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

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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.