是特设。 研究人员致力于发展这种数学支持，以及创建计算近似解的令人讨厌的证明算法。 该项目包括通过研究重要的跨学科问题来培训数学博士生。

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.