A Free Discontinuity Approach to Brittle Fracture Mechanics: Analysis and Numerical Implementation

脆性断裂力学的自由间断方法：分析和数值实现

• 批准号: 0605320
• 负责人: Blaise Bourdin
• 金额: $ 15.3万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605320&HistoricalAwards=false
• 关键词: Free; Discontinuity; Approach; Brittle; Fracture

BourdinDMS-0605320 The investigator extends the analysis and the numericalimplementation of a Free-Discontinuity approach to brittlefracture mechanics proposed by G. Francfort and J-J. Marigo. This formulation departs from the classical Griffith theory whilepreserving its essence, the competition between surface and bulkterms. Doing so, it allows to address the issues of crack pathdetermination, creation of new cracks, and interactions betweencracks. Its numerical implementation is based on aGamma-convergence approximation, which gives a natural way toconsider global minimizations over all possible crack sets. Theinvestigator extends the existing model to account for thepropagation of cracks under thermal loads and in heterogeneousmedia and conduct numerical experiments in these areas. Hebuilds a robust numerical algorithm avoiding most localminimizers, and studies the link between Gamma-convergence andlocal minimizers for this model. He implements an overlappingdomain decomposition method on supercomputers and studies therelation between discretization and regularization parameters. Fracture mechanics is a very active area of research, withvital applications. In recent years, the unexpected collapse ofterminal 2F at Charles de Gaulle airport in France, thedisintegration the Columbia space shuttle upon re-entry, and thecrash of American Airlines Flight 582 over Queens, NY were alllinked to unpredicted and unexplained fracture. In the area ofbrittle fracture (which encompasses materials as diverse asceramics, glass, and concrete), most commonly accepted theoriesare based on Griffith's criterion and are limited to thepropagation of an isolated, pre-existing crack along a givenpath. The investigator extends the analysis and the numericalimplementation of a generalization of Griffith's theory, proposedby G. Francfort and J.J. Marigo, that eliminates theserestrictions. He extends the current model to account for moregeneral problems (thermal loads, heterogeneous materials), andimproves the current numerical implementation on supercomputers.

在BourdinDMS-0605320中，研究者扩展了G.Francfort和J-J提出的脆性断裂力学的自由不连续方法的分析和数值实现。马里戈。这个公式不同于经典的格里菲斯理论，同时保留了它的本质，即表面项和体项之间的竞争。这样做，它就可以解决裂纹路径确定、新裂纹的产生以及支架之间的相互作用等问题。它的数值实现基于Gamma收敛近似，这给出了一种自然的方法来考虑所有可能的裂纹集上的全局最小化。研究人员扩展了现有的模型以考虑热载荷和非均匀介质中裂纹的扩展，并在这些区域进行了数值实验。建立了一个稳健的数值算法，避免了大多数局部极小点，并研究了该模型的Gamma收敛与局部极小点之间的联系。他在超级计算机上实现了重叠区域分解方法，并研究了离散化和正则化参数之间的关系。断裂力学是一个非常活跃的研究领域，有着重要的应用。近年来，法国戴高乐机场2F航站楼的意外坍塌，哥伦比亚号航天飞机在重返大气层时解体，以及美国航空公司582航班在纽约皇后区上空坠毁，都与不可预测和无法解释的骨折有关。在脆性断裂领域(包括各种材料，如陶瓷、玻璃和混凝土)，最普遍接受的理论是基于格里菲斯准则的，并且局限于孤立的、预先存在的裂纹沿给定路径的扩展。研究人员扩展了G.Francfort和J.J.Marigo提出的格里菲斯理论的推广，消除了这些限制，并进行了分析和数值实现。他扩展了目前的模型以考虑更一般的问题(热负荷、非均质材料)，并改进了目前在超级计算机上的数值实现。